Anna University
Digital Signal Processing
Question Bank
Subject Code :CS2403
Subject Name : Digital Signal Processing
Year / Sem : 4th Yr / 7th Sem
UNIT 1
1. Determine the energy of the discrete time sequence (2)
x(n) = (½)n, n≥0
=3 n, n<0
2. Define multi channel and multi dimensional signals (2)
3. Define symmetric and anti symmetric signals. (2)
4. Differentiate recursive and non recursive difference equations. (2)
5. What is meant by impulse response? (2)
6. What is meant by LTI system? (2)
7. What are the basic steps involved in convolution? (2)
8. Define the Auto correlation and Cross correlation? (2)
9. What is the causality condition for an LTI system? (2)
10. What is zero padding? What are it uses? (2)
11. State the Sampling Theorem. (2)
12 What is an anti imaging and anti aliasing filter? (2)
13. Determine the signals are periodic and find the fundamental period (2)
in√ 2 Ï€t
i) sin 20Ï€t+ sin5Ï€t
14. Give the mathematical and graphical representations of a unit sample, unit step sequence. (2)
15. Sketch the discrete time signal x(n) =4 δ (n+4) + δ(n)+ 2 δ (n-1) + δ (n-2) -5 δ (n-3) (2)
16. Find the periodicity of x(n) =cost(2Ï€n / 7) (2)
17. What is inverse system? (2)
18. Write the relationship between system function and the frequency response. (2)
19. Define commutative and associative law of convolutions. (2)
20. What is meant by Nyquist rate and Nyquist interval? (2)
21. What is an aliasing? How to overcome this effect? (2)
22. What are the disadvantages of DSP? (2)
23. State initial value theorem of Z transform. (2)
24 What are the different methods of evaluating inverse z transform? (2)
25 What is meant by ROC? (2)
26 What are the properties of ROC?(2)
27 What is zero padding? What are it uses?(2)
28 State convolution property of Z transform. (2)
29 State Cauchy residue theorem. (2)
30 Define fourier transform. (2)
31 Define discrete fourier series. (2)
32 Compare linear and circular convolution. (2)
33 Distinguish between Fourier series and Fourier transform. (2)
34 What is the relation between fourier transform and z transform. (2)
35 What is the use of Fourier transform? (2)
36. Define system function. (2)
37. State Parseval relation in z transform (2)
CLASSIFICATION OF SYSTEMS:
1. Determine whether the following system are linear, time-invariant (16)
i)y(n) = Ax(n) +B
ii)y(n) =x(2n)
iii)y(n) =n x2 (n)
iv)y(n) = a x(n)
2. Check for following systems are linear, causal, time in variant, stable, static (16)
i) y(n) =x(2n)
ii) y(n) = cos (x(n))
iii) y(n) = x(n) cos (x(n)
iv) y(n) =x(-n+2)
v) y(n) =x(n) +n x (n+1)
3.a) For each impulse response determine the system is i) stable ii) causal (8)
i) h(n)= sin (Ï€ n / 2)
ii) h(n) = δ(n) + sin π n
iii) h(n) = 2 n u(-n)
. b)Find the periodicity of the signal x(n) =sin (2Ï€n / 3)+ cos (Ï€ n / 2) (8)
4. Explain in detail about A to D conversion with suitable block diagram and to
reconstruct the signal. (16)
5 a) State and proof of sampling theorem. (8)
b)What are the advantages of DSP over analog signal processing? (8)
6 a)Explain successive approximation technique. (8)
b)Explain the sample and hold circuit. (8)
Z TRANSFORM:
1. a)State and proof the properties of Z transform. (8)
b)Find the Z transform of (8)
i) x(n) =[ (1/2)n – (1/4)n ] u(n)
ii) x(n) = n(-1)n u(n)
iii) x(n) (-1)n cos (Ï€n/3) u(n)
iv) x(n) = (½) n-5 u(n-2) +8(n-5)
2 a) Find the Z transform of the following sequence and ROC and sketch the pole zero
diagram (8)
i) x(n) = an u(n) +b n u(n) + c n u(-n-1) , |a| <|b| <| c|
ii) x(n) =n2 an u(n)
b)Find the convolution of using z transform (8)
x1(n) ={ (1/3) n, n>=0
(1/2) - n n<0 }
x2(n) = (1/2) n
INVERSE Z TRANSFORM:
5. Find the inverse z transform (16)
X(z) = log (1-2z) z < |1/2 |
X(z) = log (1+az-1) |z| > |a|
X(z) =1/1+az-1 where a is a constant
X(z)=z2/(z-1)(z-2)
X(z) =1/ (1-z-1) (1-z-1)2
X(z)= Z+0.2/(Z+0.5)(Z-1) Z>1 using long division method.
X(z) =1- 11/4 z-1 / 1-1/9 z-2 using residue method.
X(z) =1- 11/4 z-1 / 1-1/9 z-2 using convolution method.
6.. A causal LTI system has impulse response h(n) for which Z transform is given by H(z)
1+ z -1 / (1-1/2 z -1 ) (1+1/4 z -1 ) (16)
i) What is the ROC of H (z)? Is the system stable?
ii) Find THE Z transform X(z) of an input x(n) that will produce the output y(n) = - 1/3
(-1/4)n u(n)- 4/3 (2) n u(-n-1)
iii) Find the impulse response h(n) of the system.
ANALYSIS OF LTI SYSTEM:
7. a)The impulse response of LTI system is h(n)=(1,2,1,-1).Find the response of the system to
the input x(n)=(2,1,0,2) (8)
b). Determine the response of the causal system y(n) – y(n-1) =x(n) + x(n-1) to inputs
x(n)=u(n) and x(n) =2 –n u(n).Test its stability (8)
8. Determine the magnitude and phase response of the given equation
y(n) =x(n)+x(n-2) (16)
9. a)Determine the frequency response for the system given by
y(n)-y3/4y(n-1)+1/8 y(n-2) = x(n)- x(n-1) (8)
b). Determine the pole and zero plot for the system described difference equations
y(n)=x(n)+2x(n-1)-4x(n-2)+x(n-3) (8)
10. Find the output of the system whose input- output is related by the difference equation
y(n) -5/6 y(n-1) +1/6 y(n-2) = x(n) -1/2 x(n-1) for the step input. (16)
11. Find the output of the system whose input- output is related by the difference equation
y(n) -5/6 y(n-1) +1/6 y(n-2) = x(n) -1/2 x(n-1) for the x(n) =4 n u(n). (16)
CONVOLUTION:
12. Find the output of an LTI system if the input is x(n) =(n+2) for 0≤ n≤ 3
and h(n) =an u(n) for all n (16)
13. Find the convolution sum of x(n) =1 n = -2,0,1
= 2 n= -1
= 0 elsewhere
and h(n) = δ (n) – δ (n-1) + δ( n-2) - δ (n-3) (16).
14. Find the convolution of the following sequence x(n) =(1,2,-1,1) , h(n) =(1, 0 ,1,1) (16)
15.Find the output sequence y(n) if h(n) =(1,1,1) and x(n) =(1,2,3,1) using a circular
Convolution. (16)
16. Find the convolution y(n) of the signals (16)
x(n) ={ α n, -3 ≤ n ≤ 5 and h(n) ={ 1, 0 ≤ n ≤ 4
0, elsewhere } 0, elsewhere }
UNIT 2
1. How many multiplication and additions are required to compute N point DFT using
radix 2 FFT? (2)
2. Define DTFT pair. (2)
3. What are Twiddle factors of the DFT? (2)
4. State Periodicity Property of DFT. (2)
5. What is the difference between DFT and DTFT? (2)
6. Why need of FFT? (2)
7. Find the IDFT of Y (k) = (1, 0, 1, 0) (2)
8. Compute the Fourier transform of the signal x(n) = u(n) – u(n-1). (2)
9. Compare DIT and DIF? (2)
10. What is meant by in place in DIT and DIF algorithm? (2)
11. Is the DFT of a finite length sequence is periodic? If so, state the reason. (2)
12. Draw the butterfly operation in DIT and DIF algorithm? (2)
13. What is meant by radix 2 FFT? (2)
14. State the properties of W N
k ? (2)
15. What is bit reversal in FFT? (2)
16. Determine the no of bits required in computing the DFT of a 1024 point sequence
with SNR of 30dB. (2)
17. What is the use of Fourier transform? (2)
18. What are the advantages FFT over DFT?
FOURIER TRANSFORM:
1. a) Determine the Fourier transform of x (n) =a |n|; -1<a<1
(8)
b) Determine the Inverse Fourier transform H (w) = (1-ae-jw) -1 (8)
2. State and proof the properties of Fourier transform (16)
FFT:
3. Determine the Discrete Fourier transform x (n) = (1, 1, 1, 1) and
Proof x(n)*h(n) =X(z) H(z (16)
4. Derive and draw the 8 point FFT-DIT butterfly structure. (16)
5. Derive and draw the 8 point FFT-DIF butterfly structure. (16)
6.Compute the DFT for the sequence.(0.5,0.5,0.5,0.5,0,0,0,0) (16)
7.Compute the DFT for the sequence.(1,1,1,1,1,1,0,0) (16)
8.Find the DFT of a sequence x(n)=(1,1,0,0) and find IDFT of Y(k) =(1,0,1,0) (16)
9. If x (n) = sin (nÎ /2), n=0, 1, 2, 3 (16)
10. h (n) = 2 n , n=0,1,2,3.Find IDFT and sketch it. (16)
11.Find 4 point DFT using DIF of x(n) =(0,1,2,3) (16)
12.a)Discuss the properties of DFT. (10)
b).Discuss the use of FFT algorithm in linear filtering. (6)
UNIT 3& 4
1. Define canonic and non canonic form realizations. (2)
2. Draw the direct form realizations of FIR systems? (2)
3. Mention advantages of direct form II and cascade structure? (2)
4. Define Bilinear Transformation. (2)
5. What is prewar ping? Why is it needed? (2)
6. Write the expression for location of poles of normalized Butterworth filter. (2)
7. Distinguish between FIR and IIR Filters. (2)
8. What is linear phase filter? (2)
9. What are the design techniques available for IIR filter? (2)
10. What is the main drawback of impulse invariant mapping? (2)
11. Compare impulse invariant and bilinear transformation. (2)
12. Why IIR filters do not have linear phase? (2)
13. Mention the properties of Butterworth filter? (2)
14. Mention the properties of Chebyshev filter? (2)
15. Why impulse invariant method is not preferred in the design of high pass IIR filter? (2)
16. Give the transform relation for converting LPF to BPF in digital domain. (2)
17. What are Gibbs oscillations? (2)
18. Explain briefly Hamming window (2).
19. If the impulse response of the symmetric linear phase FIR filter of length 5 is h(n) =
{2, 3, 0, x, y), then find the values of x and y. (2)
20. What are the desirable properties of windowing technique? (2)
21. Write the equation of Bartlett window. (2)
22.Why IIR filters do not have linear phase? (2)
23.Why FIR filters are always stable? (2)
24.Why rectangular window are not used in FIR filter design using window method? (2)
25.What are the advantages of FIR filter? (2)
26.What are the advantages and disadvantages of window? (2)
27.What is the necessary condition and sufficient condition for the linear phase characteristic of a
FIR filter? (2)
28.Compare Hamming and Hanning window? (2)
29.Why triangular window is not a good choice for designing FIR Filter? (2)
30.Why Kaiser window is most used for designing FIR Filter? (2)
31.What is the advantages in linear phase realization of FIR systems? (2)
Structures of IIR systems:
1. Obtain the cascade and parallel form realizations for the following systems (16)
Y (n) = -0.1(n-1) + 0.2 y (n-2) + 3x (n) +3.6 x (n-1) +0.6 x (n-2)
2.a) Obtain the Direct form II
y (n) = -0.1(n-1) + 0.72 y(n-2) + 0.7x(n) -0.252 x(n-2) (8)
b) .Find the direct form II
H (z) =8z-2+5z-1+1 / 7z-3+8z-2+1 (8)
3. Obtain the i) Direct forms ii) cascade iii) parallel form realizations for the following systems
y (n) = 3/4(n-1) – 1/8 y(n-2) + x(n) +1/3 x(n-1) (16)
4.Find the direct form –I, cascade and parallel form for (16)
H(Z) = z -1 -1 / 1 – 0.5 z-1+0.06 z-2
IIR FILTER DESIGN:
6. Explain the method of design of IIR filters using bilinear transform method. (16)
7. a)Derive bilinear transformation for an analog filter with system function H(s) = b/ s + a (8)
b) For the analog transfer function H(s) = 2 / (s+1) (s+3) .
Determine H (z) using bilinear transformation. With T=0.1 sec (8)
8. a)Convert the analog filter H(s) = 0.5 (s+4) / (s+1)(s+2) using impulse invariant transformation
T=0.31416s (8)
b)The normalized transfer function of an analog filter is given by H a (sn) = 1/ sn
2 +1.414 s n +1.
Convert analog filter to digital filter with cut off frequency of 0.4 π using bilinear transformation.
(8)
9. Design a single pole low pass digital IIR filter with -3db bandwidth of 0.2Î by using bilinear
transformation. (16)
10. For the constraints
0.8 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ 0.2Ï€
|H (e jw)| ≤0.2, 0.6Ï€ ≤ ω ≤Ï€ with T= 1 sec .Determine system function H(z) for a Butterworth
filter using Bilinear transformation. (16)
11.Design a digital Butterworth filter satisfying the following specifications
0.7 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ 0.2Ï€
|H (e jw)| ≤0.2, 0.6Ï€ ≤ ω ≤Ï€ with T= 1 sec .Determine system function H(z) for a Butterworth
filter using impulse invariant transformation. (16)
12. Design a digital Chebyshev low pass filter satisfying the following specifications 0.707 ≤ |H (e
jw)| ≤1, 0 ≤ ω ≤ 0.2Ï€
|H (e jw)| ≤0.1 0.5 ≤ ω ≤Ï€ with T= 1 sec using for bilinear transformation. (16)
13.Design a digital Butterworth High pass filter satisfying the following specifications
0.9 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ Ï€/2
|H (e jw)| ≤0.2, 3Ï€/4 ≤ ω ≤Ï€ with T= 1 sec. using impulse invariant transformation (16)
14. Design a realize a digital filter using bilinear transformation for the following specifications
i) Monotonic pass band and stop band
ii) -3.01 db cut off at 0.5 π rad
iii) Magnitude down at least 15 db at ω = 0.75 π rad. (16)
FIR FILTER
15.a) Prove that an FIR filter has linear phase if the unit sample response satisfies the condition h(n)
= ± h(M-1-n), n =0,1,….. M-1.Also discuss symmetric and anti symmetric cases of FIR filter.
(8)
b) Explain the need for the use of window sequence in the design of FIR filter. Describe the
window sequence generally used and compare the properties. (8)
16. Design a HPF of length 7 with cut off frequency of 2 rad/sec using Hamming window. Plot the
magnitude and phase response. (16)
17. Explain the principle and procedure for designing FIR filter using rectangular window (16)
18. Design a filter with
H d (e
jÏŽ) = e - 3 jÏŽ , Ï€/4 ≤ ω ≤ Ï€/4
0. Ï€/4 ≤ ω ≤ Ï€ using a Hamming window with N=7. (16)
19. H (w) =1 for | ω | ≤ Ï€/3 and | ω | ≥2 Ï€/3
0 otherwise for N=11. and find the response. (16)
20.Design a FIR filter whose frequency response (16)
H (e jÏŽ) = 1 Ï€/4 ≤ ω ≤ 3Ï€/4
0. | ω | ≤3 Ï€/4.
Calculate the value of h(n) for N=11 and hence find H(z).
21.Design an ideal differentiator with frequency response H (e jÏŽ) = jw -Ï€ ≤ ω ≤ Ï€
using hamming window for N=8 and find the frequency response. (16)
22.Design an ideal Hilbert transformer having frequency response
H (e jÏŽ) = j -Ï€ ≤ ω ≤ 0
-j 0 ≤ ω ≤ Ï€ for N=11 using rectangular window. (16)
FIR structures:
23.a) Determine the direct form of following system (8)
H (z) =1+2z-1 - 3z-2 + 4z-3 - 5z-4
b). Obtain the cascade form realizations of FIR systems (8)
H (z) = 1+5/2 z-1+ 2z-2 +2 z-3
UNIT 5
1) Give some example of DSP
2) Explain Interpolation
3) Explain decimation
4) What is know to be subband coding
5) Define sampling rate conversion
6) How the image enchancement is achieved using DSP
7) Define compression
8) What are various compression technique
9) Explain subband coding
10) Define vocoders
11) Explain adaptive filtering
Part B
1) Explain the concept of deciation by a factor D and interpolation by factor I
2) With help of equation explain sampling rate conversion by a rational factor I/D
3) Explain the following application
i) speech compression
ii) sound processing
4) With help diagram explain adaptive filtering process
5) Explain speech vocoders and subband coding
6) Explain how image enchancement was achieved
Anna University
DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING
Software Quality Assurance QUESTION BANK
SUBJECT CODE: CS2055
YEAR: IV
SUBJECT NAME: Software Quality Assurance
SEM : VII
UNIT-1 Introduction to Software Quality
PART-A
1) Define software quality.
2) Write down the different views of quality.
3) Describe the three areas addressed by McCall model.
4) Define McCall’s quality criteria
5) How the quality criteria interrelated
6) Give the conditions that quality metrics should meet.
7) What are the two types of metrics?
8) Give the characteristics of quality of software?
9) Why software is considered to be problematical?
10) What are the seven criteria suggested by watts for a good metric?
11) How the metrics are classified?
12) Write down the limitations of metrics?
13) What are the problem areas associated with implementation of the method?
14) Write down the Gilb’s quality attributes
15) Gilb’s approach becomes obsolete State reason.
PART - B
1. What are the views of quality? Explain in Detail the views of quality. (15)
2. Explain the hierarchical model of Quality. (15)
3. a) Plain in detail the GE Model. (07)
b) Plain the Boehm model. (08)
| 4. Explain how the software quality can be measured and the problems associated with them. | (15) |
| 5. Explain the work of Gilb. | (15) |
| 6. Explain in detail GQM model. | (15) |
Unit-II: SOFTWARE QUALITY ASSURANCE
PART-A
1) What are five factors affecting software quality assurance?
2) Write down the guidelines for effective leadership?
3) Write down the five effective methods to ensure the failure of software quality assurance?
4) What is SRS?
5) What is SDD?
6) What is Software Interfaces documentation?
7) Write down the principles behind the review process?
8) Write down the specification for reviews?
9) What are the inputs given to the management review process?
10) Write down the objective of Technical review ?
11)Write down the procedures involved in auditing?
12)Write down the preparations that has to be made by the audit team?
13)What are the requirements required for the document audit and verification?
14)When the auditing is said to be complete?
15)What is the purpose of performing Review and auditing?
Part-B
| 1.Explain in detail the Quality tasks and responsibilities. | (15) |
| 2. Explain in detail about the Documentation. | (15) |
| 3. Explain the Procedural description template and Action items | (15) |
| 4. Explain in detail the CMM Compatibility of Reviews and audits. | (15) |
| 5. Explain the types of reviews. | (15) |
| 6. a) Explain the software inspection process | (08) |
| b) Explain the factors affecting the SQA effort. | (07) |
Unit- III QUALITY CONTROL AND RELIABILITY
PART-A
1) What are different types of Reliability growth models?
2) What are assumptions made in J-M model?
3) What are the assumptions made in fault count model?
4) Write down the criteria involved in reliability models
5) Write down the procedures involved in modeling software reliability
6) Define test compression factor
7) Write down the advantages of using reliability growth model
8) What are Ishikawa’s seven basic tools for quality control?
9) Write down the assumptions made in the phases of defect removal activities
10) How will u calculate the total defects for the life of the software?
11) Write down the equation for Goel generalized non homogenous Poisson process model.
12) What are the two types of inspector phase defined by knight and Myers?
PART-B
1 a) Explain in detail about the Reliability growth models. (08)
b) Explain the Defect Prevention Process. (07)
| 2. Explain the Defect removal Effectiveness. | (15) |
| 3. Explain the Reliability models. | (15) |
| 4. Explain in detail about the Rayleigh model. | (15) |
| 5. Explain Reliability growth model for quality assessment | (15) |
Unit - IV QUALITY MANAGEMENT SYSTEMS
PART - A
1) How will u calculate the total defects for the life of the software?
2) What is single inspector phase?
3) Name the two metrics for DRE
4) What is the use of software reliability models
5) What is the need of assessing the software reliability?
6) Write down the classification of reliability models
7) What are the assumptions made in the rayleigh model curve to model the software development activity?
8) What is DUD?
9) What are the strengths of Rayleigh model?
10) How the Reliability growth models are classified?
11) What are different types of Reliability growth models?
12) What are the assumptions made in fault count model?
13) Write down the criterias involved in reliability models?
14) Write down the procedures involved in modeling software reliability?
15)What are the four types of scenarios?
PART-B
| 1. Explain in detail the elements of QMS. | (15) |
| 2. Explain the Rayleigh model framework. | (15) |
| 3. Explain the Reliability Growth models. | (15) |
| 4. Explain the complexity metrics and its models | (15) |
| 5. Explain Lines of Code and Halstead’s Software Science. | (15) |
Unit – V QUALITY STANDARDS
PART-A
1) Define CASE tool?
2) What are advantages of CASE Tools?
3) What are different types of CASE tools.
4) Define QMS?
5) Write down the SPC techniques?
6) List out the ISO 9000 series of quality management standards.
7) What is six sigma?
8) What is CMMI?
9) What is ISO 9000 certification?
10) Define CMM?
11) What is SEI?
PART-B
1. Discuss in detail about the needs for standards (15)
2. Explain the ISO9000 series standard (15)
3. Explain the ISO9000-3 standard for software development. (15)
4 .Explain in detail the CMM Model (15)
5. Explain the CMMI Model (15)
6. Explain the Six Sigma Concepts. (15)
