Asked by David
on 29 Dec 2012

Hi guys. I am struggling with a homework question.

*A triangular wave with period T may be written as: 1/(2n+1)^2 * cos((2n+1)*w0*t) (this is a series, n starts at 0 and goes on until infinity). where w0 = 2pi/T. This wave form is sampled, with a sampling time of TS = T/200, to yield the sampled signal x(n).

Use MATLAB to demonstrate how the series converges to the triangular wave.

Generate a plot(properly labelled) with 6, 10 and 30 terms for a value of T = 2.*

The code i inputted into matlab is

t=2; Ts=t/200; w=(2*pi)/t; n=0:9999; x=((2*n+1).^-2).*(cos((2*n+1)*w*Ts)); plot(x)

When i plot this it doesn't give a triangular wave. I must have done something wrong or missed a detail. Any help would be appreciated.

Thank you very much

Answer by Matt J
on 29 Dec 2012

Edited by Matt J
on 29 Dec 2012

- You evaluate x(t) only at a single point t=Ts. You're supposed to evaluate at many sampling times, t, spaced apart by Ts.
- You haven't summed over n.
- You will make life easier on yourself (and on us, and on your graders) if you define T, Ts, and t in your code the same way as the homework exercise defines them. Instead, your code changes T to t.

David
on 1 Jan 2013

Using this code i do get a triangular wave but when i plot for n=10,30 terms the graph doesn't really change much.

n=0; T=2; Ts=T/200; t=-T/2 : Ts : T/2; w=(2*pi)/T; s = 0; for n = 0 : 5 s = s + ((2*n+1)^-2) * (cos((2*n+1)*w*t)); end plot(t,s)

Is this the correct code to demonstrate how the series converges to a triangular wave? and do i just use new number of n terms to complete question 2?

I really do appreciate the help

Image Analyst
on 1 Jan 2013

Try it like this:

n=0; T=2; Ts=T/200; t=-T/2 : Ts : T/2; w=(2*pi)/T; s = 0; figure; maxTerms = 6; % also use 10 and 30 for n = 0 : maxTerms - 1 s = s + ((2*n+1)^-2) * (cos((2*n+1)*w*t)); end % Make wave start at 0 s = s - s(1); plot(t,s) grid on; hold on; maxTerms = 10; for n = 0 : maxTerms - 1 s = s + ((2*n+1)^-2) * (cos((2*n+1)*w*t)); end % Make wave start at 0 s = s - s(1); plot(t,s) maxTerms = 30; for n = 0 : maxTerms - 1 s = s + ((2*n+1)^-2) * (cos((2*n+1)*w*t)); end % Make wave start at 0 s = s - s(1); plot(t,s)

Matt J
on 1 Jan 2013

**Using this code i do get a triangular wave but when i plot for n=10,30 terms the graph doesn't really change much.**

Looks fine to me. The difference between nmax=10 and nmax=30 is subtle, but I still do see a noticeable sharpening of the triangle. At some point, i.e., as convergence occurs, it is supposed to stop changing. visibly

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