DSP_CSE_7th SEM (2Mark Q&A).pdf

7/25/2019 DSP_CSE_7th SEM (2Mark Q&A).pdf

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Prepared by Prof. U. Vinothkumar AP / ECE/ Dr.NGPIT

Dr. N.G.P.INSTITUTE OF TECHNOLOGY, COIMBATORE - 641048.

Department of Computer Science Engineering

Question Bank

Anna University, Chennai.

CS2403 - DIGITAL SIGNAL PROCESSING

Prepared by,

Prof. U. Vinothkumar, AP/ECE/Dr.N.G.P.IT


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UNIT - 1

SIGNALS AND SYSTEMS

Syllabus:

Basic elements of DSP concepts of frequency in Analog and Digital Signals

sampling theorem Discrete time signals, systems Analysis of discrete time LTIsystems Z transform Convolution (linear and circular) Correlation.

Two mark questions:

1. Define Signal.

Signal is a physical quantity that varies with respect to time, space or anyother independent variable.

(Or)

It is a mathematical representation of the systemEg y(t) = t. and x(t)= sin t.

2. Define system.A set of components that are connected together to perform the particular

task. E.g. Filters

(Or)

A System is defined as a physical device that generates a response or an output

signal, for a given input signal.

3. State the classification of discrete time signals. (APR-96)

The types of discrete time signals are* Energy and power signals* Periodic and A periodic signals* Symmetric (Even) and Ant symmetric (Odd) signals

4. State the classification of discrete time system.

They types of discrete time systems are* Static and Dynamic systems* Causal and non-causal systems* Linear and non-linear systems* Time variant and time in-variant systems


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5. Define Discrete-time system.A discrete time system is one which operates on a discrete-time signal and

produces a discrete-time output signal. If the input and output of discrete-timesystem are x(n) and y(n), then we can write y(n)= T[x(n)].

6.

Define Discrete-time signal.

The signal that are defined at discrete instants of time are known as discrete-time signals. The discrete-time signals are continuous in amplitude and discrete intime. They are denoted by x(n).

7. Give some applications of DSP? (APR-98)* Speech processing Speech compression & decompression for voicestorage system* Communication Elimination of noise by filtering and echo cancellation.

* Bio-Medical Spectrum analysis of ECG, EEG etc.

8. Define sampling theorem.A continuous time signal can be represented in its samples and recovered back

if the sampling frequency Fs 2B. Here Fs is the sampling frequency and B isthe maximum frequency present in the signal.

9. What are the properties of convolution?* Commutative property x(n) * h(n) = h(n) * x(n)

* Associative property [x(n) * h1(n)]*h2(n) = x(n)*[h1(n) * h2(n)]* Distributive property x(n) *[ h1(n)+h2(n)] = [x(n)*h1(n)]+[x(n) * h2(n)]

10.Define DSP.

DSP - Digital Signal Processing. It is defined as changing or analyzinginformation which is measured as discrete time sequences.

11.List out the basic elements of DSP. (MAR-99)

signal in Analog to Digital converter

Digital Signal processor

Digital to Analog converter signal out


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12.Mention the advantages of DSP.

Veracity Simplicity Repeatability

13.

What are the major classifications of the signal?

(i) Discrete time signal(ii) Continuous time signal

14.

Define discrete time signals and classify them. (APR-98)

Discrete time signals are defined only at discrete times, and for these signals,the independent variable takes on only a discrete set of values.

Classification of discrete time signal:

1. Periodic and A periodic signal

2. Even and Odd signal

15.Define continuous time signals and classify them.Continuous time signals are defined for a continuous of values of the

Independent variable. In the case of continuous time signals the independentVariable is continuous.

For example:(i) A speech signal as a function of time(ii) Atmospheric pressure as a function of altitude

Classification of continuous time signal:(i) Periodic and Aperiodic signal(ii) Even and Odd signal

16.Define even and odd signal. (MAY-2000)A discrete time signal is said to be even when,

x[-n]=x[n]The continuous time signal is said to be even when,

x(-t)= x(t)For example, Cosine wave is an even signal.

The discrete time signal is said to be odd when,x[-n]= -x[n]

The continuous time signal is said to be odd when,x(-t)= -x(t)

Odd signals are also known as nonsymmetrical signal. Sine wave signal is an oddsignal.


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17.Define Energy and power signal.A signal is said to be energy signal if it have finite energy and zero power. A

signal is said to be power signal if it have infinite energy and finite power. If theAbove two conditions are not satisfied then the signal is said to be neither energynor power signal.

18.What is analog signal?

The analog signal is a continuous function of independent variables. Theanalog Signal is defined for every instant of independent variable and so magnitudeof Independent variable is continuous in the specified range. Here both theindependent Variable and magnitude are continuous.

19. What is digital signal?The digital signal is same as discrete signal except that the magnitude of signal

is quantized.20. Define periodic and non-periodic discrete time signals?

If the discrete time signal repeated after equal samples of time then it is calledperiodic signal. When the discrete time signal x[n] satisfies the conditionx[n+N]=x(n), then it is called periodic signal with fundamental period N samples.If x(n) * x(n+N) then it is called non periodic signals.

21. What are all the blocks are used to represent the CT signals by its samples?

Sampler

Quantizer

22. Define sampling process.

Sampling is a process of converting Continuous time signal into discrete timesignal.

23. State sampling theorem. (APR-98,2000)The sampling frequency must be at least twice the maximum frequency

present in the signal.That is Fs = > 2fm

Where, Fs = sampling frequencyfm = maximum frequency

24.

Define aliasing or folding.

The superimposition of high frequency behavior on to the low frequencybehavior is referred as aliasing. This effect is also referred as folding.


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25. What is the condition for avoid the aliasing effect?To avoid the aliasing effect the sampling frequency must be twice the

maximum frequency present in the signal.

26. Define z transform? (APR-2002)The Z transform of a discrete time signal x(n) is defined as,

X(z)= () z-n

Where, z is a complex variable. In polar form z=re-j

27. What is meant by ROC?The region of convergence (ROC) is defined as the set of all values of z for

Which X(z) converges.

28. What are the properties of ROC? (MAY-2004)a. The roc is a ring or disk in the z plane centered at the origin.

b. The roc cannot contain any pole.c. The roc must be a connected regiond. The roc of an LTI stable system contains the unit circle.

29. Explain the linearity property of the z transform.If z{x1(n)}=X1(z) and z{X2(n)}=x2(z) then,z{ax1(n)+bx2(n)}=aX1(z)+bX2(z)a&b are constants.

30. State the time shifting property of the z transform.

If z{x(n)}=X(z) then z{x(n-k)}=z-kX(z)

31. What is the need for Z-transform?Z-transform is used for analysis the both periodic and a periodic signals.

32.

State the convolution properties of Z transform? (MAY-98,2002)The convolution property states that the convolution of two sequences in

time domain is equivalent to multiplication of their Z transforms.

33. What are the conditions of stability of a causal system?All the poles of the system are within the unit circle. The sum of impulse

response for all values of n is bounded.


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34. Explain convolution property of the z transform.If z{x(n)}=X(z) & z{h(n)}=H(z) then, z{x(n)*h(n)}=X(z)H(z)

35.

State the time reversal property of the z transform.

If z{x(n)}=X(z) then z{x(-n)}=X(z-1)

36.State the scaling property of the z transform.

If z{x(n)}=X(z) then z{anx(n)}=X(a-1z)

37.Explain the linearity property of the z transform. (MAY-2006)

If z{x1(n)}=X1(z) and z{X2(n)}=x2(z) then,z{ax1(n)+bx2(n)}=aX1(z)+bX2(z)a&b are constants.


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UNIT - 2

FREQUENCY TRANSFORMATIONS

Syllabus:

Introduction to DFT Properties of DFT Filtering methods based on DFT

FFT Algorithms Decimation in time Algorithms, Decimation in frequencyAlgorithms Use of FFT in Linear Filtering DCT.

Two mark questions:

1. Define DFT. (APR-2006)It is a finite duration discrete frequency sequence, which is obtained by

sampling one period of Fourier transform. Sampling is done at N equally spacedpoints over the period extending from w=0 to 2.

DFT is defined as X(w)= x(n)e-jwn. Here x(n) is the discrete time sequenceX(w) is the fourier transform of x(n).

2. Define Twiddle factor.

The Twiddle factor is defined as WN=e-j2 /N

3. Define Zero padding.The method of appending zero in the given sequence is called as Zero padding.

4. State circular convolution. (MAY-2004)

This property states that multiplication of two DFT is equal to circularconvolution of their sequence in time domain.

5. State parsevals theorem.

Consider the complex valued sequences x(n) and y(n).If x(n)y*(n)=1/NX(k)Y*(k)

6. List the properties of DFT.Linearity, Periodicity, Circular symmetry, symmetry, Time shift, Frequency

shift, complex conjugate, convolution, correlation and Parsevals theorem.

7. What is the disadvantage of direct computation of DFT?For the computation of N-point DFT, N2 complex multiplications and

N[N-1] Complex additions are required. If the value of N is large than the numberof computations will go into lakhs. This proves inefficiency of direct DFTcomputation.


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8. What is the way to reduce number of arithmetic operations during DFT

computation? (MAR-2008)

Number of arithmetic operations involved in the computation of DFT isgreatly reduced by using different FFT algorithms as follows.

1. Radix-2 FFT algorithms. -Radix-2 Decimation in Time (DIT) algorithm. -Radix-2 Decimation in Frequency (DIF) algorithm.

2. Radix-4 FFT algorithm.

9. What is the computational complexity using FFT algorithm?1. Complex multiplications = N/2 log2N2. Complex additions = N log2N

10.Why FFT is needed?The direct evaluation of the DFT using the formula requires N2 complex

multiplications and N (N-1) complex additions. Thus for reasonably large values ofN (inorder of 1000) direct evaluation of the DFT requires an inordinate amount ofcomputation. By using FFT algorithms the number of computations can be reduced.For example, for an N-point DFT, The number of complex multiplications requiredusing FFT is N/2log2N. If N=16, the number of complex multiplications requiredfor direct evaluation of DFT is 256, whereas using DFT only 32 multiplications arerequired.

11.

What is a decimation-in-time algorithm? (APR-2009)

Decimation-in-time algorithm is used to calculate the DFT of a N-pointSequence. The idea is to break the N-point sequence into two sequences, the DFTsof which can be combined to give the DFT of the original N-point sequence. Initiallythe N-point sequence is divided into two N/2-point sequences xe(n) and x0(n), whichhave the even and odd members of x(n) respectively. The N/2 point DFTs of thesetwo sequences are evaluated and combined to give the N point DFT. Similarly the

N/2 point DFTs can be expressed as a combination of N/4 point DFTs. This processis continued till we left with 2-point DFT. This algorithm is called Decimation-in-time because the sequence x(n) is often splitted into smaller sub sequences.

12.

What are the applications of FFT algorithms?1. Linear filtering2. Correlation3. Spectrum analysis


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13.What are the differences and similarities between DIF and DIT algorithms?

Differences:1. For DIT, the input is bit reversal while the output is in naturalorder, whereas for DIF, the input is in natural order while the output is bit reversed.2. The DIF butterfly is slightly different from the DIT butterfly, the difference beingthat the complex multiplication takes place after the add-subtract operation in DIF.

Similarities:Both algorithms require same number of operations to computethe DFT. Bot algorithms can be done in place and both need to perform bit reversalat some place during the computation.

14.What is a decimation-in-frequency algorithm? (MAR-2006)

In this the output sequence X (K) is divided into two N/2 point sequences andeach N/2 point sequences are in turn divided into two N/4 point sequences.

15.Distinguish between DFT and DTFT.

16.Calculate the number of multiplications needed in the calculation of DFT

using FFT algorithm with 32-point sequence. (APR-2004)

For N-point DFT the number of complex multiplications needed using FFTalgorithm is [N/2] log2N.

For N =32, the number of complex multiplications is equal to [32/2]log232=16 x5 = 80.

17.How many multiplications and additions are required to compute N-point

DFT using radix-2 FFT?The number of multiplications and additions required to compute N-point

DFT using radix-2 FFT are Nlog2N and [N/2] log2N respectively.

18.

What is meant by radix-2 FFT? (MAY-2009)The FFT algorithms is most efficient in calculating N-point DFT. If the

number of output points N can be expressed as a power of 2, that is, N=2M, whereM is an integer, then this algorithm is known as radix-2 FFT algorithm.

S.No. DFT DTFT

1.

2.

Obtained by performing samplingoperation in both the time andfrequency domains.

Discrete frequency spectrum

Sampling is performed only in timedomain.

Continuous function of


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19.What is bin spacing?The N-point DFT of x(n) is given by,

X(k) = ()/

=

Where, WNnk= (e-j2)[nk/N]is the phase factor or twiddle factor.

The phase factors are equally spaced around the unit circle at frequency incrementsof Fs/N where Fsis the sapling frequency of the time domain signal. This frequency

increment or resolution is called bin spacing. (The x (k) consists of N-numbers offrequency samples whose discrete frequency locations are given by fk= kFs/N, fork=0, 1, 2, ..N-1).

20.Arrange the 8-point sequence, x(n) = {1,2,3,4,-1,-2,-3,-4} in bit reversed

order.The x(n) in bit reversed order= {1,-1,3,-3,2,-2,4,-4}.

21.

What is the speed improvement factor in calculating 64-point DFT of a

sequence using direct computation and FFT algorithms? (MAR-2006)The number of complex multiplications required using direct computation is

N2= 642= 4096.The number of complex multiplications required using FFT is

[N/2] log2N = [64/2] log264 = 192.Speed improvement factor = [4096/192] = 21.33

22.What are the properties of convolution?

* Commutative property x(n) * h(n) = h(n) * x(n)* Associative property [x(n) * h1(n)]*h2(n) = x(n)*[h1(n) * h2(n)]* Distributive property x(n) *[ h1(n)+h2(n)] = [x(n)*h1(n)]+[x(n) * h2(n)]

23.Define sampling theorem. (APR-2010)A continuous time signal can be represented in its samples and recovered back

if the sampling frequency Fs 2B. Here Fs is the sampling frequency and B is

the maximum frequency present in the signal.

24.Give some applications of DSP?

* Speech processing Speech compression & decompression for voicestorage system* Communication Elimination of noise by filtering and echo cancellation.* Bio-Medical Spectrum analysis of ECG, EEG etc.


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25. Define Discrete-time signal.The signal that are defined at discrete instants of time are known as discrete-

time signals. The discrete-time signals are continuous in amplitude and discrete intime. They are denoted by x(n).

26.

Define Discrete-time system. (MAY-2009)

A discrete time system is one which operates on a discrete-time signal andproduces a discrete-time output signal. If the input and output of discrete-timesystem are x(n) and y(n), then we can write y(n)= T[x(n)].

28. Draw the basic butterfly diagram for DIT algorithm?

The basic butterfly diagram for DIT algorithm is

Xm (p)P Xm+1 (p) = Xm (p) =+ Wkm Xm (q)

WkN

Xm (q)q Xm+1 (q) = Xm (p) - WkN Xm (q)

29. What is meant by in-palce in DIT and DIF algorithms?

The basic butterfly diagrams used in DIT and DIF algorithms are shown below

Xm(p)p Xm(p)+Xm(q)

Xm(p)p Xm(p)+Wmk Xm(q) W

W Xm(q)q

Xm(q)q Xm(p)-WnkXm(q) [Xm(p)-

Xm(q)]WNk

30.What is basic operation of the DIF algorithms?

The basic operation of the DIF algorithm is the so called butterfly in which twoinputs Xm(p) and Xm(q) are combined to give the outputs Xm+1(p) and Xm+1(q) via

the operation

Xm+1(p)=Xm(p)+Xm(q) ; Xm+1(q)=|Xm(p)-Xm(q)|WNk


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UNIT - 3

IIR FILTER DESIGN

Syllabus:

Structures of IIR Analog filter design Discrete time IIR filter from analogfilter IIR filter design by Impulse Invariance, Bilinear transformation,

Approximation of derivatives (HPF, BPF, BRF) filter design using frequency

translation

Two mark questions:

1. Define IIR filter?IIR filter has Infinite Impulse Response.

2.

What are the various methods to design IIR filters?

* Approximation of derivatives* Impulse invariance* Bilinear transformation.

3. Which of the methods do you prefer for designing IIR filters? Why?Bilinear transformation is best method to design IIR filter, since there is no

aliasing in it.

4.

What is the main problem of bilinear transformation?Frequency warping or nonlinear relationship is the main problem of bilinear

transformation.

5. What is pre-warping?Pre-warping is the method of introducing nonlinearly in frequency

relationship to compensate warping effect.

6. Why an impulse invariant transformation is not considered to be one-to-

one? (MAY-2009)

In impulse invariant transformation any strip of width 2/T in the s-plane forvalues of s-plane in the range (2k-1)/T (2k-1) /T is mapped into the entire z-

plane. The left half of each strip in s-plane is mapped into the interior of unit circlein z-plane, right half of each strip in s-plane is mapped into the exterior of unit circlein z-plane and the imaginary axis of each strip in s-plane is mapped on the unit circlein z-plane. Hence the impulse invariant transformation is many-to-one.


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7. What is Bi-linear transformation?The bilinear transformation is conformal mapping that transforms the s-plane

to z-plane. In this mapping the imaginary axis of s-plane is mapped into the unitcircle in z-plane, the left half of s-plane is mapped into interior of unit circle in z-

plane and the right half of s-plane is mapped into exterior of unit circle in z-plane.The Bilinear mapping is a one-to-one mapping and it is accomplished.

8. How the order of the filter affects the frequency response of Butterworth

filter. (MAY-2010)The magnitude response of butterworth filter is shown in figure, from which

it can be observed that the magnitude response approaches the ideal response as theorder of the filter is increased.

9. What is the importance of poles in filter design?

The stability of a filter is related to the location of the poles. For a stable analogfilter the poles should lie on the left half of s-plane. For a stable digital filter thepoles should lie inside the unit circle in the z-plane.

10.How analog poles are mapped to digital poles in impulse invariant

transformation? (APR-2010)In impulse invariant transformation the mapping of analog to digital poles

are as follows,* The analog poles on the left half of s-plane are mapped into the interior of

unit circle in z-plane.

* The analog poles on the imaginary axis of s-plane are mapped into the unitcircle in the z-plane.

* The analog poles on the right half of s-plane are mapped into the exteriorof unit circle in z-plane.

11.What is impulse invariant transformation?The transformation of analog filter to digital filter without modifying the

impulse response of the filter is called impulse invariant transformation.

12.Where the j axis of s-plane is mapped in z-plane in bilinear

transformation? (DEC-2010)

The j axis of s-plane is mapped on the unit circle in z-plane in bilineartransformation

13.

State the frequency relationship in bilinear transformation?

= (2/T) tan (/2)


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14.Compare the digital and analog filter. (NOV-2010)

Digital filter Analog filter

i)

Operates on digital samples ofthe signal.ii) It is governed by linear

difference equation.iii) It consists of adders,

multipliers and delaysimplemented in digital logic.

iv)

In digital filters the filtercoefficients are designed tosatisfy the desired frequency

response.

i)

Operates on analog signals.ii)

It is governed by lineardifference equation.

iii)

It consists of electricalcomponents like resistors,capacitors and inductors.

iv) In digital filters theapproximation problem issolved to satisfy the desiredfrequency response.

15.

What are the advantages and disadvantages of digital filters?

Advantages of digital filters High thermal stability due to absence of resistors, inductors and capacitors. Increasing the length of the registers can enhance the performance

characteristics like accuracy, dynamic range, stability and tolerance. The digital filters are programmable.

Multiplexing and adaptive filtering are possible.Disadvantages of digital filters The bandwidth of the discrete signal is limited by the sampling frequency. The performance of the digital filter depends on the hardware used to

implement the filter.

16.Define ripples in a filter.

The limits of the tolerance in the magnitude of passband and stopband arecalled ripples. The tolerance in passband is denoted as p and that in stopband is

denoted as s.

17.Classify the filters based on frequency response.Based on frequency response, the filters can be classified into lowpass,

highpass bandpass and bandstop filters.


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18.What are the requirements for an analog filters to be stable and causal?i.

The analog filter transfer function H(s) should be a rational function of sand the coefficients of s should be real.

ii.

The poles should lie on the left half of s-plane.iii. The number of zeros should be less than or equal to number of poles.

19.Distinguish between IIR and FIR filters. (NOV-2010)

The filter design starts from ideal frequency response. By taking inversefourier transform of ideal frequency response, the desired impulse response isobtained, which consists of infinite number of samples.

The digital filter design by selecting only N samples of the impulse responseare called FIR filters. The digital filters designed by considering all the infinitesamples of impulse response are called IIR filters.

20.

Compare IIR and FIR filters.IIR Filter FIR Filter

i. All the infinite samples ofimpulse response areconsidered.

ii. The impulse response cannotbe directly converted to digitalfilter transfer function.

iii.

The design involves design of

analog filter and thentransforming analog filter todigital filter.

iv.

The specifications include thedesired characteristics formagnitude response only.

v. Linear phase characteristicscannot be achieved.

i. Only N samples of impulseresponse are considered.

ii.

The impulse response can bedirectly converted to digitalfilter transfer function.

iii. The digital filter can bedirectly designed to achieve

the desired specification.iv.

The specifications include thedesired characteristics for

both magnitude and phaseresponse.

v.

Linear phase filter can beeasily designed.

21.How a digital IIR filter is designed?

For designing a digital IIR filter, first an equivalent analog filter is designedusing any one of the approximation technique and the given specifications. Theresult of the analog filter design will be an analog filter transfer function H(s). Theanalog filter transfer function is transformed to digital filter transfer function H(z)using either Bilinear or impulse invariant transformation.


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22.Mention any two techniques for digitizing the transfer function of an analog

filter.

The bilinear transformation and the impulse invariant transformation are thetwo techniques available for digitizing the analog filter transfer function.

23.

What are the properties that are maintained same in the transformation of

analog to digital filer?

The analog filter should be stable and causal for effective transformation todigital filters. While transforming the analog filer to digital filters these two

properties (i.e. stability and causality) are maintained same, which means that thetransformed digital filer should also be stable and causal.

24.What is aliasing? (MAY-2012)The phenomena of high frequency sinusoidal components acquiring the

identity of low frequency sinusoidal components after sampling is called aliasing.The aliasing problem will arise if the sampling rate does not satisfy the Nyquistsampling criteria.

25.What is frequency warping?In bilinear transformation the relation between analog and digital frequencies

is non-linear. When the s-plane is mapped in to z-plane using bilineartransformation, this non-linear relationship introduce distortion in frequency axis,which called frequency warping.

26.

What is butterworth approximation?

In butterworth approximation, the error function is selected such that themagnitude is maximally flat in the origin (i.e., at = 0) and monotonicallydecreasing with increasing .

27.How the poles of butterworth transfer function are located in s-plane?The poles of the normalized butterworth transfer function symmetrically lies

on a unit circle in s-plane with angular spacing of /N.28.

What is the properties of butterworth filter? (APR-2014)

i.

The butterworth filters are pole design.ii.

At the cutoff frequency c, the magnitude of normalized butterworth filteris 1/2.

iii.

The filter order N, completely specifies the filter and as the value of Nincreases the magnitude response approaches the ideal response.

iv.

The magnitude is maximally flat at the origin and monotonicallydecreasing with increasing .


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29.What is chebyshev approximation?In chebyshev approximation, the approximation function is selected such that

the error is minimized over a prescribed band of frequencies.

30.How does the order of the filter affect the frequency response of chebyshev

filter? (MAY-2012)

From the magnitude response of type-I chebyshev filter it can be observedthat the magnitude response approaches the ideal response as the order of the filteris increased.


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UNIT - 4

FIR FILTER DESIGN

Syllabus:

Structures of FIR Linear phase FIR filter Filter design using windowing

techniques, Frequency sampling techniques Finite word length effects in digitalFilters

Two mark questions:

1. What is FIR filters?The specifications of the desired filter will be given in terms of ideal

frequency response Hd(w). The impulse response hd(n) of the desired filter can beobtained by inverse fourier transform of Hd(w), which consists of infinite samples.

The filters designed by selecting finite number of samples of impulse response arecalled FIR filters.

2. What are the different types of filters based on impulse response?Based on impulse response the filters are of two types 1. IIR filter 2. FIR filter

The IIR filters are of recursive type, whereby the present output sampledepends on the present input, past input samples and output samples.

The FIR filters are of non- recursive type, whereby the present outputsample depends on the present input, and previous output samples.

3.

What are the different types of filter based on frequency response?The filters can be classified based on frequency response. They are,

i)

Low pass filterii) High pass filteriii)

Band pass filteriv) Band reject filter.

4. What are the techniques of designing FIR filters? (APR-2012)There are three well-known methods for designing FIR filters with linear

phase. These are 1) windows method 2) Frequency sampling method 3) Optimal ormini-max design.

5. What is the reason that FIR filter is always stable?FIR filter is always stable because all its poles are at origin.


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6. What are the properties of FIR filter?1. FIR filter is always stable.

2. A realizable filter can always be obtained.

3. FIR filter has a linear phase response.

7. Write the steps involved in FIR filter design.

Choose the desired (ideal) frequency response Hd(w). Take inverse fourier transform of Hd(w) to get hd(n). Convert the infinite duration hd(n) to finite duration h(n). Take Z-transform of h(n) to get the transfer function H(z) of the FIR

filter.

8. What are the advantages of FIR filters? (Nov-2006) Linear phase FIR filter can be easily designed.

Efficient realization of FIR filter exist as both recursive and non-recursive structures.

FIR filters realized non-recursively are always stable.

The round-off noise can be made small in non-recursive realization ofFIR filters.

9. What are the disadvantages of FIR filters?

The duration of impulse response should be large to realize sharp cutofffilters.

The non-integral delay can lead to problems in some signal processingapplications.

10.What is the necessary and sufficient condition for the linear phase

characteristic of an FIR filter? (DEC-2007)The necessary and sufficient condition for the linear phase characteristic of an

FIR filter is that the phase function should be a linear function of w, which in turnrequires constant phase and group delay.

11.

When cascade form realization is preferred in FIR filters?The cascade form realization is preferred when complex zeros with absolutemagnitude less than one.


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12.What are the conditions to be satisfied for constant phase delay in linear

phase FIR filters?

The conditions for constant phase delay are Phase delay, = (N-1)/2 (i.e., phase delay is constant)

Impulse response, h(n) = -h(N-1-n) (i.e., impulse response isantisymmetric)

13.How constant group delay & phase delay is achieved in linear phase FIR

filters?

The following conditions have to be satisfied to achieve constant group delay& phase delay. Phase delay, = (N-1)/2 (i.e., phase delay is constant) Group delay, = /2 (i.e., group delay is constant) Impulse response, h(n) = -h(N-1-n) (i.e.,impulse response is antisymmetric)

14.

What are the possible types of impulse response for linear phase FIR filters?There are four types of impulse response for linear phase FIR filters

Symmetric impulse response when N is odd.

Symmetric impulse response when N is even.

Antisymmetric impulse response when N is odd.

Antisymmetric impulse response when N is even.

15.List the well-known design techniques of linear phase FIR filters.

There are three well-known design techniques of linear phase FIR filters. They

are Fourier series method and window method

Frequency sampling method.

Optimal filter design methods.

16.What are the desirable characteristics of the frequency response of

window function? (NOV-2007)The desirable characteristics of the frequency response of window function are

The width of the main lobe should be small and it should contain as much

of the total energy as possible. The side lobes should decrease in energy rapidly as w tends to .

17.What is Gibbs phenomenon (or Gibbs Oscillation)? (APR-2012)In FIR filter design by Fourier series method the infinite duration impulse

response is truncated to finite duration impulse response. The abrupt truncation ofimpulse response introduces oscillations in the passband and stopband. This effectis known as Gibbs phenomenon (or Gibbs Oscillation).


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18.Write the procedure for designing FIR filter using frequency-sampling

method.

Choose the desired (ideal) frequency response Hd(w). Take N-samples of Hd(w) to generate the sequence

Take inverse DFT of to get the impulse response h(n). The transfer function H(z) of the filter is obtained by taking z-transform

of impulse response.

19.What are the drawback in FIR filter design using windows and frequency

sampling method? How it is overcome? (APR-2013)The FIR filter design using windows and frequency sampling method does

not have Precise control over the critical frequencies such as wp and ws. Thisdrawback can be overcome by designing FIR filter using Chebyshev approximationtechnique. In this technique an error function is used to approximate the ideal

frequency response, in order to satisfy the desired specifications.

20.Write the characteristic features of rectangular window.

The main lobe width is equal to 4/N. The maximum side lobe magnitude is 13dB.

The side lobe magnitude does not decrease significantly with increasing w.

21.List the features of FIR filter designed using rectangular window.

The width of the transition region is related to the width of the main lobe

of window spectrum.

Gibbs oscillations are noticed in the passband and stopband.

The attenuation in the stopband is constant and cannot be varied.

22.Write the characteristic features of hanning window spectrum.

The main lobe width is equal to 8/N. The maximum side lobe magnitude is 41dB.

The side lobe magnitude remains constant for increasing w.

23.

List some of the finite word length effects in digital filters. Errors due to quantization of input data. Errors due to quantization of filter co-efficient Errors due to rounding the product in multiplications Limit cycles due to product quantization and overflow in addition.


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24.What do finite word length effects mean? (APR-2004)The effects due to finite precision representation of numbers in a digital

system are called finite word length effects.

25.What are the different formats of fixed-point representation?

Sign magnitude format Ones Complement format Twos Complement format.

In all the three formats, the positive number is same but they differ only inrepresenting negative numbers.

26.

Explain the floating-point representation of binary number.

The floating-point number will have a mantissa part. In a given word size thebits allotted for mantissa and exponent are fixed. The mantissa is used to represent

a binary fraction number and the exponent is a positive or negative binary integer.The value of the exponent can be adjusted to move the position of binary point inmantissa. Hence this representation is called floating point.

27.What are the types of arithmetic used in digital computers?The floating point arithmetic and twos complement arithmetic are the two

types of arithmetic employed in digital systems.

28.What is truncation?

The truncation is the process of reducing the size of binary number bydiscarding all bits less significant than the least significant bit that is retained. Intruncation of a binary number of b bits all the less significant bits beyond b thbit arediscarded.

29.

What is rounding? (NOV-2014)

Rounding is the process of reducing the size of a binary number to finite wordsize of b-bits such that, the rounded b-bit number is closest to the original un-quantized number.

30.

Explain the process of upward rounding?In upward rounding of a number of b-bits, first the number is truncated to b-

bits by retaining the most significant b-bits. If the bit next to the least significant bitthat is retained is zero, then zero is added to the least significant bit of the truncatednumber. If the bit next to the least significant bit that is retained is one then one isadded to the least significant bit of the truncated number.


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31.What are the errors generated by A/D process?The A/D process generates two types of errors. They are quantization error

and saturation error. The quantization error is due to representation of the sampledsignal by a fixed number of digital levels. The saturation errors occur when theanalog signal exceeds the dynamic range of A/D converter.

32.What is quantization step size?

In digital systems, the numbers are represented in binary. With b-bit binarywe can generate 2b different binary codes. Any range of analog value to berepresented in binary should be divided into 2blevels with equal increment. The 2blevels are called quantization levels and the increment in each level is calledquantization step size. If R is the range of analog signal then, Quantization step size,q = R/2b

33.

How the digital filter is affected by quantization of filter coefficients?The quantization of the filter coefficients will modify the value of poles &

zeros and so the location of poles and zeros will be shifted from the desired location.This will create deviations in the frequency response of the system. Hence theresultant filter will have a frequency response different from that of the filter withun-quantized coefficients.

34.

What is meant by product quantization error? (NOV-2012)

In digital computations, the output of multipliers i.e., the product arequantized to finite word length in order to store them in registers and to be used insubsequent calculations. The error due to the quantization of the output of multiplieris referred to as product quantization error.

35.

Why rounding is preferred for quantizing the product?

In digital system rounding due to the following desirable characteristic ofrounding performs the product quantization

The rounding error is independent of the type of arithmetic The mean value of rounding error signal is zero.

The variance of the rounding error signal is least.

36.What are limit cycles? (DEC-2012)In recursive systems when the input is zero or some nonzero constant value,

the nonlinearities die to finite precision arithmetic operations may cause periodicoscillations in the output. These oscillations are called limit cycles.


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37.What is zero input limit cycles?In recursive system, the product quantization may create periodic oscillations

in the output. These oscillations are called limit cycles. If the system output enters alimit cycles, it will continue to remain in limit cycles even when the input is madezero. Hence these limit cycles are also called zero input limit cycles.

38.What is dead band? (NOV-2006)

In a limit cycle the amplitudes of the output are confined to a range of values,which is called dead band of the filter.

39.Define noise transfer function (NTF)?The Noise Transfer Function is defined as the transfer function from the noise

source to the filter output. The NTF depends on the structure of the digital networks.

40.

How the sensitivity of frequency response to quantization of filtercoefficients is minimized? (DEC-2011)

The sensitivity of the filter frequency response to quantization of the filtercoefficients is minimized by realizing the filter having a large number of poles andzeros as an interconnection of second order sections. Hence the filter can be realizedin cascade or parallel form, in which the basic buildings blocks are first order andsecond order sections.


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UNIT - 5

APPLICATIONS

Syllabus:

Multi-rate signal processing Speech compression Adaptive filter

Musical sound processing Image enhancement.

Two mark questions:

1. What is multi-rate signal processing?The theory of processing signals at different sampling rates is called multi-

rate signal processing.

2. Define down sampling. (NOV-2012)

Down sampling a sequence x(n) by a factor M is the process of picking everyMthsample and discarding the rest.

3. What is mean by up-sampling?

Up-sampling by a factor L is the process of inserting L-1 zeros between twoconsecutive samples.

4.

If the spectrum of sequence x(n) is X(ejw), then what is the spectrum of a

signal down-sampled by factor 2?Y(ejw)=(1/2)[X(ejw/2)+ X(ejw((w/2)-)]

5.

If the Z-transform of a sequence x(n) is X(z) then what is the Z-transform of

a sequence down-sampled by a factor M?

Y(z)= (1/M) (z(1/M)e(-j2k/M))

6. If the z-transform of a sequence x(n) is X(z) then what is the z-transform of

a sequence up-sampled by a factor L? (DEC-2012)Y(z)= X(zL)

7.

What is the need for anti-imaging filter after up-sampling a signal?The frequency spectrum of up-sampled signal with a factor L, contains (L-1)

additional images of the input spectrum. Since we are not interested in image spectra,a low-pass filter with a cutoff frequency wc= (/L) can be used after up-sampler.This filter is known as anti-imaging filter.


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8. What is the need for anti-aliasing filter prior to down-sampling?The spectra obtained after down-sampling a signal by a factor M is the sum

of all uniformly shifted and stretched version of original spectrum scaled by a factor(1/M). If the original spectrum is not band limited to (/M), then down-samplingwill cause aliasing. In order to avoid aliasing the signal x(n) is to be band limited to (/M). This can be done by filtering the signal x(n) with a low pass filterwith acutoff frequency of (/M). This filter is known as anti-aliasing filter.

9. Define Sampling rate conversion. (APR-2004)Sampling rate conversion is a process of converting a signal from a given rate

to a different rate. Sampling rate conversion by a rational factor (L/M) can beachieved by first performing interpolation by the factor L and then performingdecimation by the factor M.

10.

What is multirate DSP system?The discrete time system that employs sampling rate conversion while

processing the discrete time signal is called multirate DSP system.

11.What are the various basic methods of sampling rate conversion in digital

domain? (MAY-2012)

The basic methods of sampling rate conversion are decimation (ordownsampling) and interpolation (or upsampling).

12.Give any two applications of multirate DSP system.1.

Sub-band coding of speech signals and image compression.2. Oversampling A/D and D/A converters for high quality audio systems and

digital storage systems.

13.

Write some advantages of multirate processing.

1. The reduction in number of computation.2.

The reduction in memory requirement.3. The reduction in finite word length effects.

14.

What is anti-aliasing filter? (MAY-2010)The low pass filter used at the input of decimator is called anti-aliasing filter.it

is used to limit the bandwidth of an input signal to (/D) in order to prevent thealiasing of output spectrum of decimator for decimation by D.


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15.What is an anti-imaging filter?The low pass filter used at the output of an interpolator is called anti-imaging

filter.it is used to eliminate the multiple images in the output spectrum of theinterpolator.

16.

Write a short note on sampling rate conversion by a rational factor.

When sampling rate conversion is required by a non-integer factor, thensampling rate conversion is performed by the rational factor [I/D]. In this method,the signal is first interpolated by an integer factor I, then passed through a low passfilter with bandwidth minimum of [(/I), (/D)], and finally decimated by an integerfactor, D.

17.What is poly-phase decomposition? (APR-2014)The process of dividing a filter into a number of sub-filter which differ only

in phase characteristics is called poly-phase decomposition.

18.Write a short note on multistage implementation of sampling rate

conversion.

When the sampling rate conversion factor I or D is very large then themultistage sampling rate conversion will be computationally efficient relalization.

In multistage interpolation, the interpolation by I is realized as cascade ofinterpolators with sampling rate multiplication factors I1,I2,IL,where I= I1x I2xx IL.

In multistage decimation, the decimation by D is realized as a cascade ofdecimator with sampling rate reduction factors D1, D2,.DL, where D= D1 x D2x..x DL.

19.Draw the structure of anti-aliasing filter. (NOV-2012)The structure of anti-aliasing filter is

x(n) anti-aliasing filter down sampler y(n)

v(n)

20.Draw the frequency domain representation of downsampler. (DEC-2010)

x(n) y(n) = x(Dn)

x(ejw) Y(ejw)=[1/D] x(ejw/D)

h n D

D


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21.Write the expression for output spectrum, Y(ejw) of an interpolator in

terms of input spectrum, X(ejw).

Output spectrum, Y(ejw) = X(ejwI)Where, I = integer sampling rate multiplication factor of interpolator.

22.

Write the expression for output spectrum, Y(ejw) of decimator in terms of

input spectrum, X(ejw). (APR-2010)

Output spectrum, Y(ejw) = [1/D] (()/

)

Where, D= integer sampling rate reduction factor of decimator.

23.Draw the Multirate signal processing system with analysis and synthesis

filter banks.

24.

Draw the structure of Brickwall filters.


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25.Draw the Characteristics of real filters in subband decomposition.

26.Draw the Time-frequency resolutions of a signal of length N = 8 with the

three-stage filter bank.

27.Draw the structure of M-fold decimator.

X(n) yD(n)

yD(n)= x(Mn)For an input sequence x(n), select only the samples which occur at integer

multiples of M. The other samples are thrown away.Aliasing will occur in yD(n) unless x(n) is sufficiently bandlimited loss of

information.

28.Draw the structure of L-folder expander. (DEC-2005)

For an input sequence x(n), insert L 1 zeros between each sample.x(n) can always be recovered from yE(n) no loss of information, no aliasing.

M


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X(n) yE(n)

YE(n)= x(Mn)

29.Develop an expression for the output y(n) as a function of the input x(n)

for the multirate structure of below fig. (APR-2014)

30.Determinr the computational complexity of a single stage decimator

designed to reduce the sampling rate from 60kHz to 3kHz. The decimation

filter is to be designed as in equiripple FIR filter with a passband edge at

1.25kHz, a passband ripple of 0.02, and a stopband ripple of 0.01. use the

total multiplications per second as a measure of the computational

complexity. (DEC-2012)

Answer:

L

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