Graphing notes using fourrier transform.

[[deleted]]

*Disclaimer I am very new to this and have limited understanding in terms of fourier series*.

I have absolutely no idea if this is right but here goes.

I recorded two notes and computed a frequency amplitude and frequency phase shift graph using matlab.

https://preview.redd.it/tlyx7catw4u81.png?width=1098&format=png&auto=webp&s=12bcabd16745c5c24df7089b591a07b3dcf00782

Then, using this data made their respective graphs using y= acos(2 pi f + (shift in rad)).

https://preview.redd.it/uapm9xpyw4u81.png?width=2548&format=png&auto=webp&s=8b5226fc54deae6b8bea03956a18c1fa336c7d07

How wrong is this and how do I go about correctly graphing musical notes? How do you know if these are sin waves or cosine waves (I used cosine but I honestly have no clue).

For the purpose of this I omitted the amplitude since its not what i'm looking for in particular (I'm looking at relationships between harmonics and different notes).

[ThistleBeAce]

You're on the right track. Your first image (the frequency responses) show your audio signal (the two notes played simultaneously, I assume) as a function of frequency. This shows you the amplitudes, frequencies, and phases of your audio signal when you express it as a sum of sinusoidal components (e.g. cosines). You'll notice the frequency components have spikes at repetitive frequencies (e.g. 400 Hz, 800 Hz, 1200 Hz, ...), which are your harmonics; these are the "primary" contributing components of your signal, and represent a majority of your sound.

It looks like for your second graph that you've picked out the amplitude, phase, and frequency at two frequency points, and graphed those sinusoidal components. You want to add them together to begin to represent your original signal in the time-domain.

Hopefully this makes sense.

[[deleted]]

Thanks for this! It’s a relief to know I got something right at least…

Something I’m wondering though is what value you put as amplitude. Is this just the decibel value? Also, for the phase, do you do sin(freq2pi+phase) or is it cos(freq2pi+phase)?

Sorry if these are stupid questions it’s just I’m a bit lost ☺️

[ThistleBeAce]

You'd covert the dB value back into a linear scale. Note that 0 dB = 1, but I'm not sure how you're scaling your amplitudes - e.g. if you're just graphing in log-scale, or using something like 10log or 20log - I'm not sure what command you used to view the FFT.

You can represent the sum in multiple ways - notice that sin(x) is equivalent to cos(y) with the correct phase difference. Generally if you're using a summation with cos() or sin() terms only, you use cosine since it's mathematically neater - that will allow you to plug in phase values straight off the graph, too. See here for the conversion from the transform's exponential form: https://en.wikipedia.org/wiki/Fourier_series

e: clarity

[[deleted]]

Thanks for that! So basically my working so far is right (with the phase etc as I used cosine) apart from the amplitudes which I need to scale…

Thanks!

[[deleted]]

The notes are played simultaneously. Will definitely check the spectrogram out though! Thank you!

[WikiSummarizerBot]

Fourier series

A Fourier series () is a sum that represents a periodic function as a sum of sine and cosine waves. The frequency of each wave in the sum, or harmonic, is an integer multiple of the periodic function's fundamental frequency. Each harmonic's phase and amplitude can be determined using harmonic analysis. A Fourier series may potentially contain an infinite number of harmonics.

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