1. Problem 5.1

2. Problem 5.8

3. Problem 5.9

4. Problem 5.14

5. Problem 5.17

6. We want to implement the linear convolution of a 10,000-point sequence with an FIR impulse response that is 100 points long. The convolution is to be implemented by using DFTs and inverse DFTs of length 256.

(a) If the overlap-save method is used, what is the minimum number of 256-point DTFs and the minumum number of 256-point inverse DFTs needed to implement the convolution for the entire 10,000-point sequence? Justify your answer.

(b) If the overlap-add method is used, what is the minimum number of 256-point DTFs and the minumum number of 256-point inverse DFTs needed to implement the convolution for the entire 10,000-point sequence? Justify your answer.

(c) We will see in Chapter 6 that when N is a power of 2, an N-point DFT or inverse DFT requires (N/2) log_{2} N complex multiplications and N log_{2} N complex additions. For the same filter and impulse response length considered in (a) and (b), compare the number of arithmetic operations (multiplications and additions) required in the overlap-save method, overlap-add method, and direct convolution.