Digital Signal Processing short question and answers

8/10/2019 Digital Signal Processing short question and answers

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Electronics & Communication Engineering.

Digital Signal Processing

1. What is a continuous and discrete time signal?Ans:Continuous time signal: A signal x(t) is said to be continuous if it is defined for all time t.Continuous time signal arise naturally when a physical waveform such as acoustics wave

or light wave is converted into a electrical signal. This is effected by means of

transducer.(e.g.) microphone, photocell.

Discrete time signal: A discrete time signal is defined only at discrete instants of time.The independent variable has discrete values only, which are uniformly spaced. Adiscrete time signal is often derived from the continuous time signal by sampling it at a

uniform rate.

2. Give the classif ication of signals?Ans:Continuous-time and discrete time signals

Even and odd signals

Periodic signals and non-periodic signalsDeterministic signal and Random signal

Energy and Power signal

3. What are the types of systems?Ans:Continuous time and discrete time systems

Linear and Non-linear systemsCausal and Non-causal systems

Static and Dynamic systemsTime varying and time in-varying systems

Distributive parameters and Lumped parameters systems

Stable and Un-stable systems.

4. What are even and odd signals?Ans:

Even signal: continuous time signal x(t) is said to be even if it satisfies the condition

x(t)=x(-t) for all values of t.

Odd signal: he signal x(t) is said to be odd if it satisfies the condition x(-t)=-x(t) for all t.In other words even signal is symmetric about the time origin or the vertical axis, but odd

signals are anti-symmetric about the vertical axis.


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5. What are determin istic and random signals?Ans:Deterministic Signal: deterministic signal is a signal about which there is no certainty

with respect to its value at any time. Accordingly we find that deterministic signals may bemodeled as completely specified functions of time.

Random signal: random signal is a signal about which there is uncertainty before its actualoccurrence. Such signal may be viewed as group of signals with each signal in the

ensemble having different wave forms,(e.g.) The noise developed in a television or radioamplifier is an example for random signal.

6. What are energy and power signal?Ans:Energy signal: signal is referred as an energy signal, if and only if the total energy of the

signal satisfies the condition 0


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the past inputs.

Invertibility: A system is said to be invertible if the input of the system con be recovered

from the system output.Time invariance: A system is said to be time invariant if a time delay or advance of the

input signal leads to an identical time shift in the output signal.

Linearity: A system is said to be linear if it satisfies the super position principle

i.e.) R(ax1(t)+bx2(t))=ax1(t)+bx2(t)

10. What i s memory system and memory less system?Ans:A system is said to be memory system if its output signal at any time depends on the pastvalues of the input signal. circuit with inductors capacitors are examples of memory

system..

A system is said to be memory less system if the output at any time depends on the

present values of the input signal. An electronic circuit with resistors is an example formemory less system.

11. What i s an inverti ble system?Ans:A system is said to be invertible system if the input of the system can be recovered from thesystem output. The set of operations needed to recover the input as the second system

connected in cascade with the given system such that the output signal of the second system

is equal to the input signal applied to the system.H

-1{y(t)}=H

-1{H{x(t)}}.

12. What are time invariant systems?Ans:A system is said to be time invariant system if a time delay or advance of the input signal

leads to an idenditical shift in the output signal. This implies that a time invariant systemresponds idenditically no matter when the input signal is applied. It also satisfies the

condition

R{x(n-k)}=y(n-k).

13. Is a discrete time signal described by the input output relati on y[n ]= rnx[n] time

invariant.

Ans:A signal is said to be time invariant if R{x[n-k]}= y[n-k]

R{x[n-k]}=R(x[n]) / x[n]x[n-k]=rnx [n-k] ---------------- (1)

y[n-k]=y[n] / nn-k=r

n-kx [n-k] -------------------(2)

Equations (1)Equation(2)Hence the signal is time variant.

14. Show that the discrete time system descri bed by the input-output r elationshi p y[n]=nx[n ] is linear?

Ans:


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For a system to be linear R{a1x1[n]+b1x2[n]}=a1y1[n]+b1y2[n]L.H.S:R{ a1x1[n]+b1x2[n] }=R{x[n]} /x[n] a1x1[n]+b1x2[n]

= a1 nx1[n]+b1 nx2[n] -------------------(1)R.H.S: a1y1[n]+b1y2[n]= a1 nx1[n]+b1 nx2[n] --------------------(2)Equation(1)=Equation(2)

Hence the system is linear

15. What i s SISO system and MIMO system?Ans:A control system with single input and single output is referred to as single input singleoutput system. When the number of plant inputs or the number of plant outputs is more

than one the system is referred to as multiple input output system. In both the case, the

controller may be in the form of a digital computer or microprocessor in which we can

speak of the digital control systems.

16. What i s the output of the system with system function H1 and H2 when connected in

cascade and parall el?

Ans:When the system with input x(t) is connected in cascade with the system H1 and H2 the

output of the system is

y(t)=H2{H1{x(t)}}

When the system is connected in parallel the output of the system is given byy(t)=H1x1(t)+H2x2(t).

17. What do you mean by per iodic and non-peri odic signals?A signal is said to be periodic if

x(n+N)=x(n)

Where N is the time period.

A signal is said to be non-periodic ifx(n+N)x(n) .

18.Determine the convolu tion sum of two sequences x(n) = {3, 2, 1, 2} andh(n) = {1, 2, 1, 2}

Ans: y(n) = {3,8,8,12,9,4,4}

19.Find the convolution of the signalsx(n) = 1 n=-2,0,1

= 2 n=-1

= 0 elsewhere.

Ans: y(n) = {1,1,0,1,-2,0,-1}

20.Detemine the solution of the difference equationy(n) = 5/6 y(n-1)1/6 y(n-2) + x(n) for x(n) = 2n u(n)

Ans: y(n) = -(1/2)n

u(n) + 2/3(1/3)n

u(n)+8/5 2nu(n)

21.Determine the response y(n), n>=0 of the system descri bed by the second order

dif ference equationy(n)4y(n-1) + 4y(n-2) = x(n)x(n-1) when the input is x(n) = (-1)n u(n) and the

initial condition are y(-1) = y(-2)=1.

Ans:y(n) = (7/9-5/3n)2n u(n) +2/9(-1)n u(n)


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22. Dif ferentiate DTF T and DFT

DTFT output is continuous in time where as DFT output is Discrete in time.

23.Dif ferentiate between DI T and DI F algori thmDITTime is decimated and input is bi reversed format output in natural orderDIFFrequency is decimated and input is natural order output is bit reversedformat.

24. How many stages are there for 8 point DFT8

25 How many mul tipl ication terms are requir ed for doing DFT by expressional

method and FFT methodexpressionN /2 log N

26. Distinguish I IR and FI R fil ters

FIR IIR

Impulse response is finite

They have perfect linear phase

Impulse Response is infinite

They do not have perfect linearphase

Non recursive Recursive

Greater flexibility to control theshape of magnitude response

Less flexibility

27. Distinguish analog and digital fi lters

Analog Digital

Constructed using active orpassive components and it is

described by a differential

equation

Consists of elements like adder,subtractor and delay units and it is

described by a difference equation

Frequency response can be

changed by changing thecomponents

Frequency response can be

changed by changing the filtercoefficients

It processes and generatesanalog output

Processes and generates digitaloutput

Output varies due to externalconditions

Not influenced by externalconditions

28. Wr ite the expression for order of Butterwor th f il ter?

The expression is N=log (/)1/2/log (1/k)


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29. Wri te the expression for the order of chebyshev fi lter?

N=cosh-1

(/e)/cosh-1(1/k)

30. Wr ite the vari ous frequency transformations in analog domain?

LPF to LPF:s=s/cLPF to HPF:s=c/sLPF to BPF:s=s2xlxu/s(xu-xl)LPF to BSF:s=s(xu-xl)?s2=xlxu. X=

31. Wri te the steps in designing chebyshev fi l ter?1. Find the order of the filter.2. Find the value of major and minor axis. 3. Calculate the poles.

4. Find the denominator function using the above poles.5. The numerator polynomial value depends on the value of n. If

n is odd: put s=0 in the denominator polynomial.If n is even put s=0 and divide it by (1+e2)

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32. Wr ite down the steps for designing a Butterworth fi lter?

1. From the given specifications find the order of the filter

2 find the transfer function from the value of N

3. Find c4 find the transfer function ha(s) for the above value of cby su s by that value.

33. State the equation for f inding the poles in chebyshev fi lter

sk=acosk+jbsink,where k=/2+(2k-1)/2n)

34. State the steps to design digi tal I IR fi lter using bil inear method

Substitute s by 2/T (z-1/z+1), where T=2/(tan (w/2) in h(s) to get h (z)

35. What is warping eff ect?

For smaller values of w there exist linear relationship between w and .but forlarger values of w the relationship is nonlinear. This introduces distortion in thefrequency axis. This effect compresses the magnitude and phase response. This

effect is called warping effect

36. Wr ite a note on pre warping.

The effect of the non linear compression at high frequencies can be compensated.When the desired magnitude response is piecewise constant over frequency, this

compression can be compensated by introducing a suitable rescaling or prewar ping

the critical frequencies.


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37. Give the bil inear transform equation between s plane and z plane

s=2/T (z-1/z+1)

38. Why impulse invariant method is not preferr ed in the design of I IR fi lters other

than l ow pass fi lter?

In this method the mapping from s plane to z plane is many to one. Thus there irean infinite number of poles that map to the same location in the z plane, producing

an aliasing effect. It is inappropriate in designing high pass filters. Therefore thismethod is not much preferred.

39. By impulse invariant method obtain the digital fi lter transfer function and the

dif ferential equation of the analog fi lter h(s) =1/s+1

H (z) =1/1-e-T

z-1

Y/x(s) =1/s+1

Cross multiplying and taking inverse lap lace we get,D/dt(y(t)+y(t)=x(t)

40. What is meant by impulse invariant method?In this method of digitizing an analog filter, the impulse response of the resultingdigital filter is a sampled version of the impulse response of the analog filter. For

e.g. if the transfer function is of the form, 1/s-p, thenH (z) =1/1-e-

pTz

-1

41. What do you understand by backward dif ference?One of the simplest methods of converting analog to digital filter is toapproximate the differential equation by an equivalent difference equation.

d/dt(y(t)/t=nT=(y(nT)-y(nT-T))/T

42. What are the properti es of chebyshev fi lter?1. The magnitude response of the chebyshev filter exhibits ripple either in the stopband or the pass band.2. The poles of this filter lies on the ellipse

43. Give the Butterworth f il ter tr ansfer function and its magnitude character istics for

diff erent orders of fi lter.The transfer function of the Butterworth filter is given byH (j) =1/1+j (/c) N

44. Give the magnitude function of Butterworth f il ter.The magnitude function of Butterworth filter is|h(j)=1/[1+(/c)2N]1/2 ,N=1,2,3,4,.

45. Give the equation for the order N, major , minor axis of an ell ipse in case of

chebyshev fi l ter?The order is given by N=cosh

-1(((10

.1p)-1/10

.1s-1)1/2))/cosh

-1s/p

A= (1/N

--1/N

)/2pB=p (1/N+ -1/N)/2

46. Give the expression for poles and zeroes of a chebyshev type 2 f il ters


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The zeroes of chebyshev type 2 filter SK=js/sinkk, k=1.NThe poles of this filter xk+jyk

xk=sk/ s2+k2yk=sk/s2+k2 k=acosk

47. How can you design a digi tal f il ter fr om analog fi lter?Digital filter can de designed from analog filter using the following methods1. Approximation of derivatives2. Impulse invariant method

3. Bilinear transformation

48. wri te down bili near transformation.s=2/T (z-1/z+1)

49. L ist the Butterworth polynomial for vari ous orders.

N Denominator polynomial

1 S+1

2 S +.707s+1

3 (s+1)(s +s+1)

4 (s +.7653s+1)(s +1.84s+1)

5 (s+1)(s +.6183s+1)(s +1.618s+1)

6 (s +1.93s+1)(s +.707s+1)(s +.5s+1)

7 (s+1)(s +1.809s+1)(s +1.24s+1)(s +.48s+1)

50. Di ff erenti ate Butterworth and Chebyshev fi lter .

Butterworth dampimg factor 1.44 chebyshev 1.06Butterworth flat response damped response.

51. What is fi lter?Filter is a frequency selective device ,which amplify particular range offrequencies and attenuate particular range of frequencies.

52. What are the types of digital fi lter according to their impul se response?IIR(Infinite impulse response )filterFIR(Finite Impulse Response)filter.

53. How phase distortion and delay distorti on are in troduced?The phase distortion is introduced when the phase characteristics of a filter is

nonlinear with in the desired frequency band.The delay distortion is introduced when the delay is not constant with in the

desired frequency band.

54. what is mean by FIR fil ter?The filter designed by selecting finite number of samples of impulse response(h(n) obtained from inverse fourier transform of desired frequency response

H(w)) are called FIR filters

55. Wri te the steps involved in F IR f il ter design


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Choose the desired frequency response Hd(w)Take the inverse fourier transform and obtain Hd(n)Convert the infinite duration sequence Hd(n) to h(n)Take Z transform of h(n) to get H(Z)

56. What are advantages of F IR fi lter?

Linear phase FIR filter can be easily designed .Efficient realization of FIR filter exists as both recursive and non-recursive

structures.

FIR filter realized non-recursively stable.The round off noise can be made small in non recursive realization of FIR filter.

57. What are the disadvantages of F IR F I LTERThe duration of impulse response should be large to realize sharp cutoff filters.The non integral delay can lead to problems in some signal processing

applications.

58. What is the necessary and suff icient condition for the li near phase character istic of aFI R filter?

The phase function should be a linear function of w, which inturn requiresconstant group delay and phase delay.

59. L ist the well known design technique for li near phase FIR fi lter design?Fourier series method and window methodFrequency sampling method.

Optimal filter design method.

60. Define I IR fi lter?

The filter designed by considering all the infinite samples of impulse response arecalled IIR filter.

61. For what kind of application , the antisymmetri cal impulse response can be used?The ant symmetrical impulse response can be used to design Hilbert transformsand differentiators.

62. For what kind of appl ication , the symmetr ical impulse response can be used?The impulse response ,which is symmetric having odd number of samples can beused to design all types of filters ,i.e , lowpass,highpass,bandpass and band reject.

The symmetric impulse response having even number of samples can be used

to design lowpass and bandpass filter.

63.What is the reason that F IR f il ter is always stable?FIR filter is always stable because all its poles are at the origin.

64.What conditi on on the F IR sequence h(n) are to be imposed n order that this fi lter

can be called a liner phase f il ter?The conditions are

(i) Symmetric condition h(n)=h(N-1-n)

(ii) Antisymmetric condition h(n)=-h(N-1-n)


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65. Under what conditi ons a fini te duration sequence h(n) wil l yield constant group

delay in i ts frequency response characteristics and not the phase delay?If the impulse response is anti symmetrical ,satisfying the conditionH(n)=-h(N-1-n)

The frequency response of FIR filter will have constant group delay and not the

phase delay .

66. State the condition for a digital fi lter to be causal and stable?A digital filter is causal if its impluse response h(n)=0 for n


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x

72. Compare Hamming window with Kaiser window.

Hamming window Kaiser window

1.The main lobe width is equal to8/Nand the peak side lobe level is41dB.

2.The low pass FIR filter designed willhave first side lobe peak of53 dB

The main lobe width ,the peak side lobe

level can be varied by varying the

parameter and N.The side lobe peak can be varied by

varying the parameter .

73.What is the necessary and suffi cient condition for li near phase characteri stics in

FI R filter?The necessary and sufficient condition for linear phase characteristics in FIR filteris the impulse response h(n) of the system should have the symmetry property,i.e,

H(n) = h(N-1-n)

Where N is the duration of the sequence .

74.What are the advantage of Kaiser widow?1.It provides flexibility for the designer to select the side lobe level and N .

2. It has the attractive property that the side lobe level can be varied

continuously from the low value in the Blackman window to the high value in therectangle window .

75.What is the principle of designing FI R fil ter using fr equency sampling method?In frequency sampling method the desired magnitude response is sampled and a linear

phase response is specified .The samples of desired frequency response are defined asDFT coefficients. The filter coefficients are then determined as the IDFT of this set ofsamples.

76.For what type of fi lters frequency sampling method is sui table?Frequency sampling method is attractive for narrow band frequency selectivefilters where only a few of the samples of the frequency response are non-zero.

77.What is meant by autocorrelati on?The autocorrelation of a sequence is the correlation of a sequence with its shifted

version, and this indicates how fast the signal changes.

78.Define whi te noise?A stationary random process is said to be white noise if its power density

spectrum is constant. Hence the white noise has flat frequency response spectrum.SX(w) =

2, - w

79.what do you understand by a fi xed-point number?In fixed point arithmetic the position of the binary point is fixed. The bit to the right

represent the fractional part of the number & those to the left represent the integer part.


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For example, the binary number 01.1100 has the value 1.75 in decimal.

80.What i s the objective of spectrum estimation?The main objective of spectrum estimation is the determination of the power

spectral density of a random process. The estimated PSD provides information about the

structure of the random process which can be used for modeling, prediction or filtering ofthe deserved process.

81.L ist out the addressing modes supported by C5X processors?1. Direct addressing2. Indirect addressing

3. Immediate addressing4. Dedicated-register addressing

5. Memory-mapped register addressing

6. Circular addressing

82.what is meant by block f loating point representation? What are its advantages?In block point arithmetic the set of signals to be handled is divided into blocks. Each

block have the same value for the exponent. The arithmetic operations with in the block

uses fixed point arithmetic & only one exponent per block is stored thus saving memory.This representation of numbers is more suitable in certain FFT flow graph & in digital

audio applications.

83.what are the advantages of f loating point ari thmetic?1. Large dynamic range2. Over flow in floating point representation is unlike.

84.what are the three-quantization errors to finite word length registers in digital filters?

1. Input quantization error 2. Coefficient quantization error 3. Product quantizationerror

85.How the mul tipli cation & addition are carr ied out in fl oating point ari thmetic?In floating point arithmetic, multiplication are carried out as follows,Let f1 = M1*2c1 and f2 = M2*2c2. Then f3 = f1*f2 = (M1*M2) 2(c1+c2)

That is, mantissa is multiplied using fixed-point arithmetic and the exponents are

added.

The sum of two floating-point number is carried out by shifting the bits of the mantissaof the smaller number to the right until the exponents of the two numbers are equal and

then adding the mantissas.

86.What do you understand by input quanti zation error?In digital signal processing, the continuous time input signals are converted into digital

using a b-bit ACD. The representation of continuous signal amplitude by a fixed digitproduce an error, which is known as input quantization error.


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87.L ist the on-chip peri pheral s in 5X.The C5X DSP on-chip peripherals available are as follows:

1. Clock Generator2. Hardware Timer

3. Software-Programmable Wait-State Generators

4. Parallel I/O Ports5. Host Port Interface (HPI)

6. Serial Port

7. Buffered Serial Port (BSP)

8. Time-Division Multiplexed (TDM) Serial Port9. User-Maskable Interrupts

88.what i s the relati onship between truncation error e and the bits b for representi ng a

decimal i nto binary?For a 2's complement representation, the error due to truncation for both positive and

negative values of x is 0>=xt-x>-2-bWhere b is the number of bits and xt is the truncated value of x.

The equation holds good for both sign magnitude, 1's complement if x>0

If x


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change in value of filter coefficients modify the pole-zero locations. Some times the polelocations will be changed in such a way that the system may drive into instability.

92.which reali zation is less sensiti ve to the process of quantization?Cascade form.

93.what i s meant by quant ization step size?Let us assume a sinusoidal signal varying between +1 and -1 having a dynamic range

2. If the ADC used to convert the sinusoidal signal employs b+1 bits including sign bit,

the number of levels available for quantizing x(n) is 2b+1. Thus the interval between

successive levels

q= 2 =2-b

--------

2b+1

Where q is known as quantization step size.

94.How would you relate the steady-state noise power due to quantization and the b bits

represent ing the binary sequence?Steady state noise powerWhere b is the number of bits excluding sign bit.

95.what is overf low oscill ation?The addition of two fixed-point arithmetic numbers cause over flow the sum exceeds

the word size available to store the sum. This overflow caused by adder make the filter

output to oscillate between maximum amplitude limits. Such limit cycles have beenreferred to as over flow oscillations.

96.what are the methods used to prevent overflow?There are two methods used to prevent overflow

1. Saturation arithmetic 2. Scaling

97.what are the two kinds of l imi t cycle behavior in DSP?1.zero input limit cycle oscillations2.Overflow limit cycle oscillations

98.What is meant by " dead band" of the fi lterThe limit cycle occur as a result of quantization effect in multiplication. The

amplitudes of the output during a limit cycle are confined to a range of values called the

dead band of the filter.

99.Explain briefl y the need for scali ng in the digital fi lter implementation.To prevent overflow, the signal level at certain points in the digital filter must be

scaled so that no overflow occurs in the adder.


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100.What are the diff erent buses of TMS320C5X and their functions?The C5X architecture has four buses and their functions are as follows:

Program bus (PB):It carries the instruction code and immediate operands from program memory

space to the CPU.

Program address bus (PAB):It provides addresses to program memory space for both reads and writes.

Data read bus (DB):It interconnects various elements of the CPU to data memory space.

Data read address bus (DAB):It provides the address to access the data memory space.

Part B

1. Determine the DFT of the sequence

x(n) =1/4, for 0


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WWWWW

WWWWW

N

8

X(k)={0,- /3,- /6,0, /6, /3}

3.Given x(n) = {0,1,2,3,4,5,6,7} find X(k) using DIT FFT algorithm.Ans: Given N = 8

k

= e-j(2/N)k

0

= 11

=0.707-j0.7072

= -j3

= -0.707-j0.707

Using butterfly diagramX(k) = {28,-4+j9.656,-4+j4,-4+j1.656,-4,-4-j1.656,-4-j4,-4-j9.656}

4.Given X(k) = {28,-4+j9.656,-4+j4,-4+j1.656,-4,-4-j1.656,-4-j4,-4-j9.656} ,find x(n)

using inverse DIT FFT algorithm.

k= e

j(2/N)k

0= 1

1=0.707+j0.707

2= j

3= -0.707+j0.707

x(n) = {0,1,2,3,4,5,6,7}

5.Find the inverse DFT of X(k) = {1,2,3,4}

Ans: The inverse DFT is defined as

N-1x(n)=(1/N ) x(k)ej2nk/N n=0,1,2,3,N-1

k=0x(0) = 5/2x(1) = -1/2-j1/2x(2) = -1/2

x(3) = -1/2+j1/2

x(n) = {5/2, -1/2-j1/2, -1/2, -1/2+j1/2}

6. Design an ideal low pass filter with a frequency response Hd(ejw

) =1 for/2


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h(1)=h(-1)=0.3183h(2)=h(-2)=0

h(3)=h(-3)= -0.106

h(4)=h(-4)=0

h(5)=h(-5)=0.06366d.

Find the transfer function H(Z) which is not realizable conver in to realizable bymultiplying by z-(N-1/2)

e. H(Z) obtained is 0.06366-0.106z-2+.3183Z-4+.5Z-5+.3183Z-6-.106Z-8+0.06366Z-10

f. Find H (ejw

) and plot amplitude response curve.

7. Design an ideal low pass filter with a frequency response Hd(ejw

) =1 for/4


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9. Design band reject filter with a frequency response Hd(ejw

) =1 for /4


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15 Consider the transfer function H(Z)=H1(Z)H2(Z) where H1(Z) =1/1-a1Z-1H2(z) =1/ 1-a2Z-1

Find the o/p Round of noise power Assume a1=0.5 and a2= 0.6 and find o.p

round off noise power.

Draw the round of Noise Model.By using residue method find 01By using residue method find 02= 01 2+ 02 2

22b (5.43)Ans:

12

16.Explain the architecture of DSP processor .

Diagram. & explanation.

17.Describe briefly the different methods of power spectral estimation?1. Bartlett method

2. Welch method3. Blackman-Tukey method

and its derivation.

18.what is meant by A/D conversion noise. Explain in detail?

A DSP contains a device, A/D converter that operates on the analog input x(t) to

produce xq(t) which is binary sequence of 0s and 1s.At first the signal x(t) is sampled at regular intervals to produce a sequence x(n) is of

infinite precision. Each sample x(n) is expressed in terms of a finite number of bits given

the sequence xq(n). The difference signal e(n)=xq(n)-x(n) is called A/D conversion noise.

+ derivation.

19 onsider the transfer function H(Z)=H1(Z)H2(Z) where H1(Z) =1/1-a1Z-1

H2(z) =1/ 1-a2Z-1Find the o/p Round of noise power Assume a1=0.7 and a2= 0.8and find o.p round

off noise power.

Draw the round of Noise Model.By using residue method find 01By using residue method find 02= 01 2+ 02 2

20.Given X(k) = {1,1,1,1,1,1,1,1,} ,find x(n) using inverse DIT FFT algorithm.


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Wk

= ej(2/N)k

Find x(n)

21.Find the inverse DFT of X(k) = {3,4,5,6}Ans: The inverse DFT is defined as

N-1x(n)=(1/N ) x(k)ej2nk/N n=0,1,2,3,N-1

k=0

22. Explain various addressing modes of TMS processor.

Immediate.Register

Register indirect

Indexed

& its detail explanation.

23 Derive the expression for steady state I/P Noise Variance and Steady state O/PNoise Variance

Write the derivation.

24. Explain briefly the periodogram method of power spectral estimation?

Write the derivation with explanation.

25. Explain various arithmetic instruction of TMS processor.

All arithmetic instruction with explanation.


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PART AQUESTION1. Define discrete time signal.

A di sc ret e ti me si gn al x (n) is a func ti on of an ind ep en de nt va ri ab le that is an int eg er . adiscrete time signal is not defined at instant between two successive samples.

2. Define discrete timesystem.A di sc ret e or an al go rit hm th at pe rf or ms some presc ribed operat io n on a discrete timesignal is called discrete time system.

3. What are the elementary discrete time signals? Unit sample sequence (unit impulse) (n)= {1 n=0 0 Otherwise Unit step signal U (n) ={ 1 n>=00 Otherwise Unit ramp signalUr(n)={n for n>=00 Otherwise Exponential signal x (n)=an where a is realx(n)-Real signal4. State the classification of discrete t ime signals.The types of discrete time signals are Energy and power signals Periodic and Aperiodic signals Symmetric(even) and Antisymmetric (odd) signals 5. Define energy and power signal.E=x (n) 2n= -If E is f in i te i.e. 0system.Linear system is one which satisfies superposition principle.Superposition principle:The response of a system to a weighted sum of signals be equal to the correspondingweighted sum of responses of system to each of individual input signal.

i.e., T [a1x1(n)+a2x2(n)]=a1T[x1(n)]+a2 T[x2(n)]
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i f x(n)X(Z)then Zx(n-k)Z-KX(Z)

ii i)Scaling in Z-domainZi f x(n)X(Z)Z

then anx(n)X(a-1Z)

iv)Time reversalZi f x(n) X(Z)Zthen x(-n) X(Z-1 )

v)Differtiation in Z domainZnx(n)-Zdz X(Z)

vi)convolution of two sequences Z Zi f x1(n)X1(Z) and x2(n)x2(Z) Zthen x1(n)*x2(n)X(Z)=X1(Z).X2(Z)

vii)correlationZ Zi f x1(n)X1(Z) and x2(n)X2(Z)

then Zrx1x2(l=x1(n) x2(nl)Rx1x2(Z)=X1(Z) .X2(Z -1 )n= -

25.State the methods for evaluating inverse Z- transform. Direct valuation by contour integration. Expansion into series of terms in the variable Z and Z-1.

Partial fraction expansion and look up table. 26.Define DFT and IDFT (or) What are the analysis and synthesis equations of DFT?

DFT(Analysis Equation)N-1 nkX(k)= x(n) WN , W N = e-j2 / Nn=0IDFT(Synthesis Equation)

N-1 - nkx(n)= 1/N X(k) WN , W N = e -j2 / Nk=0

27.State the properties of DFT.

1)Periodicity2)Linearity and symmetry3)Multiplication of two DFTs4)Circular convolution5)Time reversal6)Circular t ime shift and frequency shift7)Complex conjugate8)Circular correlation

28.Define circular convolution. Let x1(n) and x2(n) are finite duration sequences both of length N with DFTs X1(K) andX2(k)If X3(k)=X1(k)X2(k) then the sequence x3(n) can be obtained by circular convolutiondefined as

N-1


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x3(n)= x1(m)x2((n-m))Nm=0

29.How to obtain the output sequence of linear convolution through circularconvolution?Consider two finite duration sequences x(n) and h(n) of duration L samples and Msamples. The linear convolution of these two sequences produces an output sequence ofduration L+M-1 samples, whereas , the circular convolution of x(n) an d h(n) give N

samples where N=max(L,M).In order to obtain the number of samples in circularconvolution equal to L+M-1, both x(n) and h(n) must be appended with appropriatenumber of zero valued samples. In other words b y increasing the length of the sequencesx(n) and h(n) to L +M-1 points and then circularly convolving the resulting sequences weobtain the same result as that of l inear convolution.

30.What is zero padding?What are its uses? Let the sequence x(n) has a length L. If we want to f ind the N-point DFT(N>L) of thesequence x(n), we have to add ( N-L) zeros to the sequence x(n). This is known as zeropadding.The uses of zero padding are1)We can get better display of the frequency spectrum.2)With zero padding the DFT can be used in linearf i ltering.

31.Define sectional convolution. If the data sequence x(n) is of long duration it is very diff icult to obtain the outputsequence y(n) due to limited memory of a digital computer. Therefore, the da ta sequenceis divided up into smaller sections. These sections are processed separately one at atime and controlled later to get the output.

32.What are the two methods used for the sectional convolution? The two methods used for the sectional convolution are1)the overlap-add method and 2)overlap-save method.

33.What is overlap-add method?In this method the size of the input da ta block xi(n) is L. To each data block we appendM-1 zeros and perform N point cicular convolution of xi(n) and h(n). Since each data

block is terminated with M-1 zeros the last M-1 points from each output block must beoverlapped and added to first M-1 points of the succeeding blocks.This method is calledoverlap-add method.

34.What is overlap-save method?In this method the data sequence is divided into N point sections xi(n).Each sectioncontains the last M-1 data points of the previous section followed by L new data points toform a data sequence of length N=L+M-1 .In circular convolution of xi(n) with h(n ) the firstM-1 points will not agree with the linear convolution of xi(n) and h(n) because of aliasing,the remaining points will agree with linear convolution. Hence we discard the first (M-1)points of f i ltered section xi(n) N h(n). This pr ocess is repeated for all sections and thefiltered sections are abutted together.

35.Why FFT is needed? The direct evaluation DFT requires N2 complex multiplications and N2 N complex

additions. Thus for large values of N d irect evaluation of the DFT is diff icult. By usingFFT algorithm the number of complex computations can be reduced. So we use FFT.

36.What is FFT? The Fast Fourier Transform is an algorithm used to compute the DFT. It makes use of thesymmetry and periodicity properties of twiddle factor to effectively reduce the DFTcomputation time.It is based on the fundamental principle of decomposing thecomputation of DFT of a sequence of length N into successively smaller DFTs.

37.How many multiplications and additions are required to compute N point DFTusing redix-2 FFT?The number of multiplications and additions required to compute N point DFT using radix -2 FFT are N log2 N and N/2 log2 N respectively,.

38.What is meant by radix-2 FFT?

The FFT algorithm is most efficient in calculating N point DFT. If th e number of output
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points N can be expressed as a power of 2 that is N=2M, where M is an integer, then thisalgorithm is known as radix-2 alg orithm.

39.What is DIT algorithm?Decimation-In-Time algorithm is used to calculate the DFT of a N point sequence. Theidea is to break the N point sequence into two sequences, the DFTs of which can becombined to give the DFt of the original N point sequence.This algorithm is called DITbecause the sequence x(n) is often splitted into smaller sub - sequences.

40.What DIF algorithm? It is a popular form of the FFT algorithm. In this the output sequence X(k) is divided intosmaller and smaller sub-sequences , that is why the n ame Decimation In Frequency.

41.Draw the basic butterfly diagram of DIT algorithm. The basic butterfly diagram for DIT algorithm isWhere a and b are inputs and A and B are the outputs.

42.Draw the basic butterfly diagram of DIF algorithm. The basic butterfly diagram for DIF algorithm isWhere a and b are inputs and A and B are outputs.

43.What are the applications of FFT algorithm? The applications of FFT algorithm includes1) Linear f i ltering2) Correlation3) Spectrum analysis

44.Why the computations in FFT algorithm is said to be in place? Once the butterfly operation is performed on a pair of complex numbers (a,b) to produce(A,B), there is no need to save the input pair. We can store the result (A,B) in the samelocations as (a,b). Since the same storage locations are used troughout the computationwe say that the computations are done in place.

45.Distinguish between linear convolution and circular convolution of twosequences.

Linear convolution If x(n) is a sequence of L number of samples and h(n) with M number of samples, afterconvolution y(n) will have N=L+M-1 samples.It can be used to find the response of a linear f i lter.Zero padding is not necessary to find the response of a linear f i lter.

Circular convolution

If x(n) is a sequence of L number of samples and h(n) with M samples, after convolutiony(n) will have N=max(L,M) samples.It cannot be used to find the response of a fi lter.

Zero padding is necessary to find the response of a fi lter.

46.What are differences between overlap-save and overlap-add methods.Overlap-save method

In this method the size of the input da ta block is N=L+M-1Each data block consists of the last M-1 data points of the previous data block followedby L new data pointsIn each output block M-1 points are corrupted due to aliasing as circular convolution isemployedTo form the output sequence the firstM-1 data points are discarded in each output block and the remaining data are fittedtogetherOverlap-add methodIn this method the size of the input da ta block is LEach data block is L points and we append M-1 zeros to compute N point DFTIn this no corruption due to aliasing as linear convolution is performed using circularconvolutionTo form the output sequence the lastM-1 points from each output block is added to the first M-1 points of the succeeding

block


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47.What are the differences and similarit ies between DIF and DIT algorithms?

Differences:1)The input is bit reversed while the output is in natural order for DIT, whereas for DIFthe output is bit reversed while the input is in natural order.

2)The DIF butterfly is slightly different from the DIT butterfly, the difference being thatthe complex multiplication takes place after the add-subtract operation in DIF.

Similarit ies:Both algorithms require same number of operations to compute the DFT.Both algorithmscan be done in place and both need to perform bit reversal at some place during thecomputation.

48. What are the different types of f i lters based o n impulse response?Based on impulse response the fi lters are of two types1. IIR fi lter2. FIR fi lterThe IIR fi lters are of recursive type, whereby the present output sample depends on thepresent input, past input samples and output samples.The FIR fi lters are of non r ecursive type, whereby the present output sample depends onthe present input sample and previous input samples.

49. What are the different types of f i lters based on frequency response?Based on frequency response the fi lters can be classif ied as1. Lowpass fi lter2. Highpass fi lter3. Bandpass fi lter4. Bandreject f i lter

51.Distinguish between FIR fi lters and IIR fi lters.FIR fi lter

These fi lters can be easily designed to have perfectly l inear phase.

FIR fi lters can be realized recursively and non -recursively.

Greater f lexibil ity to control the shape of their magnitude response.

Errors due to round off noise are less severe in FIR fi lters, mainly because feedback isnot used.

IIR fi lter

These fi lters do not have linear phase.

IIR fi lters are easily realized recursively.

Less flexibil ity, usually l imited to specific kind of f i lters.

The round off noise in IIR fi lters is more.

52. What are the design techniques of designing FIR fi lters?There are three well known methods for designing FIR fi lters with linear phase .They are(1.)Window method (2.)Frequency sampling method (3.)Optimal or minimax design.

53.What is Gibbs phenomenon? One possible way of f inding an FIR fi lter that approximates H(ejw) would be to truncatethe infinite Fourier series at n=(N-1/2).Direct truncation of the series will lead to fixedpercentage overshoots and undershoots before and afte r an approximated discontinuityin the frequency response.


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54. List the steps involved in the design of FIR fi lters using windows.1.For the desired frequency response Hd(w), f ind the impulse response hd(n) usingEquationhd(n)=1/2 Hd(w)ejwndw -2.Multiply the infinite impulse response with a chosen window sequence w(n) o f length Nto obtain fi lter coefficients h(n),i.e.,

h(n)= hd(n)w(n) for |n|(N -1)/2= 0 otherwise

3.Find the transfer function of the realizable fi lter(N-1)/2H(z)=z-(N-1)/2 [h(0)+ h(n)(zn+z-n)]n=0

55. What are the desirable characteristics of the window function?The desirable characteristics of the window are1.The central lobe of the frequency response of the window should contain most of theenergy and should be narrow.2.The highest side lobe level of the frequency response should be small.3.The side lobes of the frequency response should decrease in energy rapidly as t endsto .

56.Give the equations specifying the following windows.a. Rectangular windowb. Hamming windowc. Hanning windowd. Bartlett windowe. Kaiser windowa. Rectangular window:The equation for Rectangular window is given byW(n)= 1 0 n M -10 otherwiseb. Hamming window:The equation for Hamming window is given by

WH(n)= 0.54-0.46 cos 2n/M-1 0 n M -10 otherwisec. Hanning window:The equation for Hanning window is given byWHn(n)= 0.5[1- cos 2n/M-1 ] 0 n M -10 otherwised. Bartlett window:The equation for Bartlett window is given byWT(n)= 1-2|n-(M-1)/2| 0 n M -1M-10 otherwisee. Kaiser window:The equation for Kaiser window is given byWk(n)= Io[1 -( 2n/N-1)2] for |n| N -1Io() 2

0 otherwisewhere is an independent parameter.

57. What is the necessary and sufficient condition for l inear phase characteristic in FIRfilter?The necessary and sufficient condition for l inear phase characteristic in FIR fi lter is, theimpulse response h(n) of the system should have the symmetry property i.e.,H(n) = h(N-1-n)where N is the duration of the sequence.

58.What are the advantages of Kaiser window?o It provides flexibil ity for the designer to select the side lobe level and No It has the attractive property that the side lobe level can be varied continuously fromthe low value in the Blackman window to the high value in the rectangular window

59. What is the principle of designing FIR fi lter using frequency sampling method?


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In frequency sampling method the desired magnitude response is sampled and a linearphase response is specified .The samples of desired frequency response are identif iedas DFT coefficients. The fi lter coefficients are then determined as the IDFT of this set ofsamples.

60. For what type of f i lters frequency sampling method is suitable?Frequency sampling method is attractive for narrow band frequency sel ective fi lters

where only a few of the samples of the frequency response are non zero.

61. Draw the direct form realization of FIR system.

DIRECT REALIZATION FIR SYSME Diagram

62. Draw the direct form realization of a linear Phase FIR system for N even.

LINEAR PHASE FIR SYSTEM FOR N EVEN DIAGRAM

63.Draw the direct form realization of a linear Phase FIR system for N odd

LINEAR PHASE FIR SYSTEM N ODD DIAGRAM

64. When cascade form realization is preferred in FIR fi lters?The cascade form realization is preferred when complex zeros with absolute magnitude isless than one.

64. Draw the M stage lattice filter. M STAGE LATTICE FILTER DIAGRAM

65. State the equations used to convert the latt ice fi lter coefficients to direct form FIRFilter coefficient.m(0) = 1

m(m) = km m-1(m-k)m(k) = m-1(k) + m(m)

66. State the equations used to convert the FIR fi lter coefficients to the latt ice fi lterCoefficient.

For an M_stage fi lter , m-1(0) =1 and km = m(m)

m(m-k) , 1km -1m -1(k) = m (k) - m(m)

1- m2 (m)

67. State the structure of IIR filter?

IIR fi lters are of recursive type whereby the present o/p sample depends on present i/p,past i/p samples and o/p samples. The design of IIR fi lter is r ealizable and stable.The impulse response h(n) for a realizable fi lter ish(n)=0 for n0

68. State the advantage of direct form structure over direct form st ructure. In direct form structure, the number of memory locations required is less than that ofdirect form structure.

69. How one can design digital filters from analog filters? Map the desired digital fi l ter specifications into those for an equivalent analog fi lter. Derive the analog transfer function for the analog prototype. Transform the transfer function of the analo g prototype into an equivalent digital f i ltertransfer function.

70. Mention the procedures for digit izing the transfer function of an analog fi lter.
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The two important procedures for digit izing the transfer function of an analog fi lter are Impulse invariance method. Bil inear transformation method.

71. What do you understand by backward difference?One of the simplest method for converting an analog fi lter into a digital f i lter is toapproximate the differential equation by an equivalent difference equation.

d/dt y(t)=y(nT)-y(nT-T)/T

The above equation is called backward difference equation.

72. What is the mapping procedure between S-plane & Z-plane in the method of mappingdifferentials? What are its characteristics?The mapping procedure between S-plane & Z-plane in the method of mapping ofdifferentials is given by

H(Z) =H(S)|S=(1-Z-1)/TThe above mapping has the follo wing characteristics The left half of S-plane maps inside a circle of radius centered at Z= in the Z-plane. The right half of S-plane maps into the region outside the circle of radius in the Z-plane. The j -axis maps onto the perimeter of the circle of radius in the Z-plane.

73. What is meant by impulse invariant method of designing IIR fi lter?In this method of digit izing an analog fi lter, the impulse response of resulting digital f i lteris a sampled version of the impulse response of the analog fi lter.The transfer function of analog fi lter in partial fraction form,

74. Give the bil inear transform equation between S-plane & Z-plane.

S=2/T(1-Z-1/1+Z-1)

75. What is bil inear transformation?The bilinear transformation is a mapping tha t transforms the left half of S-plane into theunit circle in the Z-plane only once, thus avoiding aliasing of frequency components.The mapping from the S-plane to the Z-plane is in bil inear transformation is

S=2/T(1-Z-1/1+Z-1)

76. What are the properties of bil inear transformation? The mapping for the bil inear trans formation is a one -to-one mapping that is for everypoint Z, there is exactly one corresponding point S, and vice-versa. The j -axis maps on to the unit circle |z|=1,the left half of the s-plane ma ps to the

interior of the unit circle |z|=1 and the half of the s-plane maps on to the exterior of theunit circle |z|=1.

77. Write a short note on pre-warping.The effect of the non-linear compression at high frequencies can be compensated. W henthe desired magnitude response is piece-wise constant over frequency, this compressioncan be compensated by introducing a suitable pre-scaling, or pre-warping the crit icalfrequencies by using the formula.

78. What are the advantages & disadvantages of bil inear transformation?Adva nt ag es : The bil inear transformation provides one -to-one mapping. Stable continuous systems can be mapped into realizable, stable digital systems.

There is no aliasing.


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93. What is input quantization error?.The input quantization errors arise due to A/D conversion.

94.What are the different quantization methods?Truncation and Rounding

95.What is truncation?

Truncation is a process of discarding all bits less significant than LSB that is retained

96. What is Rounding?

Rounding a number to b bits is accomplished by choosing a rounded result as the b bitnumber closest number being unrounded.

97.What are the two t ypes of limit cycle behavior of DSP?.

1.Zero limit cycle behavior 2.Over flow limit cycle behavior

98.What are the methods to prevent overflow?1.Saturation arithmetic and2.Scaling

99.State some applications of DSP? Speech processing ,Image processing, Radar signal processing.

Q2.-What is the use of Random Signals?

Ans2. Random signals are used to test dynamic response statistically for very small amplitudes and time-

duration.

Q3.- Classify Systems.

Ans3. Linear, stable and time-invariant.

Q4.-What do you mean by aliasing in digital signal processing? How it can be avoided?

Ans4. Aliasing refers to an effect due to which different signals become indistinguishable. It also refers to

distortion in the reconstructed signal when it is reconstructed from the original continuous signal. To avoid

aliasing we can simply filter out the high frequency components of the signal by using anti-aliasing filter like

optical anti-aliasing filter.

Q5. What are the differences between a microprocessor and a DSP processor?

Ans5. DSP processors are featured to support high performance and repeatitive and intensive tasks whereas

microprocessors are not application specific and they are designed to process control-oriented tasks.

Q6. What is the convolution?

Ans6. Convolution is the technique of adding two signals in time domain. We can also do this quite easily by

changing the domain of signals from time domain to frequency domain using Fast Fourier Transform (FFT).

Q7.- What is FFT?

Ans7. FFT is a fast way to calculate Discrete Fourier Transform (DFT). It is much more efficient then DFT and

require less number of coding lines. Due to FFT several kind of techniques are feasible.

Q8.- What is the advantage of a Direct form II FIR over fom I?

Ans8. Direct Form II FIR filters requires half the number of delay units as much as used by Form I.

Q9.- What is interpolation and decimation?

Ans9. Interpolation is the process of increasing the sample rate in dsp whereas decimation is the opposite of

this that is, it is the process of decreasing the sample rate in dsp.

10.- Difference between DFT and DTFT.

Ans10.


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DFT DTFT

1-Limited number of samples of periodic signal 1-unlimited number of samples.

2- input is always periodic 2-input may not always be periodic

3- physically realizable 3- mathematically precise

4- frequency becomes discrete 4- frequency is continuous

Digital Signal Processing short question and answers

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