Thapar University 2006 B.Tech Electronics and Communications Engineering DIGITAL SIGNAL PROCESSING FOR COMMUNICATIONS - Question Paper

Thapar Institute of Engineering & Technology
B.Tech ECE (3rdYear)
Final Term exam
EC025 (DIGITAL SIGNAL PROCESSING FOR COMMUNICATIONS)

Question 1.2: What is application of Hilbert Transformer in the field of radar and speech signal processing?

(4)

Question 2.1: Consider an HR filter transfer function

h[_z]₌Li24

^lJ 1 + 3 z"¹

Obtain its Two-Band Decomposition using polyphase decomposition technique.

Question 2.2: Design a Decimator for the reduction of sampling rate of a signal from YlKHz to 400Hz (as shown in Fig. 1) for the following specifications.    (2)

Passband edge frequency F_p =180Hz    Passband ripple S_p = 0.002

Stopband edge frequency F_s - 200Hz    Stopband ripple S_t = 0.001

Fig. 1: Single-stage Dccimator.

Design Three-Stage Decimator with

M = M_x x M₂ x M₃ = 5 x 3 x 2 How Multistage Multirate Signal Processing helps in reducing the computational complexity?

Question 3.0: Consider a Linear Predictor of order two, described by =V-1 ^+/VV

where, the predictor coefficients and are selected to minimize the mean-square value of predictor error:

3.1) Show that the optimum values of the predictor coefficients are given by K =    and h_c2 =

1-P _ *,(1)

...... . R_x{2)

^{Pl =} M) ^Pl =(0)

3.2) Show that the minimum mean-square error equals

where, the variance <j\ = R_x (O).

Question 4.0: Using derivative method,

4.1) Derive the Continuous-Time Fourier Transform of following

_W
'2 n /2 (a) Square Function

4.2)    Derive the Discrete-Time Fourier Transform of y(n)= *(w)* w(). where, () is the Step Function in discrete-domain.

4.3)    What is relation between correlation and convolution?

Question 5.1: Determine the signal x(n), whose z-transform is given by    (3)

X[z] = log(l + az'¹)    \z\ > \a\

Question 5.2: Using z-transform, determine the Auto-Correlation Sequence of the signal

x(w) = aflu(),    -l<a<+l    (4)

Question 5.3: Describe the Goertzel Algorithm used to calculate DFT by the linear filtering approach. (5)

Question 6.1: Prove that the FIR filter has a linear phase if its unit sample response satisfies the condition h(n) = h(M -n-l) for n = 0, 1, 2, ... , M -1.    (4)

Question 6.2: Describe the Chirp-z Transform Algorithm used to calculate DFT.    (4)

Question 6.3: Design a highpass filter to meet the following specifications.    (4)

Cutoff frequency = 250Hz, Sampling frequency F_s = 1 KHz, and Filter length = 7.

Question 7.1: Design a lowpass filter for the following specifications.

di63)-and //,(*>)={(), j<\a>\<x    (5)

Use rectangular window W_R(n) = 1, 0 < n < 4

Question 7.2: Use Bilinear transformation to design a highpass digital filter using Butterworth approximation to meet the following specifications.

Stopband ripple 515dB

Passband edge = 150Hz    (7)

Passband attenuation > 1 dB Stopband edge = 100Hz Sampling frequency = 1 KHz

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