STUPIDSID
1 (a)
The first five points of eight point DFT of real valued signal are {0.25, 0.125 -j0.3018, 0, 0.125 -j0.0150, 0}. Determine the remaining three points.
5 M
1 (b)
Sketch the frequency response and identify the following filters based on their passband. \[ i) \ h(n) = \left \{1, - \dfrac {1}{2} \right \} \\
ii) \ H(z) = \dfrac {z^{-1}-a}{1-az^{-1}} \]
5 M
1 (c)
What is multirate DSP? State its applications.
5 M
1 (d)
An analog filter has transfer function \( H(s)= \dfrac {S+0.1}{(S+0.1)^1 + 16} \)
Determine transfer function of digital filter using bilinear transformation. The digital filter should have a specification of Ω, = π/2.
Determine transfer function of digital filter using bilinear transformation. The digital filter should have a specification of Ω, = π/2.
5 M
2 (a)
Compute DFT of sequence r(n)={1, 2, 2, 2, 1, 0, 0, 0} using DIT-FFT algorithm.
10 M
2 (b)
Explain the effects coefficients quantization in FIR filters.
10 M
3 (a)
Implement a two stage decimator for the following specification:
Sampling rate of the input signal = 20,000Hz,
Decimating factor M=100,
Passband=0 to 40Hz,
Passband ripple = 0.01,
Transition band = 40 to 50Hz.
Stop band ripple = 0.002.
Sampling rate of the input signal = 20,000Hz,
Decimating factor M=100,
Passband=0 to 40Hz,
Passband ripple = 0.01,
Transition band = 40 to 50Hz.
Stop band ripple = 0.002.
10 M
3 (b)
If x(n)={1+2j, 3+4j, 5+6j, 7+8j}. Find DFT X(k) using DIF-FFT algorithm.
10 M
4 (a)
Explain upsampling process in detail and derive for input-output relationship in time domain and frequency domain.
10 M
4 (b)
Obtain cascade and parallel realization structures for the system described by y(n)= -0.1y(n-1) + 0.72y(n-2) + 0.7x(n) - 0.252 x(n-1).
10 M
5 (a)
Design a FIR digital filter using windo method for following specifications \[ \begin {align*} H(e^{j\omega}) &= e^{-j3\omega} & 0\le |\omega | \le \dfrac {3\pi}{4} \\ &=0 & \text{otherwise } \ \ \ \end{align*} \] Use Hamming window of length 7.
10 M
5 (b)
Design a digital low pass IIR Butterworth filter for the following specification
Use bilinear transformation.
| Passband ripple | : ≤1 dB |
| Passband edge | : 4 KHz |
| Stopband attenuation | : 40 dB |
| Stop edge | : 8 KHz |
| Sampling Rate | : 24 KHz |
Use bilinear transformation.
10 M
Write a short note on.
6 (a) (i)
Dual tone multi frequency signal detection.
5 M
6 (a) (ii)
Different methods for digital signal synthesis.
5 M
6 (b)
Determine the zeros of the following FIR systems and indicate whether the system is minimum phase, maximum phase or mixed phase, \[ i) \ H_1 (z)= 6+z^{-1}- 6z^{-2} \\
ii) \ H_2 (z)= 1-z^{-1} - 6z^{-2} \\
iii) \ H_3 (z) = 1-\dfrac {5}{2}z^{-1} - \dfrac {3}{2}z^{-2}\\
iv) \ H_4 (z) = 1-\dfrac {5}{2}z^{-1} - \dfrac {2}{3}z^{-2} \] Comment on stability of minimum and maximum phase system.
10 M
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