UNIT IV: FINITE WORD LENGTH EFFECTS

PART-A

1. What are the errors that arise due to the quantization of numbers? The errors that arise due to the quantization of numbers

Input quantization error Product quantization error Coefficients quantization error

2. Define input quantization error.The conversion of continuous time input signal into digital value produce an error

is known as input quantization error. This error arises due to the representation of input signal by a fixed number of digits in analog to digital conversion process.

3. Define product quantization error.The product quantization error arises at the output of multiplier. Multiplication

of a b-bit data with a b-bit coefficient result a product 2b bits. Since a b-bit register is used, the multiplier output must be rounded or truncated to b-bits which produce an error.

4. Define co-efficient quantization error.The filter co-efficient are computed to infinite precision in theory. If quantized,

the frequency response of resulting filter may differ from desired response and sometimes the filter may fail to meet desired specifications. If the poles of desired filter are close to unit circle. Thus the filter with quantized co-efficient lie outside of unit circle leading to instability is called co-efficient quantization error.

5. What are the Different types of number representation?There are three forms to represent numbers in digital computers or any hardware

Fixed point representation Floating point representation Block Floating point representation

6. What are the Different ways of representing negative numbers in fixed point arithmetic?

The Different ways used to represent negative numbers in fixed point arithmetic are,

Sign magnitude form One’s complement form Two’s complement form

7. Differentiate Fixed point and Floating point arithmetic.

S.No Fixed point arithmetic Floating point arithmetic

1. It is a fast operation It is a slow operation

2. It is relatively economical It is more expensive because of costlier hardware

3. It has small dynamic range It has large dynamic range

4. Round-off errors occurs only for addition

Round-off errors occurs only for both addition and multiplication

5. Overflow occurs in addition Overflow does not arise in addition

6. It is used in small computers It is used in small computers

8. What are the two methods of quantization?The two common methods of quantization are

1. Truncation2. Rounding

9. Define Truncation.Truncation is a process of reducing magnitude of a number by discarding all bits

less significant bit(LSB) that is retained. Single value is approximated by highest quantization level that is greater than the signal.

Eg: Truncation of 8 bits results in 0.00110011 to 0.0011.10. Define Rounding.

Rounding of a number of b-bits is done by choosing the rounded result as the b-bit number closest to original number rounded. Rounding up or down has negligible effect on accuracy of computation.

Eg: The rounded value of 0.110111111 to8-bits is 0.110111111 or 0.11100000

11. What is meant truncation error?If quantization method is truncation, the number is approximated to the nearest

level that does to exceed it. If x is a number to be quantized, the truncation error is defined as xT - x, The range of error is 0 ≥ (xT-x) >-2^-b .Where, xT – truncated value of x.

12. What is meant rounding error?If quantization method is t is rounding the number is approximated to the nearest

level that does to exceed it. If x is a number to be quantized, the truncation error is defined as xT - x, The range of error is (-2^-b )/2 ≥ (xT-x) >(-2^-b)/2 . Where, xT

rounded value of x.

13. What is zero input limit cycle oscillation?When a stable IIR digital filter is excited by finite input sequence i.e., constant,

the output will ideally decay to zero. The non-linear ties due to finite precision arithmetic operations often cause periodic oscillations to occur in the output. Such oscillations in recursive system are called zero input limit cycle oscillations.

14. Define dead band band of the filter. The limit cycles occur as a result of quantization effects in multiplications. The

amplitudes of output during a limit cycle are confined to a range of values that is called the dead band of the filter.

15. What is meant by overflow oscillations?In addition to the limit cycle oscillations causing by rounding the result of

multiplication, there are several type limit cycle oscillations caused by addition which makes filter output oscillates b/w maximum and minimum amplitudes. Such limit cycle oscillation is called overflow limit cycle oscillation. An overflow in addition of two or more binary numbers occurs when the sum exceeds the word size available in digital implementation of the system.

16. What is signal scaling?Signal scaling is one of the methods used to eliminate the overflow limit cycles. It

is important to scale the input signal and the unit sample response b/w input and any internal summing node in system such that an overflow becomes a rare event.

17. What are methods to prevent overflow limit cycle?1. Saturation2. Arithmetic

18. What is an anti – aliasing filter?To avoid aliasing errors caused by undesired high frequency signal, an analog low

pass filter called anti – aliasing filter is used prior to sampler to filter high frequency components before the signal is sampled.

19. List the important finite word length effects in digital filter implementation?1. Quantization2. Limit cycle oscillations3. Overflow error4. Truncation error

20. Define Quantization and Quantization error.The process of converting continuous time signal amplitude in to discrete

amplitude levels is called as Quantization.The Difference b/w the quantized signal x q (n) and the actual amplitude x(n) is

called the quantization error e(n).

UNIT V: DIGITAL SIGNAL PROCESSORS

PART-A

1. What are the advantages of VLIW Architecture? Increased performance

Better compiler targets Containing more execution unit and more instruction set Potentially scalable, easier to program.

2. What are the advantages of VLIW Architecture? High power consumption Increased memory Misleading MIPS ratings New kind of programmer complexity

3. What are the different stages in pipelining? The fetch phase The decode phase Memory read phase Execute phase

4. What are the classifications of Digital Signal processors?i) General purpose Digital Signal processorsii) Special purpose Digital Signal processors

5. List the buses in TMS320C5X.i) Program busii) Program address busiii) Data read busiv) Data read address bus

6. What are the elements in the CPU at TMS320C5X?i) Central arithmetic logic unitii) Parallel logic unitiii) Auxiliary register arithmetic logic unitiv) Memory mapped registersv) Program controller

7. What is the function of Parallel logic unit?It is a second logic unit, which executes logic operations on data without affecting

the contents of accumulator.

8. List the various registers used in TMS320C5X. Eight auxiliary registers (AR0-AR7) Auxiliary register pointer (ARP) Unsigned 16-bit ALU.

9. What are the applications of programmable DSP’s?1. Noise cancellation2. Medical Imaging3. Satellite Communications4. Voice mail

10. List out the fixed point DSP’s.1. TMS320C502. TMS320C543. TMS320C55

4. ADSP-219X5. ADSP-219XX

11. What are the main features of Von-Neumann architecture?1. It consists of three buses such as address bus , data bus and control bus.2. CPU can be either reading an instruction or reading/writing data from/to the memory.3. Program instruction stored in ROM.

12. What are the main features of Harvard architecture?1. Separate memory and bus for their instruction and data.2. Instructions and operands fetched simultaneously.

13. List out the types of addressing modes in TMS320C50.1. Immediate addressing mode2. Indirect addressing mode3. Direct addressing mode4. Register addressing mode5. Memory mapped addressing mode6. Circular addressing mode.

14. What are the applications of TMS320C50?1. Tele Communications2. Computers3. Commercial applications.4. Industrial and military applications

15. List the features of TMS320C50. C50 has powerful instruction set and speed is high. It is a 16-bit fixed point processor. It has 32-bit arithmetic logic unit,32-bit accumulator and 16-bit Parallel

logic unit It has RAM based memory location It has Eight Auxiliary Registers

16. List out the types of instruction set in TMS320C50.1, Load/store Instructions2. Addition/Subtraction Instructions3. Move Instructions4. Multiplication Instructions5. Shift/logic Instructions6. Program control Instructions7. Norm Instructions8. Peripheral Instructions

PART – B UNIT IV

1. Consider the transfer function H (Z) = H1 (Z). H2 (Z), where H1 (Z) = 1 / (1-a1z-1) and H2 (Z) = 1 / (1-a2z-1) Find the output noise power.

2. The input to the system y (n) = 0.999(n-1) + x (n) is applied toan A/D converter. What is the power produced by the quantization noise at the output of the filter if the input is quantized to a) 8-bits b) 16-bits

3. For the given transfer function H (Z) = H1 (Z). H2 (Z), where H1 (Z) = 1 / (1-0.5 z-1) and H2 (Z) = 1 / (1- 0.4 z-1) Find the output round off noise power.

4. Explain the characteristics of a limit cycle oscillation with respect to the system described by the difference equation

Y (n) = 0.95 y (n-1) + x (n) Determine the dead band of the filter.

5. A digital system is characterized by the difference equation Y (n) = 0.9 y (n-1) + x (n)With x(n) = 0 and initial condition y(-1) = 12.Determine the dead band.

6. Compare fixed point arithmetic and Floating point arithmetic.

UNIT I: FAST FOURIER TRANSFORM

PART-A

1. Define DFT. (or) Write down the equation for forward DFTThe Discrete Fourier Transform of x (n) is given by

N-1X (k) = ∑ x (n) e^ (-j2πnk/N), k = 0 to N-1

n = 02. Define IDFT. (Or)Write down the equation for forward IDFT.

The Inverse Discrete Fourier Transform of X (k) is given byN-1

x (n) = ∑ X(k) e^(j2πnk/N) , n = 0 to N-1 k = 0

3. What is the need for FFT?The direct truncation of DFT using the formula

N-1X (k) = ∑ x (n) e^ (-j2πnk/N), k = 0 to N-1 requires N2 complex

n = 0Multiplications and N (N-1) complex additions. For large values of N, the direct evaluation requires large amount of computation. By using FFT algorithms, the number of computations can be reduced.

4. What are advantages of FFT over DFT? It reduces computation time to compute DFT It has symmetric and periodic property FFT results fast computation and save memory. Computational efficiency.

5. Define INPLACE algorithm.An algorithm which uses the same location to store both the input and output

sequences is called INPLACE algorithm.

6. What are the applications of FFT? Linear filtering Correlation Spectrum analysis Filter simulation Pattern regulation

7. What are the uses of FFT in linear filtering?1. Over lap add method2. Over save add method

8. What is the use of FFT?FFT is an algorithm used to compute the DFT with reduced number of

calculations using symmetry and periodicity properties of twiddle factor WNk. The

computational efficiency is achieved by decomposing and N-point DFT into successively smaller DFTs to increase the speed of computation.

9. Define Twiddle Factor. It is defined as, WN

k = e^ (-j2πkn/N), where N = order of filter.

10. What is radix – 2 FFT?The FFT algorithm is most efficient in calculating N – point DFT. If the number

of output points N can be expressed as a power of 2 i.e., N = 2^m, where m – integer then the algorithm is known as radix – 2 algorithm.

11. Calculate the number of complex multiplications and complex additions in the calculation of an N-point radix-2 FFT when compared to direct DFT.

In direct computation of DFT, the number of complex multiplications required is N2 and the number of complex additions N (N-1).

In FFT algorithm, the number of complex multiplications required is N/2 log 2N and the number of complex additions N log 2N .so FFT is computationally efficient than DFT.

12. Write any four properties of DFT. (AU-EXAM) Linearity Periodicity Time shifting property Convolution theorem Circular time shift

13. State Parseval’s theorem as applied to DFT. (AU-EXAM)

If x (n) = X (k) and y (n) = Y (k) then the parsevals theorem is given by N-1 N-1

∑ x (n) y*(n) = 1/N ∑ X(k) Y*(k) n = 0 n=0

This expression relates the energy in the finite duration sequence x(n) to the power in the frequency components X(k)

14. What is meant by radix-2 DIT-FFT algorithm?Decimation-in –time algorithm is used to calculate the DFT of a N-point

sequence. In this N-point sequence is divided in to two N/2- point sequences which have even and odd numbers of x(n). The N/2-point DFTs again divided into two N/4-point DFTs to get four two point DFTsand combined to get 8-point DFT15. What is meant by radix-2 DIF-FFT algorithm?16. Distinguish DIT and DIF FFT algorithm.17. Compare the DIT and DIF radix–2 FFT.18. How many multiplications and additions are required to compute N-point DFT using radix-2 FFT?19. How can we calculate IDFT using FFT algorithms?20. What is meant by Fast (sectioned) convolution?21. What are two methods which are used for the sectioned (fast) convolution?22. What is zero padding? What are its uses?23. When the sequence is called circularly even?24. What are the advantages of fast (sectioned) convolution?25. Draw the basic butterfly diagram for radix-2 DIT and radix-2 DIF.26. Why is FFT called so?27. State the computational requirements of FFT.28. State the shifting property of the DFT.29. Find N-point DFT for x(n) = a ^ n for 0<a<1

30. The first five DFT coefficients of a real valued sequence of length 8 is 2, 3+2j, 1-6j, 4, -3 & determine the remaining DFT coefficients.

31. Define FFT (Fast Fourier Transform).

FFT is an algorithm hat efficiently computes the discrete Fourier transform (DFT).The DFT of a sequence x (n) of length is given by

N-1X (k) = ∑ x (n) e^ (-j2πnk/N), k = 0 to N-1

n = 032. Name the properties of Twiddle Factor (WN

k) and define.

1) Symmetry property is given byWN

k+ N / 2 = - WN k

2) Periodicity property is given byWN

k+N = - WN k

PART-B

1. Suppose we have two 4-point sequences x (n) and h (n) as follows

x (n) = cos (nπ /2), n = 0,1,2,3h (n) = 2^n, n = 0,1,2,3

Compute the response y(n) by doing circular convolution of x(n) and h(n) (12)

2. Compute 4-point IDFT of X (k) = 0, 4j, 0, -4j by using decimation in frequency fast Fourier transformation (6)

3. Compute the 8-point DFT of the sequence x(n) = 1, 1, 1, 1, 1, 1, 1, 1 by using decimation in time FFT algorithm. (6)

4. From the first principle derive the decimation in frequency FFT algorithm (6)

5. Compute the FFT sequence x (n) = n+1 where N=8 using DIT algorithm. (6)

6. State and prove the following properties of DFT (12)(a) Circular frequency shifting property(b) Complex conjugate property(c) Circular convolution property

7. Develop the algorithm for radix-2, 8-point decimation in frequency FFT method.(12)

8. Find the output y (n) of a filter whose impulse response is h(n) = 1, 1, 1 and input signal x(n) = 3, -1, 0, 1, 3, 2, 0, 1, 2, 1using over lap add and overlap save method. (12)

9. An LTI system has the input x(n) = 1, 1, 1 and the impulse response h (n) = -1, -1.Determine the response of LTI system by radix-2 DIT FFT. (12)

10. a) Determine the DFT of the sequences x(n) = 1/4 , 0<= n <= 2 (4) b) Find IDFT of the sequence

X (k) = 5, 0, 1-j, 0, 1, 0, 1+j, 0 (8)

11. Compute the FFT sequence x (n) = n2+1 where N=8 using DIT algorithm

12. Compute the DFT of the sequence x(n) = an , where N= 8 and a = 3.

13. Compute the 8-point DFT of the sequence x(n) = 0, 1, 2, 3, 0, 0, 0, 0

UNIT-IIFINITE IMPULSE RESPONSE DIGITAL FILTERS

PART – A

1. Define FIR filters.

If the duration of impulse sequence h (n) is finite, then it is called as FIR filter. FIR filter is non – recursive filter output depends only on present input value.

2. What are the properties of FIR Digital filter?

It is linear phase filter Stable filter Non-recursive type realization. They can be realized efficiently in hardware.

3. Define Window.It is defined as, w (n) = w (-n), for – ((N-1) / 2) ≤ n ≤ ((N-1) / 2).

It is used to convert Infinite Impulse Response in to Finite Impulse Response.

4. What are types of Windows?

Rectangular window Hamming window Hanning window Kaiser window Raised cosine window

5. What is Gibb’s phenomenon?In the design of FIR filter the Infinite duration impulse response is truncated in to

Finite duration impulse response. T he abrupt truncation introduced oscillations in pass band and stop band. This effect is known as Gibb’s oscillations or Gibb’s phenomenon.

6. What are the designing methods of FIR filters? Fourier series method Windowing method Frequency sampling method

7. Define Hamming window

W hm (n) = 0.54 – 0.46 COS (2π n/(M-1)) , – ((N-1) / 2) ≤ n ≤ ((N-1) / 2)

0 , otherwise

8. Define Hanning window

W hn (n) = 0.5 – 0.5 COS (2π n/(M-1)) , – ((N-1) / 2) ≤ n ≤ ((N-1) / 2)

0 , otherwise

9. Define Phase and Group delay.Phase delay is defined as, τp = θ (ω) / ωGroup delay is defined as, τg = d θ (ω) / d ω

10. Give the expression for transfer function of linear phase filter.The transfer function of FIR filter is given by

N-1H (z) = ∑ h (n) z^-1

n = 0

11. Write the condition for FIR filter. The conditions are, i) Symmetric impulse response h(n) = h (N-1-n)

ii) Anti - Symmetric impulse response h (n) = - h (N-1-n)

12. What are the types of Realization in FIR?

Direct form realization Parallel form realization Cascade form realization Linear phase realization

13. What are the characteristics of Window?

1. The central lobe of frequency response is to be having highest energy and should be a narrow.2. The first higher side lobe should be high. When compared to other side lobes.3. The side lobes should be decreased as the frequency increases.

14. What are the basic building blocks of FIR structure?

(a) Adder(b) Multiplier(c) Unit delay element.

15. Draw the frequency response of Window sequence.

UNIT-II INFINITE IMPULSE RESPONSE DIGITAL FILTERS

PART – A

1. Define IIR filters.If the duration of impulse sequence h (n) is infinite, then it is called as IIR filter.

IIR filter is recursive filter output depends present and past input output values.

2. What are types of filters based on impulse response?

1. Infinite impulse response (IIR)2. Finite impulse response (FIR)

3. What are different types of filters based on impulse response?1. Low pass filter2. High pass filter3. Band pass filter4. Band stop filter

4. What are types of analog low pass filter design?1. Butterworth filter design2. Chebyshev filter design

5. Distinguish between Butterworth filter and Chebyshev filter design.

S.No Butterworth filter design Chebyshev filter design

1. The magnitude response of BW filters decreases monotonically as the frequency increases from 0 to infinity.

The magnitude response of Chebyshev filter exhibits ripple in pass band monotonically decreasing in stop band

2. Transition band is more Transition band is less

3. The poles lies on unit circle The poles lies on ellipse

6. What are types of digital filter design techniques?1. Approximation of derivatives2. Bilinear Transformation3. Impulse Invariant method4. Matched z- transforms

7. What is Bilinear Transformation? I t is conformal mapping that maps s-plane in to z- plane by substituting S = 2/T [(1-z -1) / (1+ z-1)] , where T = sampling rate

8. State the advantages of Bilinear Transformation.1. No aliasing2. Provides one to one mapping.

9. What is meant aliasing effect?Impulse invariant method provides many to one mapping i.e., all the poles present

in the s-plane mapped in to the same location which produces aliasing effect.

10. Specify the types of realization in IIR.

Direct form – I realization Direct form – II realization Cascade form Parallel form Transposed form

11. Define warping effect. Let the relationship between analog and digital filter frequency is given by

Ω = 2/T tan (ω/2) at low freq. the relationship between analog filter frequency (Ω) and digital filter frequency (ω) is linear. At high frequency, distortion is introduced which gives non-linear characteristics. This effect is known as warping effect.

12. Draw the magnitude response of Butterworth low pass filter.

13. Draw the magnitude response of Chebyshev low pass filter.

VIDYAA VIKAS COLLEGE OF ENGINEERING AND TECHNOLOGY, Department of ECE

NAME LIST

CLASS: II ECE –A

S.No ROLL.NONAME OF THE

STUDENTH/D PHONE NUMBERS

1. 10EC01 ABINAYA.C H 9940416793 98426291952. 10EC02 AKILA.A H 94429880703. 10EC03 AKILAN.J H 9698055759

4. 10EC04 AMMU.G H 97864348325. 10EC05 ANSHIFA.J.A H 0496-2695162 094466456136. 10EC06 ANUSUYA.P H 90038582047. 10EC07 ARUL MULLAI.G.V H 94421797398. 10EC08 ARUN.E D 99650381229. 10EC09 BALAJI.P H 999428104610. 10EC10 BHARATHI.T H 9442903643 975023876911. 10EC11 BHUVANESWARAN.N D 975020636912. 10EC12 DEEPA LAKSHMI.L D 965953091513. 10EC13 DINESH.N H 909227207314. 10EC14 ELAKKIYA.S.M H 9843788533 978651746515. 10EC15 ELAMATHI.P D 9942075391 909577672716. 10EC16 GOVIND ARUN.K H 944320726317. 10EC17 INDUMATHI.D H 9944674530 967755029018. 10EC18 INDUMATHI.R H 04367-265244 944358897519. 10EC19 JAYAPRASANTH.C H 8122353776 948743058920. 10EC20 JOTHI MANI.M H 9150471940 962654906921. 10EC21 KALAI SELVAN.K.V H 9788311459 965922219822. 10EC22 KIRUTHIKARAGAVI.E H 0431-2582694 979018353423. 10EC23 KRISHNAPRABHU.T H 950084609624. 10EC24 LALITHA.S D 04288-240096 994215849925. 10EC25 MANIKANDAN.P H 880722859526. 10EC26 MANIKANDAN.T D 952421565727. 10EC27 MANO.R H 996539047928. 10EC28 MEIYALAGAN.P D 965958519829. 10EC29 MEKALA.V D 944320191530. 10EC30 MURALIDHARAN.V H 995279603631. 10EC31 NANDHINI.S(5/6/1991) H 944257402732. 10EC32 NANDHINI.S(8/8/1992) D 9597107637 995213277033. 10EC33 NANDHINI.S(20/8/1993) H 909574769434. 10EC34 NAVIN.M H 934590776735. 10EC35 NEETHU.A.K H 0496-2527592 0808687554136. 10EC36 NIRANJANA.A H 994705425 978973679137. 10EC37 NITHYAKALYANI.T D 994257689738. 10EC38 NITHYA.S D 9787703681 944368710039. 10EC39 NOWSATHALI.H H 978955700240. 10EC40 PAVITHRA.S H 0422-2322889 994283328241. 10EC41 PRABHAVATHI. V H 9842187829 909505963342. 10EC42 PRADEEP RAJA.B D 999409476943. 10EC43 PRAWINKARTHIK.K H 9150058939

VIDYAA VIKAS COLLEGE OF ENGINEERING AND TECHNOLOGY, Department of ECE

NAME LIST

CLASS: II ECE –B

S.No ROLL.NONAME OF THE

STUDENTH/D PHONE NUMBERS

1. SHAIMAHARAJA.A 9442894546 04292-2226322. VIJAY.G 96779810663. SRIRAM.K 9486582288 9442383857

4. SREEHARIVIGNESH.B 94430032835. SURESHKUMAR.S 9443096981 04172-2473166. SANKAR.N 99439279797. SUBASH.R 9025464096 04288-2359118. RAMESH.K 91713095859. SHANMUGAPRIYA.V 996526322710. VIJAY BALAJI.V 994262142311. SASIKUMAR.S 965921912712. RAMESH.S 984268901113. RAJASEKARAN.S 984206977614. SUBHASH.L 814868651015. SENTHILKUMAR.V 965586909416. VENGADACHALAM.P 978800498517. VINOTHKUMAR.V 944383347318. SRIJEEVITHA 984275148319. SOUMYASHREE 9788906017 975072326420. VINOBA.R 962613916221. SURYA.K 994336680022. SOWNDARYA.K 986111005623. PUNITHA.B 984274742424. SAVITHA 984349353025. VIDYA.K 965503899726. SUGANYA.S 994362397627. SELVASOUNDRIYA.S 975035947228. SUGANYA.R 94433232629. SHANMUGAPRIYA.M 958505929830. VINOTHINI.M 944342541631. SELVAPRIYA 978681650932. RENUGA 958514075033. PRIYANKA.L 948856275934. RABIA ANJUM35. SUNDARA BHARATHI