Buggy Code

F0 =13;
T0 =1/F0;
Ts = 0.07;
t  = 0:Ts:13*T0;
x = real(exp(j*(2*pi*F0*t-pi/2)));
plot(t,x)

The above MATLAB code is supposed to output 13 cycles of a 13 Hz sine wave. However, it instead outputs this:

Skray hw2 buggy wave ECE301Fall2008mboutin.jpg

The problem is with the sampling rate Ts. Ts is .07, and the frequency of the sine wave is 13. 1/13 is .769. A sampling rate so close to the inverse of the frequency is not going to yield enough data points to give an accurate graph. Taking a much smaller sampling rate of .005 will give a better graph of the data. Below is the graph with a sampling rate of .005, overlaid with the original graph shown by circles.

Skray hw2 buggy wave overlaid ECE301Fall2008mboutin.jpg

And here is the proper wave output by itself:

Skray hw2 proper wave ECE301Fall2008mboutin.jpg

Here is the code to output the proper wave:

F0 =13;
T0 =1/F0;
Ts = 0.005;
t  = 0:Ts:13*T0;
x = real(exp(j*(2*pi*F0*t-pi/2)));
plot(t,x)

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva