ELEC 320, Fall 1998
Prof. Rich Kozick

## Homework 9

Date Assigned: Wednesday, September 23, 1998
Date Due: Friday, September 25, 1998
** DUE DATE CHANGED TO MONDAY, SEPTEMBER 28 **

1. Reading: Please read Sections 3.1 and 3.2 for Friday. The topic is convolution for discrete-time systems and signals.

2. Lab 1: Reports are due at 9 AM on Wednesday, September 30.

NOTE THIS IS A CHANGE FROM THE PREVIOUSLY ANNOUNCED DUE DATE. I WANT TO BE FAIR AND ALLOW ALL STUDENTS THE OPPORTUNITY TO HAVE ONE MORE LAB SESSION (LAB 2) TO RESOLVE ANY FILTER DESIGN ISSUES AND TO DISCUSS A DRAFT OF THEIR REPORT WITH ME.

Each student should write a report individually. Equations and circuit diagrams can be written by hand -- it is much more important to fully and clearly explain your design approach and results.

I suggest that you show me a draft of your report (at least for the low-pass filter) before you submit your final report. Needless to say, this lab spanned several weeks, so the report will count significantly toward your lab grade in this course.

3. Please do Problem 3.1 in the text. Note that the "unit pulse response" or "impulse response" h[n] is the system output when the system input is the "unit pulse" or "impulse" delta[n], where delta[0] = 1 and delta[n] = 0 for all other values of n.

You should use the given difference equation with the input x[n] = delta[n], and compute the output y[n] = h[n]. Assume all initial conditions are equal to zero. Note that the difference equation for this system can be written equivalently as

y[n] - 2 y[n-1] + y[n-2] = x[n-1] - x[n-2]

Please explain why this difference equation is equivalent to the difference equation in the text.

Thank you.