Prof. Rich Kozick
ELEC 320, Fall 1997

## Homework 5

Date Assigned: Friday, September 5, 1997
Date Due: Monday, September 8, 1997

Reminder: We will have Quiz 1 on Wednesday, September 10, 1997.

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. For each filter given in Problem 4 of Homework 4, determine the filter type (low-pass, high-pass, band-pass, or band-stop). Also determine the order of each filter (first-order or second-order). Explain your reasoning.

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.

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 classifications, 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 and have a good weekend.