**[Total Time: 3 Hours]**

**[Total Marks: 80 M]
Note the following instructions.
1. Question No.1 is compulsory
2. Attempt any three questions from remaining five questions
3. Solve in total four questions
4. Assume suitable data wherever necessary, justify the same
5. Figures to the right indicate full marks.
**

1 a. Compare IIR and FIR digital filters** [4M]**

b. State and prove time shifting property of DFT** [4M]**

c. Compare general purpose and special purpose DSP processors **[4M]**

d. Explain limit cycles in IIR digital filters** [4M]**

e. A digital filter has the following impulse response identify the type of filter from pole zero plot. ℎ(𝑛) = 0.8 𝜕(𝑛) + 0.36(−0.8)𝑛−1𝑢(𝑛 − 1)** [4M]**

2 a. Using BLT method of IIR filter design. Design a digital Butterworth HPF, monotonic in passband with 3dB frequency of 1000 Hz and down at 10 dB at 350 Hz. The sampling frequency is 5000 Hz **[10M]**

b. Transform analog filter transfer function H(s) given below in to digital filter transfer function H(z) using Impulse Invariance Transformation method with T= 1 sec. 𝐻(𝑠) = 0.5(𝑠+4)/(𝑠+1) (𝑠+2) **[5M]**

c. Explain the effect of coefficient quantization (truncation and rounding) on IIR filter. **[5M]**

3 a. Design an FIR bandpass filter to meet following specification using frequency sampling method.** [8M]**

i. Cutoff Frequencies = 1000 Hz and 3000 Hz,

ii. Sampling Frequency = 8000 Hz,

iii. Length of filter N=7

b. The unit sample response of a system is h(n) = {1, 2} use overlap-save method of linear filtering to determine output sequence for the repeating input sequences x(n) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}** [7M]**

c. One of the zero of an antisymmetric linear phase FIR filter lies at z = 0.5, find the location of the other zeros and hence find the transfer function and impulse response of the filter. **[5M]**

4 a. For the sequences, x[n] ={ 1, 2, 4, 5}, p[n]={6, 3, 6, 9} & q(n) ={ 1, -2, 4,-5}

i. Find X[k] using DFT.

ii. Find P[k] using X[k] only.

iii. Find Q[k] using X[k] only.

where x[n], p[n], q[n] and X[k], P[k], Q[k] are DFT pairs respectively **[8M]**

b. Design a digital FIR low pass filter using Hamming window for following specification, Cutoff frequency= 500 Hz, Sampling frequency = 2000 Hz,

Order of filter = 10** [7M]**

c. Compare the truncation and rounding errors using Fixed point and Floating point representation **[5M]**

5 a. If x(n) = {1, 1, 2, 2, 3, 3, 4, 4 }, Find X(K) using DIF-FFT algorithm. Compare computational complexity of above algorithm with DFT. **[8M]**

b. Find DFT of the sample data sequence x(n) = { 1, 1, 2, 2, 3, 3} and compute the corresponding amplitude and phase spectrum **[7M]**

c. Explain DTMF detection using Gentzel algorithm **[5M]**

6. Write short notes on any Two **[20M]**

a. Effect of finite word length in digital filters.

b. Architecture of TMS320C67XX digital signal processor.

c. Application of DSP for Radar signal processing.

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