Electronics > Beginners
how to interpret the magnitude of FFT
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lordvader88:
So what does a FFT do ? Does it take a waveform, and make a spectrum of the power over some frequency range like a spectrum analyzer ?
IDEngineer:

--- Quote from: lordvader88 on July 08, 2019, 03:32:04 pm ---So what does a FFT do ? Does it take a waveform, and make a spectrum of the power over some frequency range like a spectrum analyzer ?
--- End quote ---
The way I help people understand the FFT (more properly in this context, the DFT or Discrete Fourier Transform) is as follows:

Imagine a piano with its sounding board and all its tuned strings. If you play a sine wave nearby, the strings will resonate with the sine wave. Those strings tuned closest to the sine wave's frequency will resonate the best. Thus you could discern an input frequency by measuring the resonance of the strings. This is an example of mechanical coupling; the strings mechanically resonate based on their tuned frequency.

A more complex waveform, built up from multiple sine waves, would cause multiple piano strings to resonate. The intensity of the resonance would give you an indication of the spectral content at that string's frequency. You could then plot the strength of each string's resonance on a graph, giving you a representation like the spectrum analyzer you mentioned.

In the DFT, the discrete frequencies of the piano strings are represented by "bins". Each bin mathematically resonates when the analyzed signal has content at its "tuned frequency". If you had a sine wave centered on a single bin's frequency, analyzing that sine wave would result in that bin "resonating".

Like the piano example, a more complex waveform built up from multiple sine waves would cause multiple bins to "resonate". The intensity of each DFT bin gives you an indication of the spectral content at that bin's frequency. You can then plot the magnitude of each bin on a graph like a spectrum analyzer.

This is a vastly simplified explanation that leaves out a lot of details. For example, the "Discrete" aspect of the DFT is important: There are a finite number of bins, representing a finite number of frequencies, and so there will be always be intermediate frequencies "between the bins" that won't be perfectly represented. But hopefully this piano sounding board analogy will help you grok the basic concept of how the DFT works at a macro level. From here, you can go as deep as you'd like!
engineheat:
Thanks.

I've spent some effort trying to understand how to calibrate the FFT to get an accurate SPL measurement and get an A weighted decibel reading. But I wonder if this is even necessary if all I want to do is compare two signals? Say I have a classification task where I need to classify two different sound, one is from a drum and one is from a piano key. The two sounds have different peaks among the frequency range, or even if they have the same peak, the magnitude is different. I'm interested in things like "sound A has a magnitude at 4khz that's twice the magnitude at 2khz" and "sound B has the same magnitude at 4khz as 2khz". Knowing this will allow me to classify the sound and just using the raw FFT data without calibration would be enough right?

Assuming I use a mic with a flat frequency response, is the above approach for classification reasonable?
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