ELEC 320, Fall 1998

Prof. Rich Kozick

Prof. Rich Kozick

** 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 signal amplitude.

**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? Please explain.
- Explain whether the system
*y(t) = x(2t)*is linear, time-invariant, and causal.

- Can the system be modeled as
- 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.