ST.ANNE’S COLLEGE OF ENGINEERING AND TECHNOLOGY

DEPARTMENT OF ECEQUESTION BANK

Sub Code : EC2302Subject : Digital signal Processing Faculty :R.RADHAKRISHNANDegree/Branch:B.E / ECEYear/semester/Section: III / V

PART-A

UNIT I 1. Distinguish between DFT and DTFT. (NOV 2011)2. What is zero padding? What are it’s uses? (NOV 2011)3. State the advantage of FFT over DFTs. (MAY 2011)4. What is meant by bit reversal? (MAY 2011)5. What is radix 2 FFT algorithm? (nov/dec 2009)

6. What is the relationship between z transform and DFT?(nov/dec 2009)7. What are the differences and similarities between DIF and DIT algorithms?

(May 2009)8. What are the applications of FFT algorithms? (May 2009)9. If H(k) is the N-point DFT of a sequence h(n),Prov that H(k) and H(N-K) are

comlex conjugates. (Nov2008)10. What are the differences and similarities between DIF and DIT algorithms?

(Nov2008)11. Define the properties of convolution. (Apr 2008,Nov 2005)12. Draw the basic butterfly diagram of radix-2 FFT. (Apr 2005, May 2007 & Apr

2008)13. State and prove parseval’s relation for DFT. (Nov 2007)14. What are the advantages of FFT algorithm over direct computation of DFT?

(May 2007)15. the first five DFT coefficients of a sequence x(n) are x(0) = 20, x(1) = 5+j2,

x(2) = 0, x(3)=0.2+j0.4, X(4) = 0. Determine the remaining DFT coefficients. (May 2007)

16. Define symmetric and Anti symmetric signals. How do you prevent aliasing while sampling a CT signal? (May 2007)

17. What is the necessary and sufficient condition on the impulse response for stability? (May 2007)

18. Define Complex Conjugate of DFT property. (May 2007)19. What do you mean by the term “bit reversal” as applied to FFT?20. Determine the DTFT of a sequence x(n) = an u(n). (Nov 2006)21. What is FFT? (Nov 2006)22. State sampling theorem? (Nov 2006)23. What is BIBO Stability? What is necessary and sufficient condition for BIBO

stability? (May 2006, Nov 2004)24. How will you perform linear convolution via circular convolution?

(May 2006)25. How many multiplications and additions are required to compute N-point DFT

using radix-2 FFT?26. What is decimation-in-time algorithm?27. What is decimation-in-frequency algorithm?28. Derive the necessary and sufficient condition for an LTI system to be BIBO

stable. (Apr 2005)29. Define DTFT pair? (Apr 2004 & May 2007)30. What is aliasing? (Nov 2003)31. Test the following systems for time variance.32. Give any two properties of DFT.33. Explain Linearity property of DFT.

UNIT –II1. List the properties of chebyshev filter. (NOV 2011)2. Draw the direct form structure of IIR filter. (NOV 2011)3. Why do we go for analog approximation to design a digital filter? (MAY 2011)4. Give any two properties of chebyshev filters. (MAY 2011)

5. Find the digital transfer function H(z) by using impulse invariant method for the analog transfer function H(s) = 1/ (s+2). Assume T=0.1 sec. (Nov 2007)

6. State the condition for a digital filter to be causal and stable. (May 2007)

7. Find the digital transfer function H (z) by using impulse invariant method for the analog transfer function H(s) = 1/(S+2). Assume T=0.5sec.

8. Give any two properties of Butterworth filter and chebyshev filter. (Nov/Dec 2006, May/June 2006, Apr 2005 & Nov 2004)

9. Mention any two procedures for digitizing the transfer function of an analog filter. (Nov 2006)

10. what are the parameters that can be obtained from the chebyshev filter specification? (Nov 2006/May 2007)

11. Give the equation for the order N, major, minor and axis of an ellipse in case of chebyshev filter. (Nov 2005)

12. What are the advantages and disadvantages of bilinear transformation? (May 2006)

13. Define Hanning and Blackman window functions. (May 2006)14. Write the magnitude function of Butterworth filter. What is the effect of varying order of

N on magnitude and phase response? (Nov 2005)15. What is impulse invariant mapping? What is its limitation? (Apr/May 2005)16. What is linear phase? What is the condition to be satisfied by the impulse response in

order to have a linear phase? (Apr 2005 & Nov 2003)17. What is frequency warping? (Nov2004 & May 2007)18. What are the limitations of impulse invariant mapping technique? (Apr2004)19. Give the transform relation for converting low pass to band pass in digital domain.

(Apr 2004)20. Give the bilinear transformation. (Nov2003)

UNIT – III

1) What are the desirable characteristics of window? (NOV 2011)2) What are the properties of IIR filter? (NOV 2011)3) State the properties of FIR filters (MAY 2011)4) What is meant by Gibbs phenomenon? (MAY 2011)5) List the non-parametric methods for power spectral estimation.

6) What is the need for spectrum estimation? (nov/dec 2009)7) When the power density spectrum of a random process is an even function?

i. (May 2009)8) What are the differences between Barlett’s and the Welch method of power

spectrum estimation? (May 2009)9) What are the properties of FIR filters?

(nov/dec2009)10) State the limitations of impulse invariance mapping technique.(nov/dec2009)

11) What is wraping effect? What is its effect on magnitude and phase response? (May 2009)

12) What condition on the FIR sequence h(n) is to be imposed in order that this filter can be called a linear phase filter? (May 2009)

13) Show that the filter with h (n) = [-1, 0, 1] is a linear phase filter.ii. (Nov 2008,May 2007)

14) What is prewarping? (Nov 2003,2008)15) What are the merits and demerits of FIR filters? (Nov 2005 & April 2008)16) What is the relation between analog and digital frequency in impulse invariant

transformation? (Apr 2008)

17) In the design of FIR digital filters, how is Kaiser Window different from other windows? (Nov 2007)

18) Compare FIR and IIR filters. (May 2007)19) What is the condition satisfied by linear phase FIR filter? (Nov/Dec 2003 &

May 2007)20) Obtain the block diagram representation of a FIR System. (Nov 2006)21) What are the desirable and undesirable features of FIR Filters? (May2006)22) Mention the necessary and sufficient condition for linear phase characteristics in

FIR filter. (Nov 2005)23) List the characteristics of FIR filters designed using window functions.(Nov

2004)24) Give the Kaiser Window function. (Apr 2004)25) What are the steps involved in Bartlett method?26) What are the steps involved in Welch method?27) Define Blackman and turkey method?28) Determine the frequency resolution of the bartlett method of power spectrum

estimates for a quality factor Q=15. Assume that the length of the sample sequence is 1500. (Apr 2008)

29) Define the terms autocorrelation sequence and power spectral density iii. (Apr 2007)

30) Define power spectral density and cross spectral density. iv. (May2007)

UNIT –IV1. What is overflow oscillations? (NOV 2011)2. What are the advantages of floating point arithematic? (NOV 2011)3. What is meant by fixed point arithmetic? Give example (MAY 2011)4. Explain the meaning of limit cycle oscillation (MAY 2011)

5. Compare the fixed point and floating-point arithmetic. (May 2009)6. How would you relate the steady-state noise power due to quantization to the ‘b’ bits

representing the binary sequence? (May 2009)7. Define zero input cycle oscilation. (nov/dec 2009)8. What is called dead band? (nov/dec 2009)9. Express the fraction (-9/32) in sign magnitude, 2’s complement notations using 6

bits . (Nov 2008)10. What are the various factors which degrade the performance of digital filter

implementation when finite word length is used? (Nov 2008)11. What are the three types of quantization error occurred in digital systems?

( Nov 2006 & Apr 2008)12. What is meant by limit cycle oscillations?

(May 2006,Apr 2005 May 2007, Nov 2007 & Apr 2008,2010)13. Express the fraction (-7/32) in signed magnitude and two’s complement notations

using 6 bits. (Nov 2007)14. Define Sampling rate conversion. (May 2007)15. Convert the number 0.21 into equivalent 6-bit fixed point number. (May 2007)16. Why rounding is preferred to truncation in realizing digital filter? (May2007)17. Express the fraction 7/8 and -7/8 in sign magnitude, 2’s complement and 1’s

complement. (Nov 2006)18. What are the different quantization methods? (Nov 2006)19. What is zero padding? Does zero padding improve the frequency resolution in the

spectral estimate? (Nov 2006)20. List the advantages of floating point arithmetic. (Nov 2006)21. Give the expression for signal to quantization noise ratio and calculate the

improvement with an increase of 2 bits to the existing bit (Nov2006,Nov2005)22. Draw the probability density function for rounding. (Nov 2005)23. Compare fixed point and floating point representations. (May/Jun 2006)24. What is dead band? (Nov 2004)25. How can overflow limit cycles be eliminated? (Nov 2004)26. What is zero input limit cycle oscillation? (Apr 2004)27. What is steady state noise power at the output of an LTI system due to the

quantization at the input to L bits? (Nov 2003 &Apr 2004)28. What is meant by finite word length effects in digital filters? (Nov 2003)29. What is round-off noise error?30. What is meant by fixed point arithmetic? Give example?31. What is round – off noise error?

UNIT – V1. What is multirate signal processing? (NOV 2011)

2. What is meant by down sampling and up sampling? (NOV 2011)3. State the various applications of DSP (MAY 2011)

4. What is echo cancellation? (MAY 2011)5. What is the need for multirate signal processing ?

6. Give some examples of multirate digital systems.7. Explain the interpolation process with an example.8. Explain the decimation process with an example.9. Write the input –output relationship for a decimation processing a factor of five.1) With an example explain the sampling process.2) What is meant by aliasing ?3) How aliasing can be avoided?4) 9 .Explain polyphase decomposition process.5) How can sampling rule be converted by a rational factor M/L ?6) Draw the block diagram of a multistage decimator and integrator.7) What are the characteristics of a comb filter?8) What is the need of multistage filter implementation?9) What are the drawbacks in multistage implementation?10) What are nyquist filters?11) Give the i/p-o/p relationship of Lth band filter.12) What are quadrature mirror filter banks?13) What are the errors in quadrature mirror filter banks?14) Design a five channel filter bank.15) What are multilevel filter bank?16) What are uniform DFT filter banks?17) Give polyphase implementation of uniform filter banks?18) What is signal flow graph?

PART – B

UNIT – I

1. (i) dertermine the N-point DFT of the following sequences. (6)x(n)=δ nx(n)= δ(n-n0)

(ii) compute 8-point DFT of the sequence (10)x(n)={0,1,2,3,4,5,6,7} using radix-2 dif algorithm

2. Compute the linear convolution of finite duration sequences h(n)={1,2} and x(n)={1,2,-1,2,3,-2,-3,-1,1,1,2,-1} by over lap add method. (16)

2. (a).With appropriate diagrams describe Overlap-save method (8)

Overlap-add method (8)

(b), Explain Radix-2 DIF-FFT algorithm. Compare it with DIT-FFT algorithms (16)

3. (i) consider the finite length sequence x(n)={1,2,2,1,0}. The five point DFT of x(n) is denoted by X(k). Plot the sequence whose DFT is Y(k)=e-4πk/5X(k).

(ii) Show that with x(n) as an N-point sequence and X(k) as its N-point DFT Σ|x(n)|2 = 1/N Σ|X(k)|2 (summation limit 0 to N-1). (May 2009)

4. (i) Suppose you have a number of eight-point FFT chips. Suggest a scheme to interconnect four chips to compute a 32-point DFT.

5. compute the eight point DFT of the sequence x(n) = {0.5, 0.5, 0.5, 0.5, 0, 0, 0, 0} using the inplace radix-2 DIT algorithm. (May 2009)

(i) discribe the following properties of DFT.(1) convolution(2) time reversal(3) time shift

(4) periodicity (ii) compare the computational complexity of direct of direct DFT

computation of a sequence with n=64 (nov/dec 2009)6. (i) explain decimation in time FFT algorithm for N=8 .

(ii) determine the 4 point DFT of x(n)={0,1,2,3} . (nov/dec 2009)

7. (a) Two finite duration sequences are given by (Nov 2008)(iii) x(n)=cos(n π/2) for n=0,1,2,3

0 , elsewhere(iv) h(n)=(0.5)n for n=0,1,2,3

0 , elsewhereiii. Calculate the 4 point DFT X(k)iv. Calculate the 4 point DFT H(k)v. If Y(k)=X(k)H(k),determine y(n),the inverse DFT of Y(k)

8. (a) Obtain an 8-point DIT FFT flow graph from first principles.(May 2007,Nov 2008)

(b) Using the above flow graph compute DFT of x(n) = cosn π/4 for n=0,1,…,7(Nov 2008)

9. (a) Discuss in detail the important properties of the Discrete Fourier Transformb) find the 4 point DFT of the sequence x(n) = Cos nπ/4 (Apr 2008)

10. Compute an 8 point DFT using DIF FFT radix 2 algorithm X(n) = {1,2,3,4,4,3,2,1}(May 2006 & Apr 2008)

11. (a) Obtain an 8-point DIF FFT flow graph from first principles. (v) (b) Using the above flow graph compute DFT of x(n) = cosn π/4 for

n=0,1,…,7 (Nov 2007,April 2008)

12. Two finite duration sequences are given by X(n) = sin(n π/2 for n=0.1.2.3 and h(n) =2n for n=0,1,2,3 find circular convolution using DFT method.

(Nov 2007)

13. calculate the DFT of the sequence x(n) = [ 1,1,-2,-2]

14. (i)How do you linear Filtering by FFT using save-add method?(ii)State and prove parseval’s theorem for discrete – time Fourier Transform.

(May 2006)15. Determine the response of LTI system by radix – 2 DIT FFT.16. Find the 8 point DFT of the sequence x(n) = [1,2,3,4,4,3,2,1] using decimation-in-

time radix -2 FFT algorithm. (May 2006)17. (i). finite duration sequence of length L is given as

X (n) = 1 for o≤n≤L-1 (May2007)0 for otherwise,

16.(i) Determine the N point DFT of the sequence for N=L. (ii) Perform the circular convolution of the following two sequences.

i. X1(n) = {2 1 2 1}ii. X2(n) = {1 2 3 4} (May 2007)

18. Draw the butterfly diagram using 8 point DIT – FFT for the following sequences.(i) X(n) = { 1,0,0,0,0,0,0,0}

(May2007)(ii) Compute the DFT of each of the following

1. x(n) = δ(n-n0)2. y(n) = x1(n) x2(n) (May 2007)

19. A DFT program is available, how will you this to compute inverse DFT. (May 2007)

20. Two real signals of x(n) and y(n) are of length M. find the FT of x(n) and y(n) with minimum computation. (May2007)

20.Compute the DFT of the sequence,x(n)={1,0,1,0,1,0,1,0} and hence find X(2). (APR 2005 CS)

21.Draw the FFT flowchart for radix –2,DIT algorithm. Assume N=8.(APR 2005 CS) 22. Find the 8 pt DFT of the sequence (APR 2005 IT)

x(n)={ 1 0<n<7 0 otherwise (using DIT FFT )

23. Compute the 8 pt DFT of the sequence (NOV 04 IT)x(n)={0.5,0.5,0.5,0.5,0,0,0,0} using DIT FFT

24. Determine the 8 pt DFT of the sequence (APR 04 IT)x(n)={0,0,1,1,1,0,0,0}

25.What is DIF algorithm. Write the similarities and differences between DIT and DIF. ( APR 04 IT)

26.Determine 8pt DFT of x(n)=1 for –3<n<3 using DIT-FFT algorithm. (APR 04 IT)

1. Obtain the 8pt DIT FFT algorithm 2. Obtain the 8pt DIF FFT algorithm x(n)={2,2,2,2,1,1,1,1} (NOV 04 EC)3. Obtain the 8 pt DIF FFT algorithm x(n)={0,1,2,3,,4,5,6,7} (APR 05 EC)

UNIT – II

1) (a) design a butterworth filter using impulse invariance method satisfying the constraints. Assume T=1sec.0.8 ≤|H(ejw)| ≤ 1 ; 0 ≤ w ≤0.2∏|H(ejw)| ≤0.2 ; 0.6∏ ≤ w ≤ ∏ (16) (b)obtain the direct form I ,direct form II and cascade form realization of the following system functions.y(n)=0.1 y(n-1)+0.2 y(n-2)+3x(n)+3.6x(n-1)+0.6x(n-2) (16)

2. (a) Explain in detail Butterworth filter approximation.(16)

(b) Explain the bilinear transform method of IR filter design. What is warping effect? Explain the poles and zeros mapping procedure clearly. (16)

3..Design a digital Butterworth filter that satisfies a. the following constraint using bilinear transformation. b. Assume T=0.1 sec. (NOV 08)c. 0.8 < |H(ejω)|< 1 , 0 < |ω| < 0.2d. |H(ejω)| < 0.2 , 0.6 < |ω| <

4. For the analog transfer function H(s) = 1/ (S+1) (S+2) determine H(z) using impulse invariant technique. Assume T=1sec. (Apr 2008)

5.Design a digital butterworth filter that satisfies the following constraint using bilinear transformation ( T = 1 Sec)

i. 0.9≤|H (ejω)| ≤1 for 0≤ω≤π/2ii. |H (ejω)| ≤0.2 for 3π/4≤ ω≤ π (Apr 2008)

6. Design a digital butterworth filter satisfying the following specifications e. 0.7≤|H (ejω)| ≤1 for 0≤ω≤0.2π

i. |H (ejω)| ≤0.004, for 0.6π≤ ω≤ π Assume T=1 sec. Apply impulse invariant transformation (Nov 2007)

7.Design a digital Butterworth filter satisfying the constraints0.707≤|H (ejω)| ≤1 for 0≤ω≤π/2|H (ejω)| ≤0.2 for 3π/4≤ ω≤ π with T=1 sec using Bilinear Transformation.

Realize the filter in each case using the most convenient realization form. (May 2007)

8 .Design a Chebyshev filter with a maximum pass band attenuation of 2.5 dB; at Ώ p = 20 rad/sec and the stop band attenuation of 30 dB at ΏS = 50 rad/sec.(May 2007)9.Realize the system given by difference equation (May 2007)

y (n) = -0.1 y(n-1) + 0.72y(n-2) + 0.7x(n) – 0.25 2x(n-2) in parallel form10. Using the Bilinear transform design a high pass filter, monotonic in Pass band with cutt off frequency of 1000Hz and down 10dB at 350Hz.The sampling frequency is 5000Hz (NOV05EC)11. An analog filter has a transfer function.

H(s) = 10/ s2+7s+10

12. Using impulse invariant method converts to digital filter. (NOV04 IT) Using bilinear transformation convert to z domain at T=1sec.

(NOV03IT) H(s)= 1/(s+1)(s+2)

13. Using impulse invariant mapping technique converts the following Analog transfer function to digital assume T=0.1sec (NOV 04 EC)H(s) = 2/(s+1)(s+2)

UNIT III1) (a)Design an ideal differentiator with frequency response,

H(ejw)=jw ; -∏≤w≤∏ Using hamming window with N=8. (16)

(b) deisgn an ideal high pass filter using hanning window with a frequency response Hd(ejw) = 1; ∏/4 ≤|w|∏ = 0; |w|≤∏ /4 . Assume N=11. (16)

2 (a) Realise the system function H(z)=[ ]z+1+[ ] by linear phase FIR structure.

(16)

(b) Explain the designing of FIR filters using windows(16)

3.(i) describe the frequency sampling method of designing FIR filters.

(ii) derive thee condition for linear phase FIR filters. (nov/dec 2009)

4. The desired response ff a low pass filter is

Hd(ejw)= e-j3w - 3π/4 < ω < 3π/4

= 0 3π/4 < |ω| < πa. Design the filterfor m=7 using hamming window.b. (ii) using impulse invariant mapping convert the analog transfer function in

to digitalc. Assume T=1sec.d. H(s)=2/(s+1)(s+2) e. Find the frequency response of linear phase FIR filter with symmetric

impulse response and N-odd. (nov/dec 2009)5. Design a FIR filter approximating the ideal frequency response: a.Hd(ejw) = e-jw for |ω| < π/6. Hd(ejw) = 0, for /6 < |ω| < .

b.Determine the filter coefficients for N=13. (May 2009)c.Show that a stable analog filter is mapped to a stable digital filter using bilinear transform.

6. a.An analog filter has a transfer function

b.H(s) = 10/(S2+7s+10). Design a digital filter equivalent to this using impulse invariant method for T=0.2 sec. (May 2009)

7.A band reject filter of length 7 is required. It is to have lower and upper cutoff frequencies of 3 KHz and 5 KHz resp. The sampling frequency is 20Khz. Determine the filter coefficients using Hanning window. Assume the filter to be causal.

(NOV 08)8.Determine the magnitude response of an FIR filter (M=11) and show the phase and group delays are constant H(z) = h(n) z-n (Apr 2008)

9. If the desired response of a low-pass filter is (Apr 2008)a. Hd

(ejω)= e-j3ω, -3π/4 ≤ w ≤ 3π/40, 3π/4 < |ω| < π

Determine H(ejω)=for M=7 using a Hamming Window.10. The desired frequency response of a low pass filter is given by

Hd (ejω)= e-j2ω, -π/4 ≤ w ≤ π/4

0, π/4 < |ω| < π11. Determine the filter coefficients hd(n). obtain the coefficients h(n) of FIR filter using a rectangular window defined by

w(n) = 1, 0 ≤ n ≤ 40, otherwise (Nov 2007)

12.An FIR filter is given by the difference equation y(n) = 2x(n) + 4/5x(n-1)+3/2x(n-2)+2/3x(n-3) determine its lattice form.

(May 2007)13 .Using a rectangular window technique design a low pass filter with pass band gain of unity, cut off frequency of 1000 Hz and working at a sampling frequency of 5 KHz. The length of the impulse response should be 7. (May 2007)14. Design an ideal Hilbert transformer having frequency response (May 2007)

H (ejω) = j for -π ≤ω ≤0= -j for 0 ≤ω ≤π using

a. rectangular windowb. black man window For N=11 plot the frequency response in both cases.

15. Describe the design of FIR filters using frequency sampling technique.16.Derive the frequency response of a linear phase FIR filter with symmetric impulse Response. (NOV 04EC)17. Explain in detail about frequency sampling method of designing an FIR filter.

(NOV 04 IT)18.What are the issues in designing FIR filter using window method. (APR 04 IT)19(i) Mention the advantages and disadvantages of FIR and IIR filters. (APR 04IT)

(ii).State the merits and demerits of FIR filter. (NOV 03 IT)

UNIT – IV

1.(a)With respect to finite word length effects in digital filters, with examples discuss about(i) Over flow limit cycle oscillation (10)

Signal scaling (6)

(b) (i) distinguish between fixed point and floating point arithematic . (6) (ii) consider a second order iir filter with

H(z)=( 1.0)/(1-0.5z-1)(1-0.45z-1)2. Find the effect on quantization on pole locations of the given system function in direct

form and in cascade form .Assume b=3 bits. (10)

(a) Explain the quantization process and errors introduced due to quantization.(16)

(b). i) Explain how reduction of product round-off error is achieved in digital filters.(8)

ii) Explain the effects of coefficient quantization in FIR filters.(8)

3. (i) Draw the quantization noise model of second order system H(z)=1/1-2r cos 0 z-1 +r2 z -2 and find the steady state output noise varience. (ii) what are called over flow oscillations? How can it be prevented? (nov/dec 2009)

4. (i) describe the effect of quantization on pole location with an example(ii) explain the characteristics of a limit cycle oscillation with respect to system described by the difference equation. Y(n)=0.95y(n-1)+x(n) (iii)Determine the dead band of the filter. (nov/dec 2009)

3. (i) Realize the first order transfer function H(z)=1/(1-az-1) and draw its quantization model. Find the steady state noise power due to product round off. (ii) Explain in detail about the zero-input limit cycle oscillations due to finite word length of registers. (May 2009) 4.(i) What is the need of signal scaling? How the scaling is performed?

(ii) for a second order digital filter H(z)=1/(1-2rcosθz-1+r2z-2); |r| <1.0. Draw the direct form II realization and find the scale factor S0 to avoid overflow. (May 2009)

5.(i)Consider (b+1)-bit (including sign bit) biplar ADC. Obtain an expression for signal to quantization noise ratio.State the assumptions made. (Nov 2008)

(ii)Consider the truncation of negative fraction numbers represented in (β+1) – bit fixed point binary form including sign bit. Let (β-b) bits be truncated. Obtain the range of truncation errors for signed magnitude. 2’s complement and 1’s complement representations of the negative numbers. (Nov 2007,Nov 2008)

6.(i)The coefficients fo a system defined by H(z) = 1 (1-0.3z -1) (1-0.65z-1) are represented in a number system with a sign bit and 3 data bits using signed magnitude representation and truncation. Determine the new pole locations for direct realization and for cascade realization of first order systems. (Nov 2008) (ii)An IIIR causal filter is defined by the difference equation y(n) = x(n)-0.96y(n).The unit sample response h(n) is computed such that the computed values are rounded to one decimal place. Show that under these stated conditions, the filter output exhibits dead band effect. What is the dead band range? (Nov 2008)

6. Discuss in detail the truncation error and Round-off error for sign magnitude and two’s complement representation. (Apr 2008)

7. Explain the quantization effects in converting analog signal into digital signal. (Apr 2008)

8. (a) A digital system is characterized by the difference equation Y(n) = 0.9y(n-1)+x(n) with x(n) = 0 and initial condition Y(-1) = 12. Determine the dead band of the system.Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ.16)(b) what is meant by the co-eefficient quantization? Explain. (Apr 2008)

9. An 8-bit ADC feeds a DSP system characterized by the following trnafer function H(z) = 1/(z+0.5) estimate the steady state quantization noise power at the output of the system. (Nov 2007)

10. The coefficients fo a system defined by H(z) = 1 (1-0.4z -1) (1-0.55z-1) are represented in a number system with a sign bit and 3 data bits using signed magnitude representation and truncation. Determine the new pole locations for direct realization and for cascade realization of first order systems. (Nov 2007)

11. An IIIR causal filter has the system function H(z) = z / (z-0.97) assume that the input signal is zero-valued and the computed oputput signal values are rounded to one decimal place. Show that under these stated conditions, the filter output exhibits dead band effect. What is the dead band range? (Nov 2007)

12. (i)The input to the system y(n) = 0.999y(n-1)+x(n) is applied to an ADC. What is the power produced by the quantization noise at the output of the filter if the input is quantized to (i) 8 bits (ii) 16 bits (May 2007)

(ii)convert the following decimal number into binary: (May 2007)a. (20.675)10

b. (120.75)10

13. 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 round off noise power. Assume a1 = 0.5 and a2 = 0.6 and find output round off noise power. (May 2007,Nov 2006)

14. explain the characteristics of a limit cycle oscillation with respect to the system described by the difference equation y(n) =0.95y(n-1)+x(n). determine the dead band of the filter. (Nov2006)

15. Draw the product quantization noise model of second order IIR system .(Nov 2006)

16. Expain the effect of finite word length effects. (APR 05 EC)17. Derive the steady state noise power at the output if an LTI

system due to quantization at the input. (NOV 04 EC)18. Explain about fixed point and floating point representation. (NOV 04 EC)19. Discuss limit cycles in digital filters. (NOV 03 EC)

20.Draw the quantization noise model for a second order system with system function. (APR 05 EC)

H(z) = 1 ------------------------------ 1 - 2rcos0 z-1 + r2 z-2

Determine the steady state noise.21.Explain coefficint quantization effects in direct form realization of IIR filter.

(APR 04 EC)

22.A digital sytem is characterized by the difference equation. (APR 04 EC) y(n)=0.9y(n-1)+x(n)

23.For the given transfer function H(z)= H1(z ) H2(z) where H1 (z) = 1 / (1-0.5z-1) & H2(z) = 1 / (1-0.4z-1). Find the output round off noise

power. Calculate the value if b=3 (NOV05EC)

24.Explain the characteristics of a limit cycle oscillation with respect to the system described by the difference equation y (n) =0.95y (n-1) +x (n)

Determine the dead band of the filter. (NOV05EC)

25.Find the effect of co-efficient quantization on pole location of the Given second order IIR system when it is realized in direct form I andin cascade form. Assume a word length of 4 bits through truncation H(z) = 1 ------------------------ (NOV05EC)

1 - 0.9 z-1+ 0.2 z-1

UNIT – V

1. (a) for the multirate system shown in figure , find the relation between x(n) and y(n) (16) x(n)

y(n)

(OR) (b) explain the efficient transversal structure for decimeter and interpolator. (16)

2.(a) (i) Explain how various sound effects can be generated with the help of DSP.(10)

(ii) State the applications of multirate signal processing(6)

(b) (i) Explain how DSP can be used for speech processing. (8)

(ii) Explain in detail about decimation and interpolation (8)

z-1

z z

z-1

z z+

3. Consider the signal x(n)=an u(n), |a|<1.

a) Determine the spectrum X(ω).

b)The signal x(n) is applied to a decimator that reduces the rate by a factor of 2. Determine the output spectrum.

c)Show that the spectrum in part (b) is simply the Fourier transform of x(2n).

4. The sequence x(n) is obtained by sampling an analog signal with period T. From this signal a new signal is derived having the sampling period T/2 by use of a linear interpolation method described by the equation.

y(n) = { x(n / 2), n even}

{ 1/2[x( (n-1)/2 ) + x( (n+1)/2], n odd}

a)Show that this linear interpolation scheme can be realized by basic digital signal processing elements.

b)Determine the spectrum of y(n) when the spectrum of x(n) is

X(ω) = {1, 0≤|ω|≤0.2π

0, otherwise

c)Determine the spectrum of y(n) when the spectrum of x(n) is

X(ω) = {1, 0.7π≤|ω|≤0.9π

0, otherwise

5. An analog signal xa (t) is bandlimited to the range 900≤ F ≤ 1100Hz. It is used as an input to the system shown in Fig. In this system, H(ω) is an ideal low pass filter with cutoff frequency Fc = 125Hz.

a)Determine and sketch the spectra for the signals x(n), w(n), v(n), and y(n).

b)Show that it is possible to obtain y(n) sampling xu (t) with period T=4 millisec.Your browser may not support display of this image.

6.Design a decimator that downsamples an input signal x(n) by a factor D=5. Use the Remez algorithm to determine the coefficients of the FIR filter that has 0.1 dB ripple in the passband (0≤ ω≤π/5) and is down by at least 30dB in the stopband. Also determine the corresponding polyphase filter structure for implementing the decimator.

7.Consider the two different ways of cascading a decimator with an interpolator shown in Fig.

a)If D=1, show that the outputs of the two configurations are different. Hence, in general, the two systems are not identical.

b)Show that the two systems are identical if and only if D and I are relatively prime.

8.Design a two stage decimator for the following specifications

D=100 Passband: 0≤F≤50 Transition band: 50≤F≤55 Input sampling rate: 10,000Hz Ripple: δ1 = 10-1 , δ2 = 10-3

Prepared by Reviewed by HOD/ECE