Introduction to Fourier Series

[thrx]

YOU'RE AMAZING! I've been through a lot of classes involving linear systems and calculus and never had such a clear helpful explanation!

[alexander]

Thanks for the musical application of the Fourier Series. Now we can see tangible and real world applications of this mathematical engineering tool/concept..

[ocheejembi]

Thanks for this. I went through an entire degree knowing how to calculate Fourier Series and Transforms but not why.

[DarrylMorrell]

@RoguePianistTetsuo The voltage is proportional to the change in air pressure produced by the sound wave as it passes by the microphone. So the Y axis is proportional to changes in pressure. I used Matlab to do the graphs; I actually sampled synthesized flute and trumpet waveforms, then used the DFT to get the Fourier Series coefficients. I do not know of any software that would convert from sampled signals to functions.

[robFFFtrumpet]

One thing I may add about the two samples is the the flute is a solo pitch whereas the trumpet is at least 3 octaves. That may compromise the actual waveform.

[DarrylMorrell]

@avbad12 The Y axis in these plots is proportional to the voltage that would be produced by a microphone picking up these sound signals. The X axis is time.

[Chausies]

You said the Y axiz is proportional tot he voltage a mic would produce picking up those sound signals. What physical value of the flutes sound wave would that correspond to? The amplitude or...what?

And also, what program did you use to analyze the sound signals of the flute and the trumpet, getting the graphs of their sound waves and perhaps getting functions for them? Thanks!

[DarrylMorrell]

Sorry to not be clearer. By “adding up the harmonics”, I meant that you use the amplitude and phase given by the Fourier series coefficients to get a sinusoidal waveform for the fundamental frequency, one for twice the fundamental frequency, and so on. Then you add these waveforms together (as described in the last half of the video “Signal Operations: Scaling and Addition”).

[ahmed.ea.abdalla]

How do I sketch the phase?
Thank you for the Amazing videos.

[mauroprovatos]

'adding up the harmonics', meaning you add the amplitudtes?

[avbad]

Why does the first graph of the trumpet and the flute look the way it does? what is the y axis?

[MheeMid]

That's a trumpet with a mute and oboe, not flute! but excellent excellent explanations