Audacity Forum

Hi there,

I'm carrying out Fourier analysis and synthesis on square and sawtooth waves as part of a university project, however, I've run into a problem and am unsure whether I have done something incorrectly or not. I've been effectively told "generate some waveforms and see what happens", so my knowledge of Fourier is still very limited.

Using FFT in Audacity, I was successful in building a 1 KHz square wave out of sin waves. However, when I attempted the sawtooth wave, I found that the resulting shape of my waveform was inverted (see picture below).



The top waveform is a 1 KHz sawtooth wave created using the tone generator.
The bottom wave is my reconstructed wave using the first 5 harmonics. As you can see, the shape is inverted.

Have I incorrectly analyzed the waveform or is something else happening here?

Mwhlr wrote:Have I incorrectly analyzed the waveform or is something else happening here?

Your analysis appears to be correct, but the starting phase for your sine waves is reversed (rotated 180 degrees).

Nyquist can be quite useful for playing with this sort of thing.
(also: http://wiki.audacityteam.org/wiki/Nyqui ... _Reference)

This code can be run in the "Nyquist Prompt" effect:

Here is the comparison between a measured sawtooth (256 Hz, FS = 8192) and the calculated values from Steve's code (in dB).