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 DFT s and inverse DFT s of length 256.
(a) If the overlap-add method is used, what is the minimum number of 256-poinst DFTs and the minimum number of 256-point inverse DFT s needed to implement the convolution for the entire 10,000-point sequence? Justify your answer.
(b) If the overlap-save method is used, what is the minimum number of 256-point DFT s and the minimum number of 256-point inverse DFT s needed to implement the convolution for the entire 10,000-point sequence? Justify your answer.
(c) We will see in Chapter 9 that when N is a power of 2, an N-point DFT or inverse DFT requires (N/2) log2 N complex multiplications and N log2 N complex additions. For the same filter and impulse response length considered in parts (a) and (b), compare the number of arithmetic operations (multiplications and additions) required in the overlap-add method, the overlap-save method, and direct convolution.