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Archive for June, 2009

Frequency power spectrum of Sine, Square, Sawtooth, and Triangle Waveforms

June 22, 2009 1 comment

Today I came across an interesting MATLAB code example today from the University of Maryland: http://terpconnect.umd.edu/~toh/spectrum/HarmonicAnalysis.html. Prof. Tom O’Haver did a wonderful job with this example, but I had some problems with MATLAB crashing while running it. The program may be more resource-intensive than it appears.

My screenshots can be seen in a Picasa web album for higher resolution here: http://picasaweb.google.com/kruckenberg.1/FFTOfWaveformPower

Sine wave:
The frequency analysis of a basic sine wave shows that it consists of only a single frequency at 250 Hz.

Square wave:

A square wave with the same frequency has its highest peak at the fundamental frequency and the power is reduced by 1/4 at each odd harmonic of the fundamental frequency.

Sawtooth Wave:

A sawtooth wave includes both odd and even harmonics, and the power reduces by half at each harmonic.

Triangle Wave:

A triangle wave has a similar set of harmonic frequencies to a square wave (odd harmonics), but each one is distributed over a wider range rather than focused at a specific frequency. At each odd harmonic, the power is reduced significantly.

A triangle wave was not included in the original post, but I added one for my own purposes. In MATLAB, a triangle wave is created using the sawtooth function as shown:

y=sawtooth((f1+f2/100)*x,.5);

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Categories: Math problems, PC Software

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