Compute the N-point DFT of each of the following sequences <img src='./qimages/10963-1a.jpg'>

1.(b) Prove that linear convolution is obtained using circular convolution property of DFT.

2. Explain in brief, the method to reduce complexity computation of FFT. Give practical consideration in reducing memory size for storage of coefficients, and computation time.

3.(a) Determine IDFT of the sequence 1 1-j}.

3.(b) A 4-point DFT of sampled data sequence 1}is 2 Verify


(ii)

4. If 0 n obtain using Decimation-in-frequency FFT algorithm.

5. Determine the total number of twiddle factors required to compute N-point DFT using Radix-2 Decimation-in-time FFT algorithm and compare it with that of direct computation of N-point DFT.

6. The transfer function of an analog filter is with Ts 0.1 sec. Design the digital IIR filter using BLT (Bilinear Transformation Method).

7. Find the order and cut-off frequency of a digital Butterworth filter with the following specification: <img src='./qimages/10963-7.jpg'>

Use impulse invariance method. Draw its poles also.

8. Design a digital FIR filter with <img src='./qimages/10963-8.jpg'>

Use Hamming window with N 7. Also draw the frequency response.

9. Compare the frequency domain characteristics of difference window functions used in design of FIR filters.

10. Write short notes on any two of the following: Overlap-Save Method
Lattice and Parallel Realization for Discrete Time Systems
Goertzel Algorithm