1 If x(n) and X(k) are an N-point DFT pair, then X(k+N) = ?
a) X(-k) b) -X(k) c) X(k) d) 1/X(k)
The number of multiplications and additions needed in the
2 calculations of Direct DFT and FFT with 64-point sequence
a)12 & 24 b)192 & 384 c)64 & 56 d)80 & 160
3 Circular Convolution in discrete time domain is_____ in frequency domain. a)
Correlation b) Multiplication c) Addition d) Time reversal
FIR filter is also called ____
4
a) Recursive filter b) Non-recursive c) Higher resistance d) Lower resistance
--------- window function is called as raised cosine window.
5
a) Hamming b) Rectangular c) Hanning d) Blackman
6 What is the approximate transition width of main lobe of a Hanning window? a)
4π/M b) 8π/M c) 12π/M d) 2π/M
What is the peak side lobe (in dB) for a rectangular window?
7
a) -13dB b) -27dB c) -32dB d) -58dB
Bilinear Transformation is a mapping from
8 a) z-plane to s-plane b) s-plane to z-plane
c) s-plane to j-plane d) j-plane to z-plane
In Impulse invariant transformation the analog transfer function,
H(s) = 0.3 / (s+0.7) is transformed to a digital system with transfer function
9 a) H(z) = -0.3 / 1-e-0.7Tz-1 b) H(z) = 0.3 / 1-e-0.7Tz-1
-0.3T -1
c) H(z) = -0.7 / 1-e z d) H(z) = 0.7 / 1-e-0.3Tz-1
10 What is the transfer function of Butterworth low pass filter of order 2?
a) 1/ s2+2√s+1 b) 1/ s2−2√s+1 c) s2−2–√s+1 d) s2+2–√s+1
By correlation property, the DFT if circular correlation of two sequences x(n) and y(n)
11 is,
a) X(k)Y*(k) b) X(k)*Y(k) c) X(k) Y(k) d) X*(k)Y(k)
In an N-point sequence, if N= 16, the total number of complex additions and
12 multiplications using radix 2 FFT are
a) 64 and 80 b) 80 and 64 c) 64 and 32 d) 24 and 12
Giving one period of the periodic convolution is called
13 a) periodic convolution b) aperiodic convolution
c) correlation d) circular convolution
14
The Z transform of δ (n − m) is ___________
-n m −m
a) z b) z - c) 1 / z−n d) 1 / z
15 In Hamming window spectrum the side-lobe magnitude remains constant with,
a) decreasing ω b) constant ω c)increasing ω d) ω = 0
16 Symmetric impulse response having odd number of samples with centre of symmetry
α is equal to
a) 2 b) 5 c) 3.5 d) 3
17 Give the value of h(M-1/2) if the unit sample response is anti-symmetric.
a) 0 b) 1 c) -1 d) M
In impulse invariant transformation the digital frequency ω for a given analog
18 frequency, Ω is given by,
a) ω = ΩT b) ) ω = Ω/T c) ) ω = T/Ω d) ) ω = tan ΩT
19 The zeros of the butterworth filters exist at
a) left half of s-plane b) origin c) ∞ d) right half of s-plane
The type-2 magnitude response is also called ------- response.
20 a) Chebysev b) butterworth
c) elliptical d) inverse Chebysev
PART-B
Determine the circular convolution of the following sequences x1(n)={2,1,2,1} and x2(n)={1,2,3,4}
Find the Z-transform of x(n) = n2 u(n).
Contrast the characteristic features of Rectangular, Hanning, Hamming and Blackman windows.
List the desirable characteristics of the frequency response of window function.
Determine the digital transfer function H(z) by using bilinear transformation for the analog transfer
function H(s)=2s/(s^2+0.2s+1). Assume T=1 sec.
State any four properties of DFT.
A DSP system is described by the linear difference equation y(n) = 0.2 x(n) – 0.5 x(n-2) + 0.4
x(n-3). Given that the digital input sequence is {-1, 1 ,0, -1} is applied to this DSP system. Estimate
the corresponding digital output sequence.
Distinguish between Hamming and Blackman window.
Write the magnitude and phase function of FIR filter when impulse response is symmetric, and N is
odd and even.
Modify the analog filter into a digital filter whose system function is . Assume T=1 sec. Use impulse
invariant technique.
PART-C
(i) Compute the 8-point DFT of the given x(n) by using radix-2 DIF-FFT algorithm.
x(n) = {1,1,1,1,1,1,1,1}.
(ii) Compare bilinear and impulse invariant methods.
(i) Design a linear phase FIR band pass filter to pass frequencies in the range 0.4π to 0.65 π radians /
sample by taking 7 samples of Hanning window sequence.
(ii) Design an analog Butterworth filter having -2dB passband attenuation at frequency of 20 rad/sec
and atleast -10db stopband attenuation at 30 rad/sec.
(i) Explain the possible types of impulse response for linear phase FIR filters.
(ii) Compare IIR and FIR filters.
(i) The desired response of a low-pass filter is
Hd(ejω) = e-j3ω, -3π/4 ≤ ω≤ 3π/4
0, 3π/4 < ω < π
Design FIR filter using Hamming window to determine H(ejω) for N=7.
(ii) Using impulse invariant transformation, convert the analog filter transfer function to
digital filter transfer function for T=1 second.
2
2.8 s +4.8 s+2.9
H ( s )= 2
(s+ 3)(s + s+ 0.85)
