## EE 451

**Homework Assignment 5 **

Due Sept. 29, 2000

- 1.
- Problem 4.9 (a) (d) (f)

- 2.
- Problem 4.18

- 3.
- The Fourier transform of a low-pass filter will have a value of 1 for
low frequencies and a value of 0 for high frequencies:

Let
.

- (a)
- Find the impulse response of this discrete-time system by
taking the inverse Fourier transform of
.

- (b)
*h*[*n*] has an infinite number of terms, so cannot be implemented.
We can get an approximation of *h*[*n*] by taking a limited number of
terms. Take 101 terms of *h*[*n*], *n* = -50 ... +50. Print out
a `stem` plot of this truncated impulse response, *h*[*n*].

- (c)
- Take the Fourier transform of
*h*[*n*]. Plot the
frequency response
vs *f* and
vs
*f*.

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