Derive the relationship between DFT and DTFT.

Compute the IDFT of the sequence
2j -2j

Compute the four point DFT of the sequence using linear transformation matrix.

The first five points of 8 point DFT are 1 -1·2414j, 1 -0·414j, 0}. Find the remaining three points.

3. Draw the butterfly line diagram for 8 point DIT FFT calculations and briefly explain the algorithm.

4. What are twiddle factors for the DFT Also explain their significance.

5. Design a digital Chebyshev filter to meet the following specifications


0.707 1 0 w 0.25n
0.45n w

using bilinear transformation method.

6. Derive the relation to calculate the number of poles in digital Butterworth filter.

7. The desired frequency response of a low-pass filter is equal to

e^—j3w 3n/3
0

Design the filter using Hamming window function. Also find its frequency response.

What is meant by frequency warping effect? What is the cause of this effect?

What do you understand by Gibb's phenomenon Explain.

9. Realize the following function using least number of multipliers





10. Write short notes on any two of the following:

Chirp Z Transform

Impulse Invariance Method

Computation Efficiency of FFT