Continuous Assessment Test - 1

Course Code / Name 20ECPW501/ Discrete Time signal Processing with Laboratory

Regulations 2020

Department ECE

Year / Semester III/V

Course Moderator Dr C N Savithri/ Associate professor/ SEC/ECE

Course Outcomes with Knowledge Level

Upon the completion of this course the students will be able to
CO 1 Examine the signals in the frequency domain using DFT, DIT, DIF - FFT
algorithms and compute the response of the system using linear (K3)
filtering.
CO 2 Apply Butterworth and Chebyshev methods to design analog IIR filters. (K3)
CO 3 Use approximation of derivatives, impulse invariance mapping, and
(K3)
bilinear transformation methods to design a digital IIR filter.
CO 4 Use the Fourier series method, windowing technique, and frequency
(K3)
sampling methods to design a digital FIR filter.
CO 5 Summarize the effect of finite word length in digital filters to compute
(K2)
the quantization noise.
CO 6 Illustrate the architecture of Digital signal processors and program the
(K3)
DSP processors for signal processing applications.

QP PATTERN-CAT 1

UNIT - I

Sl.
Questions
No.
1. The segmentation technique for the processing of signals are
a)Overlap and add method
b)Overlap and save method
c)Both overlap and add , overlap and save methods
d)Circular Convolution
2. The ability to determine the frequency component of the signal
is using

Page 1 of 9
 a)DFT

b)DST

c)CFT

d)AFT

3. Compute the circular convolution of the sequences

X1(n)={2,1,2,1} and x2(n)={1,2,3,4}

a){14,14,16,16}

b) {16,16,14,14}

c) {2,3,6,4}

d) {14,16,14,16}
4. What is the correct formula to calculate the value of N?

a) N=L+M-1
b) N=L-M-1
c) N=L-M+1
d) N=L+M+1
5. In DIF-FFT radix- 2 ------------------domain sequence is
decimated.
a)Frequency

b)Time

c)Both

d)Phase

6. How many complex additions are needed for 16 direct

computations in discrete Fourier transform?
A. 56
B. 240
C. 756
D. 32
7. The number of complex additions that we need to perform in
the linear filtering of any sequence using the FFT algorithm
would be:

a) Nlog₂N
b) (N/2)log₂N
c) 2Nlog₂N
d) (N/2)logN

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 8. If X(k) is the N-point DFT of a sequence x(n), then what is the
DFT of x*(n)?

a)X(N-k)

b)X*(k)

c)X*(N-k)

d)X*(N)

9. For the given data h(n)={1,2,0} and x(n)={1,2,0,5,-1,1,2} what

will be the values of x1,x2 and x3 after padding zeros?

a)x1={1,2,0};x2={5,-1,1};x3={2}

b)x1={1,2},x2={0,5,-1};x3={1,2}

c)x1={1,2,0};x2={5,-1,1};x3={2,0,0}

d)x1={0,0,1};x2={1,2,0,5};x3={-1,1,2}

10. Find the 4- point DFT for the sequence x(n)={2,1,4,3} with
DIF-FFT X(k)= —

a){10,2+j2, 2,-2-j2}

b){10,-2-j2, 2,-2-j2}

c){10,-2+j2, 2,-2+j2}

d){10,-2+j2, 2,-2-j2}

Sl.No Questions
1. State DFT pair equations
2. State the properties of DFT
3. Distinguish between linear convolution and circular convolution of
two sequences.
4. Distinguish overlap-save and overlap-add methods.
5. Define the twiddle factor of FFT.
6. Obtain the circular convolution of the following sequences x(n) =
{1,2,3}, h(n) = {4,5,6}.
7. How many stages of decimations are required in the case of a 64 point
radix 2 DIT FFT algorithm?
8. Draw the basic butterfly of DIT-FFT structure.

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9. Draw the basic butterfly of DIF-FFT structure.
10. Differentiate DIT and DIF FFT algorithm
11. Calculate the 4-point DFT of the sequence 𝒙(𝒏) = {𝟏, 𝟎, −𝟏, 𝟎}.
12. Find the 4-point DFT of the sequence x(n) = {1,1,-1,-1}
13. Calculate the IDFT of the sequence X(K)={10,-2+j2,2,-2-j2}
14. Obtain the circular convolution of the following sequences x(n) =
{1,1,2,1}, h(n) = {1,2,3,4} using the Matrix method.
15. Consider a sequence(n) = {1,2,-3,0,1,-1,4,2}. Evaluate X(4) without
computing DFT of the sequence.
16 Obtain the circular convolution of the following sequences x(n) =
{1,2,1}, h(n) = {1, -2, 2} using the Matrix method.

Sl.
No Questions
.
1. Find DFT of the sequence X(K) = {1, 1, 1, 1, 1, 1, 0, 0}
2. Compute the DFT of the sequence, x(n)={0, 1, 2, 3}. Sketch the
Magnitude and Phase Spectrum.
3.
Find IDFT of the sequence X(K) = {5, 0, 1-j, 0, 1, 0, 1+j, 0}
4. Find the circular convolution of two sequences x1(n) = { 1,2,2,1}
and x2(n) = {1,2,3,1} using
i) concentric circle method and
ii) Matrix method
5. Perform circular convolution of two sequences x(n) = {1,2,3,4} and
h(n) = {2,3,1} using DFT method
6. Compute the linear convolution of finite duration sequences h(n) =
{1,1,1} and x(n) = {3,-1,0,1,3,2,0,1,2,1} using Overlap Save
method
7. Perform the linear filtering of finite duration sequences h(n)={1, 2}
and x(n) = {1, 2, -1, 2, 3, -3, -2, -1, 1, 2, -1} by overlap save
method.
8. Using overlap-add method, compute y(n) of a FIR filter with
impulse response h(n) = {3, 2, 1} and input x(n) = {2, 1, -1, -2, -3,
5, 6, -1, 2, 0, 2, 1}. Prove that the output response is the same when
using the overlap-save method.
9. Compute the 8 point DFT of the following sequence x(n) = {0.5,
0.5, 0.5, 0.5, 0, 0, 0 0} using the inplace radix-2 DIT FFT
algorithm.
10. Compute the eight point DFT of the sequence
x(n) = { 1 0≤ n ≤ 7
= 0 otherwise using DIT algorithms.
11 Compute the 8 point DFT of the following sequence using DIT-FFT
algorithm
x(n) = {2,2,2,2,1,1,1,1}

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12 Find the response y(n) when x(n) = {1,2,3,4} and h(n) = {0,1,2,3}
using DIT-FFT algorithm

13 Compute the 8 point DFT of the following sequence using DIT-FFT

algorithm
x(n) = {1,2,3,3,2,1,-1,-2}
14 Compute the 8 point DFT of the following sequence x(n) = {1,-1,-
1,-1,1,1,1,-1} using the inplace radix-2 DIF FFT algorithm.
15 Find the response y(n) when x(n) = {1,1,1,2} and h(n) = {1,2,3,2}
using DIF-FFT algorithm
16 Compute the 8 point DFT of the following sequence using DIF-FFT
algorithm
x(n) = {1,1,1,1,1,1,1,1}
17 Compute the 8 point DFT of the following sequence using DIF-FFT
algorithm
x(n) = {1,2,3,4,4,3,2,1}
18 Find the 8-point DFT of the given sequence x(n) = {2,1,2,1} using
DIF-FFT algorithm
19 Compute the IDFT of sequence X(K) = { 7, -0.707-j0.707, -j,
0.707-j0.707, 1, 0.707+j0.707, j, -0.707+j0.707} using DIT
algorithm
20 Compute the IDFT of sequence X(K) = { 4, 1-j2.414, 0 , 1-j0.414,
0, 1+j0.414, 0, 1+j2.414} using DIF algorithm

UNIT - II

Sl.
No Questions
.
1.
What is a key characteristic of a Butterworth filter?

a) Maximally flat magnitude response in the passband

b) Equal ripple magnitude response in the passband

c) Linear phase response

d) Sharp cutoff frequency

2. What is the Butterworth polynomial of order 1?

a) S+1

b) S-1

c) S

d) S(S+2)

3. The Butterworth filters are all ---------- designs.

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 a) Zero

b) Pole

c) Poles & Zeros

d)

4. What is the order of a low pass Butterworth filter that has a -3dB
bandwidth of 500Hz and an attenuation of 40dB at 1000Hz?

a) 4

b) 5

c) 6

d) 7

5.
What does the order of an analog filter determine?

a) The type of filter (e.g., LPF, HPF)

b) The cutoff frequency

c) The steepness of the filter's roll-off

d) The ripple in the passband

6.
What is the main advantage of using IIR filters over FIR
filters?

a) Linear phase response

b) Potentially lower computational complexity for the same level

of performance

c)Simpler design process

d) Easier implementation in hardware

7.
What is the primary difference between Chebyshev Type I
and Chebyshev Type II filters?

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 a) Type I has ripple in the passband, Type II has ripple in the
stopband

b) Type I has ripple in the stopband, Type II has ripple in the

passband

c) Type I has a maximally flat passband, Type II has a maximally

flat stopband

d) Type I is used for low-pass filtering, Type II is used for high-

pass filtering

8.
Which of the following filters is known for its linear phase
response?

a) Butterworth filter

b) Chebyshev filter

c) Elliptic filter

d) FIR filter
9.
Which of the following is a disadvantage of Butterworth
filters?

a) Sharp transition between passband and stopband

b) Non-linear phase response

c) Unequal ripple in the stopband

d) Unequal ripple in the passband

10.
Which characteristic is common to both Butterworth and
Chebyshev filters?

a) Linear phase response

b) Maximally flat passband

c) Equal ripple in the passband

d) They are both IIR filters

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 11.
The poles of the butterworth filter lie on a ____________

e) Circle
f) Ellipse
g) Parabola
h) straight line

12.
The poles of the Chebyshev filter lie on a ____________

a) Circle
b) Ellipse
c) Parabola
d) straight line

Sl.No
Questions
.
1.
List out the difference between Analog and Digital Filter.
2.
Compare IIR and FIR filters.
3.
Compare Butterworth with Chebyshev filters.
4.
Write the steps to design an Analog Butterworth Lowpass Filter.
5.
Write the formula for calculating the Order of the butterworth filter
6.
Write the formula for calculating the Order of the Chebychevh filter
7.
List the different types of filters based on frequency response.
8. Determine the order and the poles of lowpass Butterworth filter that
has a 3 dB attenuation at 500Hz and an attenuation of 40dB at 1000Hz.
9. Determine the order of the filter for the given specifications ∝𝑝 =
𝑟𝑎𝑑 𝑟𝑎𝑑
1𝑑𝐵; ∝𝑠 = 30𝑑𝐵; 𝛺𝑝 = 200 𝑠𝑒𝑐 ; 𝛺𝑠 = 600 𝑠𝑒𝑐 ;
10. How the cutoff frequency, passband frequency and stopband frequency
are related to each other in the design of IIR filter using Butterworth
design.
11.
What are the different types of filters based on impulse response?
12. For the given specifications 𝛼𝑝 = 3𝑑𝐵; 𝛼𝑠 = 18𝑑𝐵; 𝑓𝑝 =
1𝑘𝐻𝑧; 𝑓𝑠 = 2𝑘𝐻𝑧.What is the order of the Butterworth filter?
13.
Write the properties of the Butterworth filter.
14.
Write the properties of Chebyshev type-1 filters.

Sl.
No Questions
.
1. Sketch the ideal and practical frequency response of four basic
types of Analog filters and mark the important filter specifications.

Page 8 of 9
2. Explain the procedure for designing analog filters using the
Butterworth approximations.
3. Explain the procedure for designing analog filters using the
Chebyshev approximations.
4. Design an analog Butterworth filter that has fp=10kHz; fs=25kHz;
αp=0.5dB; αs =22dB.
5. Design an analog butterworth filter that has a -2dB pass band
attenuation at a frequency of 20 rad/sec and atleast -10dB stopband
attenuation at 30 rad/sec.
6. Design an analog Butterworth filter satisfying the constraints,
0.75 ≤ |𝐻(𝑗𝛺)| ≤ 1; 0 ≤ 𝛺 ≤ 𝜋/2
|𝐻(𝑗𝛺)| ≤ 0.2; 3𝜋/4 ≤ 𝛺 ≤ 𝜋
7. Design an Analog Butterworth filter for the following
Specifications.
0.8 ≤ |𝐻(𝑗𝛺)| ≤ 1; 0 ≤ 𝛺 ≤ 0.2𝜋 |𝐻(𝑗𝛺)| ≤ 0.2; 0.32𝜋 ≤ 𝛺 ≤ 𝜋
8. Apply Chebyshev approximation procedure to design an analog
lowpass filter with the following specifications
Passband attenuation 2dB
Stopband attenuation 14dB
Passband frequency : 6627.42 rad/sec
Stopband frequency : 16000 rad/sec
9. Design a Chebyshev filter with a maximum passband attenuation of
2.5dB;at Ωp=20rad/sec and the stopband attenuation of 30dB at
Ωs=50 rad/sec.
10. For the given specifications find the order of the Chebyshev-I filter
Ωp=2rad/sec; Ωs=30rad/sec; αp=1.5dB; αs =10dB

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