ELEC 320, Fall 1998
Prof. Rich Kozick
Date Assigned: Monday, September 7, 1998
Date Due: Wednesday, September 9, 1998
Reminder: We will have Quiz 1 on Friday, September 11, 1998.
- 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
What order filter is required to achieve this?
Explain your reasoning.
- (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.
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.
- Can the system be modeled as y(t) = x(2t), or
y(t) = x(t/2), or neither?
- Is the system linear? Is it time-invariant? Is it causal?
- Explain whether the system y(t) = x(2t) is linear,
time-invariant, and causal.
- 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.