0.1 Lab 1 - discrete and continuous-time signals  (Page 3/5)

Start Matlab on your workstation and type the following sequence of commands.

This plot shows the discrete-time signal formed by computing the values of the function $sin\text{(}t/6\text{)}$ at points which are uniformly spaced at intervals of size 2.Notice that while $sin\text{(}t/6\text{)}$ is a continuous-time function, the sampled version of the signal, $sin\text{(}n/6\text{)}$ , is a discrete-time function.

A digital computer cannot store all points of a continuous-time signal since this would require an infinite amount of memory.It is, however, possible to plot a signal which looks like a continuous-time signal, by computing the value of the signal at closely spaced points in time,and then connecting the plotted points with lines. The Matlab plot function may be used to generate such plots.

Use the following sequence of commands to generate two continuous-time plots of the signal $sin\text{(}t/6\text{)}$ .

As you can see, it is important to have many pointsto make the signal appear smooth. But how many points are enough for numerical calculations?In the following sections we will examine the effect of the sampling interval on the accuracyof computations.

Numerical computation of continuous-time signals

For help on the following topics, click the corresponding link: MatLab Scripts , MatLab Functions , and the Subplot Command .

Background on numerical integration

To see the effects of using a different number of points to represent a continuous-time signal,write a Matlab function for numerically computing the integralof the function $si{n}^2\text{(}5t\text{)}$ over the interval $\text{[}0,2\pi \text{]}$ . The syntax of the function should be I=integ1(N) where $I$ is the result and $N$ is the number of rectanglesused to approximate the integral. This function should use the sum command and it should not contain any for loops!

Next write an m-file script that evaluates $I\left(N\right)$ for $1\le N\le 100$ , stores the result in a vector and plots the resulting vector as a function of $N$ . This m-file script may contain for loops.

Repeat this procedure for a second function J=integ2(N) which numerically computes the integral of $exp\left(t\right)$ on the interval $[0,1]$ .