## EE 451

**Homework Assignment 7 **

Due Oct. 11, 2000

- Problem 5.1.
- Problem 5.8.
- Problem 5.9.
- Problem 5.14.
- Problem 5.17.
- 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.
- If the overlap-save method is used, what is the minimum number of
256-point DFTs and the minumum number of 256-point inverse DFTs needed to
implement the convolution for the entire 10,000-point sequence? Justify your
answer.
- If the overlap-add method is used, what is the minimum number of
256-point DFTs and the minumum number of 256-point inverse DFTs needed to
implement the convolution for the entire 10,000-point sequence? Justify your
answer.
- 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.

*
Bill Rison,
<rison@ee.nmt.edu >
*