Solve any one question fromQ.1(a,b,c) and Q.2(a,b)

1(a)
With the help of neat diagram explain the basic elements of DSP.

4 M

1(b)
Consider the analog \( X_a(t)3\cos 2000\Pi t+5\sin 6000\Pi t+10\cos 8000\Pi t. \)/

i) What is the Nyquist rate for this signal?

ii) If Sampling rate F

i) What is the Nyquist rate for this signal?

ii) If Sampling rate F

_{s}= 6000 samples/s. What is the discrete - time signal obatained after sampling?
4 M

1(c)
State and prove any two properties of DFT.

2 M

2(a)
Compute 8 point DFT of a sequence x(n) = {1 2 3 4 4 3 2 1} using Decimation In Time FFT algorithm.

8 M

2(b)
Explain the concept of orthogonality.

2 M

Solve any one question fromQ.3(a,b,c) and Q.4(a,b,c)

3(a)
What is the relationship between Z transform and DFT.

3 M

3(b)
Compute the DFT of the following sequence x(n) = {0 1 2 3}

4 M

3(c)
By using partial fraction method find the Inverse Z transform of \[X(z)\frac{Z^3}{\left ( z+1 \right )\left ( z-1 \right )}\]

3 M

4(a)
Show that the computational complexity is reduced if 32 point DFT is computed using Radix-2 DIT FFT algorithm.

3 M

4(b)
Compute the z transform and draw ROC of the following sequences.

i) X(n) = n u(n) for n ≥0

ii) X(n) = 2

i) X(n) = n u(n) for n ≥0

ii) X(n) = 2

^{(n-1) u(n-1)}
3 M

4(c)
Compute the Discrete Cosine Transform of the following sequence f(x) = { 1 2 4 7}

4 M

Solve any one question fromQ.5(a,b,c) and Q.6(a,b,c)

5(a)
The system transfer function of anlog filter is given by \(H(S)=\frac{s+0.1}{\left ( s+0.1 \right )^2+16} \)/ using bilinear transformation method, determine the transfer function of digital filter H(z) the resonant frequency is \[w_r=\frac{\pi }{2}.\]

8 M

5(b)
Explain the steps used for designing an IIR filter using bilinear transformation method (BLT). What is Wraping effect in BLT?

8 M

5(c)
What are the limitations of Impulse invariance method?

2 M

6(a)
Obtain direct from I and II realization of a system described by \[ y(n)-3/4 y(n-1)-1/2 y(n-2)+1/8 y(n-3) = x(n) + 5/4 x(n-2).

8 M

6(b)
A digital filter has specifications as:

Passband frequency = w

i) Impulse Invariance Technique is used for designing.

ii)Bilinear Transformation Method is used for designing.

Passband frequency = w

_{p}= 0.2π, Stopband frequency = w_{s}=0.3π What the corresponding specifications are for pass band and stop frequencies in analog domain ifi) Impulse Invariance Technique is used for designing.

ii)Bilinear Transformation Method is used for designing.

6 M

6(c)
Write a note on, " finite word length effect in IIR filter design".

4 M

Solve any one question fromQ.7(a,b) and Q.8(a,b)

7(a)
Compare FIR filter with IIR filter.

6 M

7(b)
Design FIR digital filter to approximate and ideal low pass filter with passband gain of unity, cut off frequency 850Hz and sampling frequency 5000 Hz. The length of impulse reponse should be 5. Use Hamming window.

10 M

8(a)
Explain the Gibb's Phenomenon.

6 M

8(b)
Design a linear phase FIR low pass filter using Hanning Window the frequency characteristics of the filter is given as

\[\begin{matrix} Hd(w)=e^{-j3w} &\text{FOR}-\frac{\pi }{4 }\leq w\leq \frac{\pi }{4} \\ =0 & \text{otherwise} \end{matrix}\]

\[\begin{matrix} Hd(w)=e^{-j3w} &\text{FOR}-\frac{\pi }{4 }\leq w\leq \frac{\pi }{4} \\ =0 & \text{otherwise} \end{matrix}\]

10 M

Solve any one question fromQ.9(a,b) and Q.10(a,b)

9(a)
Design a two stage decimator for the following specifications:

Sampling rate of an input signal 20kHz

Passband = 0 to 40 Hz

Transition band =40 to 50 Hz

Passband ripple = 0.02

Stopband ripple = 0.002

Sampling rate of an input signal 20kHz

Passband = 0 to 40 Hz

Transition band =40 to 50 Hz

Passband ripple = 0.02

Stopband ripple = 0.002

10 M

9(b)
Explain the application of DSP in Image processing.

6 M

10(a)
Draw the architectural block diagram and explain the important features of TMS 320C 67XXX series DSP processor.

8 M

10(b)
Explain the necessity of:

i) MAC unit

ii) Data Address Generators in Digital Signal Processors.

i) MAC unit

ii) Data Address Generators in Digital Signal Processors.

8 M

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