ELEC 320, Fall 1998
Prof. Rich Kozick

## Homework 11

Date Assigned: Monday, September 28, 1998
Date Due: Friday, October 2, 1998

1. Lab 1: Remember that reports for Lab 1 are due at 9 AM on Wednesday, September 30.

2. Reading: For Wednesday and Friday, please review Section 1.2 on signals, with particular attention to the impulse function delta(t), step function u(t), and time-shifting operations on signals. Also read Sections 3.3 and 3.4 on convolution for continuous-time systems and signals.

3. Consider a linear, time-invariant, discrete-time system with impulse response h[n] plotted below. Plot the system output y[n] when the input is the sequence x[n] shown below.
Hint: y[n] = x[n] * h[n] where * denotes convolution!

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You can check your result using MATLAB and the conv command as follows: (you don't have to hand in your MATLAB check)

```>> h = [1.5, 1.5, 1.5];
>> x = [2, 2, 2, 2, 2];
>> y = conv(x, h);
>> n = 0:length(y)-1;
>> stem(n, y)
```

Please refer to Homework 10 for a note about on-line help in MATLAB.

4. Problem 3.4 in the text, for the signals x[n] and v[n] in Figure P3.4(b) only. Show all of the steps when you compute your answer on paper. Use the MATLAB conv command to check your results (but your MATLAB check does not need to be handed in).

5. For the function x(t) shown below, sketch x(t - 3), x(t + 3), x(-t), x(-t - 3), and x(-t + 3). Also sketch x(a - t) for an arbitrary number a.

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Thank you.