DEPARTMENT OF ELECTRONICS & COMMUNICATION ... - Spec …€¦ · Web viewIf n1 is the starting index of x(n) and n2 is the starting index of h(n), the starting index of y(n) is

Giving Wings to Thoughts

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DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING

Subject: DIGITAL SIGNAL PROCESSINGFaculty: N.SWATHI (A), N. DHANUNJAYARAO (B & C)

Class: ECE-A, B, C Sections.UNIT-1

S. No Questions Marks Course Outcomes

Bloom taxonomy levels

Performance Indicators

1 Determine the impulse response and the step response of the following causal system.

y(n)+4y(n-1)+4y(n-2) = x(n)

5M C323.1 Apply 1.1.1

2 Test the following systems for the stability, linearity and causality.

a)) h(n)=4n u(3-n) b) y(n)= sin(nπ/2)

5M C323.1 Analyze 2.1.2

3 Find the z-transform and ROC of the following sequencesa) x(n)=2,-1,3,2,5 b) (-1)nCOS(πn/3)u(n)

5M C323.1 Remember 2.1.3

4 Find H(z), the system function for the followingy(n)-3y(n-1)+2y(n-2)=x(n)-x(n-1)


5 Determine the impulse response of the system described by the difference equationy(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1) using Z transform.

5M C323.1 Apply 1.1.1

1 Evaluate the frequency response of discrete-time system with impulse function a)h(n)=bnu(n) for b<1 b) h(n)=(0.3)n for n≥0

3M C323.1 Evaluate 2.1.3

2 Discuss four advantages of Digital Signal Processing over Analog Signal Processing.

3M C323.1 Understand 1.3.1

3 Explain about conversion of Continuous to discrete signal.


4 Determine the z-transform and sketch the ROC of the following signal𝑥(𝑛) = (

1)n,n≥03

1)n, n<02

3M C323.1 Apply 2.1.3

5 Define an LSI system and write conditions of causality and stability for an LTI system.


1 Define the z-transform and what is relationship between z-transform and DTFT?


2 Show thata) δ(n)=u(n)-u(n-1)b) u(n)=∑𝑛

δ(k) = ∑𝑛 δ(n − k)𝑘=−∞ 𝑘=−∞

2M C323.1 Apply 2.1.3

3 Classify the discrete time systems 2M C323.1 Analyze 2.1.3

mailto:[email protected]





4 How can you justify step response of a system if the impulse response h (n) is known?

2M C323.1 Evaluate 1.3.1

5 Define system function. 2M C323.1 Remember 1.3.1

UNIT-2




1 Find the output y(n) of a filter whose impulse response is 1,1,1 and input signalx(n)=3,-1,0,1,3,2,0,1,2,1 by using Overlap add method


2 Show that with x(n) as an N-point sequence of X(k) as its N-

point DFT ∑𝑁−1|x(n)|2 = 1 ∑𝑁−1|X(k)|2 𝑛=0 𝑁 𝑘=05M C323.2 Apply 2.2.3

3 Using FFT and IFFT, determine the output of system if inputx (n) = 2,2,4 and impulse response h(n)= 1,1.

5M C323.2 Apply 2.4.1

4 An 8-point sequence is given by x(n)=2,2,2,2,1,1,1,1. Compute 8-point DFT of x(n) by radix-2 DIT-FFT

5M C323.2 Create 2.4.1

5 Compute 4-point DFT of a sequence x(n)=0,1,2,3 using DIT algorithm.

5M C323.2 Create 2.4.1

1 List any four properties of DFT 3M C323.2 Remember

2 Compute the N-point DFT ofa) x(n)= 1 for n even and 0 for n odd b) x(n)=an

3M C323.2 Create 2.2.3

3 Draw the 4-point radix-2 DIT-FFT butterfly structure for DFTand give the applications of FFT algorithm

3M C323.2 Create 2.2.3

4 Draw the basic butterfly diagram for DIT algorithm 3M C323.2 Create 2.2.2

5 Solve linear convolution of the sequences x(n)=1,2,3; h(n)=-1,-2 using circular convolution.

3M C323.2 Apply 2.4.1

1 Define the zero padding? What are its uses? 2M C323.2 Remember 2.1.1

2 State the difference between (i) Overlap-save method (ii) overlap-add method.


3 Explain the relation between DFT and Z-transform? 2M C323.2 Understand 2.2.4





4 List the basic operations of the DIT and DIF algorithms?


5 Define is FFT? How many multiplications and additions are required to compute N-point DFT using radix-2 FFT?


UNIT-3




1 Given the specification αP = 1 dB; αs = 30 dB; ΩP

=200rad/sec; Ωs = 600rad/sec. Determine the order of the filter.

5M C323.3 Apply 3.1.3

2 Design an analog Butterworth filter that has αP = 3 dB; αs =18 dB; fp = 1kHz; fs= 2kHz.

5M C323.3 Create 3.1.3

3 Design an analog Butterworth filter that has a -2dB passband attenuation at a frequency of 20 rad/sec and atleast -10dB stopband attenuation at 30rad/sec.

5M C323.3 Create 4.3.3

1 List out the steps to design an analog butterworth lowpass filter.


2 Express the equation for the order of N and cut off frequency Ωc of Butterworth filter.


3 How one can design digital filters from analog filters.

3M C323.4 Create 3.1.3

1 Differentiate between Digital and Analog filters. 2M C323.4 Understand 1.3.1

2 List the advantages and disadvantages of digital filters.

2M C323.4 remember 1.3.1

3 Explain any two properties of Butterworth low pass filters.






UNIT- I

FILL IN THE BLANKS:1. If a signal depends on only one independent variable, it is called a signal.2. Discrete-time signals are in time and in amplitude.3. The signals that are discrete in time and quantized in amplitude are called _

signals.4. The of a signal can be obtained by folding the signal about n = 0.5. For an odd signal, x(–n) = for all n.6. For an energy signal, E = and P = .7. For an anti-causal signal, x(n) = 0 for_____________________.8. For a dynamic system, the output depends on the______________and/or_________

values of input..9. A causal system is one whose output depends on _ values of input.10. A system obeys the principle of superposition.11. An LTI system is one which satisfies the properties of and .12. For a time-invariant system, its do not change with time.13. A system is said to be stable if every

input produces a bounded output14. Convolution is a method of finding the response of relaxed LTI systems.15. If N1 is the length of x(n) and N2 is the length of h(n), the length of y(n), the

convolution of x(n) and h(n) is .16. If n1 is the starting index of x(n) and n2 is the starting index of h(n), the starting index of

y(n) is .17. The range of values of z for which X(z) converges is called the .18. For a causal LTI system to be stable, the ROC of the system function must include the

.19. The output due to unit sample sequence is called the of the system.20. . The frequency response of a system is obtained by substituting _ in H(z).

Key:

1. One dimentional2. Discrete,continuous3. Digital4. Time reversal5. –x(n)6. Finite,zero7. n>08. past,future9. present,past10. linear11. linearity, time invariance12. input output characteristics





13. bounded14. FIR15. N1+N2-116. n1+n2

17. ROC18. Unit circle19. Impulse response20. Z=ejw

UNIT – II

1. The relation between DTFT x(n) and Z-transform X(z) is .2. The DTFT of x(n) is defined as .3. The frequency response of LTI system is given by the FT of the ____ of thesystem.4. The impulse response is the inverse Fourier transform of the of

the system.5. The frequency response is a function of ω.6. The frequency response has two components: 1. 2. .7. The direct computation of an N-point DFT requires complex

multiplications and complex additions.8. The FFT may be defined as an for computing DFT.9. In FFT, the computational efficiency is achieved by adopting a

approach.10. The basic FFT algorithms are and .

11. In 16-point DFT by radix-2 FFT, there are stages of computation with____ butterflies per stage.

12. In DIT algorithm, the sequence is decimated and in DIF algorithm the sequence _ is decimated.

13. The IDFT is computed through FFT using the formula x(n) = .14. The computation of 32-point DFT by radix-2 DIT FFT involves stages

of computation.15. In DFT computation using radix-2 FFT, the value of N should be such that___________.16. For DIT FFT, the input is in order and the output is in order.17. For DIF FFT, the input is in order and the output is in order.18. Convolution of long sequences can be done using convolution.19. In overlap save method, we use convolution.20. In overlap add method, the region are added and the

region are retained.Key:

1. X(𝜔)=X(Z) for Z= ejw





2. X (ω)= ∑n=−∞

∞

x (n )e− jwn

3. Impulse response4. Frequency response5. Continuous6. Magnitude, phase7. N X N, N X (N-1)8. Algorithm9. Divide and conquer10. DIT FFT, DIF FFT11. Four, eight12. x(n), X(K)

13. X (ω)=1/ N ∑K =0

N −1

X ¿ ( K ) W Nnk

14. Five15. N= 2m

16. Bit reversed, normal17. Normal, bit reversed18. Sectioned19. Circular20. overlapped, non-overlapped

Unit-III

1. Filters designed by considering samples of the impulse response are called IIR filters.2. The physically realizable IIR filters do not have phase.3. The IIR filter specifications includes the desired characteristics for the response only.4. Filters designed by considering samples of the impulse response are called FIR filters.5. The impulse response is obtained by taking the inverse Fourier transform of the .6. The bandwidth of the discrete signal is limited by the .

1. The popular methods for design of IIR digital filters uses the technique of an analog filter into an digital filter.2. The bandwidth of a real discrete signal is the sampling frequency.3. The three techniques used to transform an analog filter to digital filter are , and .4. The two properties which are to be preserved in analog to digital transformation are and .

c) c(-a)n

b) (-1)n+1 + (4)n+2





Key:1. All the infinite2. Linear3. Magnitude4. Only a finite number5. Ideal frequency response6. Sampling frequency7. Transforming, equivalent8. Half9. Approximation of derivatives, impulse invariant transformation, bilinear transformation10. Causality, stability

UNIT-IChoose the correct answer1. If the system is initially relaxed at time n=0 and memory equals to zero, then the

response of such state is called as:a) Zero-state response b) Zero-input responsec) Zero-condition response d) None of the mentioned

2. The solution obtained by assuming the input x(n) of the system is zero is: a) General solutionb) Particular solution c) Complete solutiond) Homogenous solution

3. What is the homogenous solution of the system described by the first order difference equation y(n)+ay(n-1)=x(n)?

a) c(a)n(where ‘c’ is a constant)

4. What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0?

d) None of the mentioned5. What is the order of the four operations that are needed to be done on h(k) in order

to convolute x(k) and h(k)?Step-1:FoldingStep-2:Multiplication with x(k) Step-3:ShiftingStep-4:Summation a) 1-2-3-4b) 1-2-4-3c) 2-1-3-4

c) (-1)n+1 + (4)n-2

a) (-1)n-1 + (4)n-2

d) c(-a)-n

b) c(a)-n




a) 2 + 4z + 5z2 + 7z3 + z4


d) 1-3-2-4

6. The impulse response of a LTI system is h(n)=1,1,1. What is the response of the signal to the input x(n)=1,2,3?a) 1,3,6,3,1b) 1,2,3,2,1c) 1,3,6,5,3d) 1,1,1,0,0

7. An LTI system is said to be causal if and only if Da) Impulse response is non-zero for positive values of n b) Impulse response is zero for positive values of nc) Impulse response is non-zero for negative values of n d) Impulse response is zero for negative values of n

8. The even part of a signal x(t) is: a) x(t)+x(-t)b) x(t)-x(-t)c) (1/2)*(x(t)+x(-t))d) (1/2)*(x(t)-x(-t))

9. The discrete time function defined as u(n)=n for n≥0;=0 for n<0 is an: a) Unit sample signalb) Unit step signal c) Unit ramp signald) None of the mentioned

10. The signal given by the equation is known as:

a) Energy signalb) Power signalc) Work done signald) None of the mentioned

11. x(n)*δ(n-k)=? a) x(n)b) x(k)c) x(k)*δ(n-k)d) x(k)*δ(k)

12. What is the z-transform of the finite duration signal

c) 2 + 4z-1 + 5z-2 + 7z-3 + z-5

13. What is the z-transform of the signal x(n)=(0.5)nu(n)?d) 2z2 + 4z + 5 +7z-1 + z-3

b) 2 + 4z + 5z2 + 7z3 + z5

a) 1/1−0.5z−1;ROC:|z|>0.

d) 1/1+0.5z−1;ROC|z|<0.5




x(n)𝑍−𝑛 is known𝑛=−∞∞The z-transform of a sequence x(n) which is given as X(Z) = ∑

c) X-1(z)b) X(z-1)


5b) 1/1−0.5z−1;ROC|z|<0.5

14.

a) |a|<|z|<|b| b) |a|>|z|>|b| c) |a|>|z|<|b| d) |a|<|z|>|b|

15. What is the ROC of z-transform of finite duration anti-causal sequence? a) z=0b) z=∞c) Entire z-plane, except at z=0 d) Entire z-plane, except at z=∞

16.

as:a) Uni-lateral Z-transform b) Bi-lateral Z-transform c) Tri-lateral Z-transform d) None of the mentioned

17. If X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal x(-n)?a) X(-z)

d) None of the mentioned

18. Which of the following conditions made digital signal processing more advantageous over analog signal processing?a) Flexibility b) Accuracy c) Storaged) All of the mentioned

19. If x(n)=(0,0,1,2,3,4,0,0) then x(n-2) is: a) (0,0,2,4,6,8,0,0)b) (0,0,1,2,3,4,0,0)c) (1,2,3,4,0,0,0,0)d) (0,0,0,0,1,2,3,4)

20. All energy signals will have an average power of: a) Infiniteb) Zeroc) Positived) Cannot be calculated

What is the ROC of the z-transform of the signal x(n)= anu(n)+bnu(-n-1)?

c) 1/1+0.5z−1;ROC|z|>0.5

b) e-j2πkn/N




b) 𝑁 ∑𝑁−1(𝑛) 𝑒−𝑗2𝜋𝑘𝑛/𝑁𝑛=0c) 1 ∑(𝑛) 𝑒𝑁+1 −𝑗2𝜋𝑘𝑛/𝑁𝑁 𝑛=0d) 1 ∑(𝑛) 𝑒𝑁−1 −𝑗2𝜋𝑘𝑛/𝑁𝑁 𝑛=0

𝑛=0𝑁 𝑗2𝜋𝑘𝑛/𝑁𝑁−1a) 1 ∑(𝑛) 𝑒

/𝑁/𝑁∑𝑁−1 𝑐𝑘 𝑒−𝑗2𝜋𝑘𝑛/𝑁𝑘=0

𝑁𝑐𝑘 𝑒𝑗2𝜋𝑘𝑛/𝑘=0∑𝑁𝑘=0∑𝑁−1 𝑐𝑘 𝑒𝑗2𝜋𝑘𝑛𝑘=0∑𝑁+1 𝑐𝑘 𝑒𝑗2𝜋𝑘𝑛


Key:1. A2. D3. C4. B5. D6. C7. D8. C9. C10. A11. C12. D13. A14. A15. D16. B17. B18. D19. D20. B

UNIT-II1. Which of the following represents the phase associated with the frequency component of

discrete-time Fourier series(DTFS)?

d) None of the mentioned2. What is the period of the Fourier transform X(ω) of the signal

x(n)? a) πb) 1c) Non-periodic d) 2π

3. Which of the following relation is true if the signal x(n) is real? a) X*(ω)=X(ω)b) X*(ω)=X(-ω)c) X*(ω)=-X(ω)d) None of the mentioned

4. What is the Fourier series representation of a signal x(n) whose period is N? a)b)

c) ej2πknN

a) ej2πkn/N

c) e-jωk. X(-ω)





c)d)

5. If X(ω) is the Fourier transform of the signal x(n), then what is the Fourier transform of the signal x(n-k)?a) ejωk. X(-ω)

6. What is the circular convolution of the sequences x1(n)=2,1,2,1 and x2(n)=1,2,3,4? a) 14,14,16,16b) 16,16,14,14c) 2,3,6,4d) 14,16,14,16

7. What is the highest frequency that is contained in the sampled signal? a) 2Fsb) Fs/2 c) Fsd) None of the mentioned

8. What is the highest frequency that is contained in the sampled signal? a) 2Fsb) Fs/2 c) Fsd) None of the mentioned

9. Which of the following is true regarding the number of computations required to compute an N-point DFT?a) N2 complex multiplications and N(N-1) complex additionsb) N2 complex additions and N(N-1) complex multiplicationsc) N2 complex multiplications and N(N+1) complex additionsd) N2 complex additions and N(N+1) complex multiplications

10. Which of the following is true regarding the number of computations required to compute DFT at any one value of ‘k’?a) 4N-2 real multiplications and 4N real additions b) 4N real multiplications and 4N-4 real additions c) 4N-2 real multiplications and 4N+2 real additions d) 4N real multiplications and 4N-2 real additions

11. How many complex multiplications are performed in computing the N-point DFT of a sequence using divide-and-conquer method if N=LM?a) N(L+M+2) b) N(L+M-2)c) N(L+M-1) d) N(L+M+1)

12. How many complex multiplications are required to compute X(k)? a) N(N+1)b) N(N-1)/2c) N2/2d) N(N+1)/2

13. The total number of complex multiplications required to compute N point DFT by radix- 2 FFT is:

b) ejωk. X(ω)

d) e-jωk. X(ω)





a) (N/2)log2N b) Nlog2Nc) (N/2)logNd) None of the mentioned

14. For a decimation-in-time FFT algorithm, which of the following is true? a) Both input and output are in orderb) Both input and output are shuffledc) Input is shuffled and output is in order d) Input is in order and output is shuffled

15. For a decimation-in-time FFT algorithm, which of the following is true? a) Both input and output are in orderb) Both input and output are shuffledc) Input is shuffled and output is in order d) Input is in order and output is shuffled

16. By means of the DFT and IDFT, determine the response of the FIR filter with impulse response h(n)=1,2,3 to the input sequence x(n)=1,2,2,1?a) 1,4,11,9,8,3b) 1,4,9,11,8,3c) 1,4,9,11,3,8d) 1,4,9,3,8,11

17. In Overlap save method of long sequence filtering, what is the length of the input sequence block?a) L+M+1 b) L+M c) L+M-1d) None of the mentioned

18. In Overlap add method, what is the length of the input data block? a) L-1b) L c) L+1d) None of the mentioned

19. Which of the following is true in case of Overlap add method? a) M zeros are appended at last of each data blockb) M zeros are appended at first of each data block c) M-1 zeros are appended at last of each data block d) M-1 zeros are appended at first of each data block

20. Which of the following is used in the realization of a system? a) Delay elementsb) Multipliersc) Addersd) All of the mentioned

KEY:1. A2. D3. B4. D5. B





6. D7. D8. B9. A10. D11. D12. D13. A14. C15. D16. B17. C18. B19. C20. DUNIT-III1. In IIR Filter design by the Bilinear Transformation, the Bilinear Transformation is a

mapping froma) Z-plane to S-plane b) S-plane to Z-plane c) S-plane to J-plane d) J-plane to Z-plane

2. If M and N are the orders of numerator and denominator of rational system function respectively, then how many multiplications are required in direct form-I realization of that IIR filter?a) M+N-1 b) M+N c) M+N+1d) M+N+2

3. If M and N are the orders of numerator and denominator of rational system function respectively, then how many memory locations are required in direct form-I realization of that IIR filter?a) M+N+1 b) M+N c) M+N-1 d) M+N-2

4. Which of the following is an method for implementing an FIR system? a) Direct formb) Cascade form c) Lattice structured) All of the mentioned

5. The realization of FIR filter by frequency sampling realization can be viewed as cascade of how many filters?a) Two b) Three c) Fourd) None of the mentioned

6. Which of the following rule is used in the bilinear




]−1−𝑧[𝑇 1 −1c) 𝑠 = 2 1+𝑧]−1+𝑧[𝑇 1 −1b) 𝑠 = 1 1−𝑧]−1+𝑧[𝑇 1 −1a) 𝑠 = 2 1−𝑧


transformation? a) Simpson’s ruleb) Backward difference c) Forward difference d) Trapezoidal rule

7. Which of the following substitution is done in Bilinear transformations?

d) None

8. If s=σ+jΩ and z=rejω, then what is the condition on σ if r<1? a) σ > 0b) σ < 0 c) σ > 1 d) σ < 1

9. If s=σ+jΩ and z=rejω and r=1, then which of the following inference is correct? a) LHS of the s-plane is mapped inside the circle, |z|=1b) RHS of the s-plane is mapped outside the circle, |z|=1c) Imaginary axis in the s-plane is mapped to the circle, |z|=1 d) None of the mentioned

10. What is the value of chebyshev polynomial of degree 0? a) 1b) 0c) -1d) 2

KEY:

1. B2. C3. A4. D5. A6. D7. A8. B9. C10. A

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DEPARTMENT OF ELECTRONICS & COMMUNICATION ... - Spec …€¦ · Web viewIf n1 is the starting index of x(n) and n2 is the starting index of h(n), the starting index of y(n) is