ELEC 320, Fall 1998
Prof. Rich Kozick

## Homework 4

Date Assigned: Monday, September 7, 1998
Date Due: Wednesday, September 9, 1998

Reminder: We will have Quiz 1 on Friday, September 11, 1998.

1. Suppose you need to design a filter for a voltage signal that has the form

v(t) = 0.05 cos(200 t) + 10 cos (20,000 t) volts

The signal component at frequency 200 rad/s is the desired signal, while the component at 20,000 rad/s is an undesired interference signal. The filter should pass the 200 rad/s component with near unity gain, and the interference at 20,000 rad/s should be attenuated by the filter so that its amplitude is at least 10 times smaller than the desired signal amplitude.
What order filter is required to achieve this? Explain your reasoning.

2. (a) Specify a circuit that performs as a band-stop filter. You do not have to analyze the cutoff frequency or do a full Bode plot, but explain why it operates as a band-stop filter.

(b) For each filter given in Problem 5 of Homework 3, determine the filter type (low-pass, high-pass, band-pass, or band-stop) and the filter order (first-order or second-order). You do not have to submit a solution for this question, but we will discuss the answer during class.

3. Consider a system that plays an audio tape at half-speed. Let x(t) represent the audio signal at full-speed, and y(t) be the output signal from the half-speed system. Assume x(t) begins at time t=0 and is defined for t>0.

1. Can the system be modeled as y(t) = x(2t), or y(t) = x(t/2), or neither?
2. Is the system linear? Is it time-invariant? Is it causal? Please explain.
3. Explain whether the system y(t) = x(2t) is linear, time-invariant, and causal.

4. For each of the following system classification properties, try to think of at least one example of a system with that property.

Linear, nonlinear, time-invariant, time-varying, memoryless (or static), with memory (dynamic), causal, non-causal.

Thank you.