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I am trying to learn about frequency domain and I am using audacity software. I selected a small YouTube video (link below):

https://www.youtube.com/watch?v=rGHrKkieqCY&ab_channel=PANKAJSAO

I converted it to .wav format using the link below: https://youtubeto.org/en/youtube-wav.html

When I imported this .wav file into my audacity and tried to analyze its frequency spectrum, I got a new frequency analysis window (as shown in attached snap). But I am unable to understand it as I have two confusions:

  1. In our books we saw frequency spectrum where zero frequency is at center and here in this plot zero frequency is at left.

  2. Why do we have here a negative sign with db values, what does that mean? -11 db has lowest magnitude/amplitude and 90 db has highest magnitude/amplitude or is it the opposite ?

enter image description here

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    $\begingroup$ Audacity adds functionality to make it a better tool for audio, and easier to use for people who aren't learning signal processing. If you are trying to learn signal processing theory, that functionality gets in the way. I suggest you use a mathematical analysis package. Python with numpy, scipy, and matplotlib is a complete scientific package that's hard to learn from scratch and easy to do projects ranging from medium sized to huge. Matlab spoon-feeds you the programming stuff, and costs a lot. Octave is a direct Matlab clone and is free. Scilab is a free, kissing cousin of Matlab. $\endgroup$
    – TimWescott
    Aug 11, 2022 at 14:59
  • $\begingroup$ "kissing cousin" w@T $\endgroup$ Jun 11, 2023 at 17:04

1 Answer 1

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  1. The frequency domain representation of a signal can be computed using the Fourier Transform. Practically the Fourier Transform is computed as the Discrete Fourier Transform (DFT) via a Fast Fourier transform (FFT) algorithm.
    • One of the properties of the DFT of a real-valued time signal (such as your .wav file) is that it is an even function of frequency: it is symmetric about $0$ (and spans the bandwidth $-f_s/2\,\texttt{Hz}$ to $f_s/2\,\texttt{Hz}$ , $f_s$ being the sampling frequency). This is what you're accustomed to seeing in your book.
    • Because it is symmetric, the information you get when using the DFT is redundant: the negative part is the flipped version of the positive part. Therefore we usually discard the negative part (from $-f_s/2\,\texttt{Hz}$ to $0\,\texttt{Hz}$). This is what you're seeing in the frequency analysis window. The negative part has been discarded, and the $0\,\texttt{Hz}$ frequency is now at the left.
  1. Per the manual:

The amplitudes are normalized such that a $0\,\texttt{dB}$ sine (pure tone) will be (approximately) $0\,\texttt{dB}$ on the graph

A $0\,\texttt{dB}$ sine (pure tone) would be a sine wave with amplitude $2$ (going from $-1.0$ to $1.0$ on your time window). As such, $-11\,\texttt{dB}$ is your peak magnitude (at $47\,\texttt{Hz}$). $-90 \,\texttt{dB}$ is the lowest.

  1. Adding a little side-note here: the software isn't computing a straight FFT of the signal. It's computing a Power Spectrum by averaging spectra computed on successive time frames of size Size. You're using Size = 1024, i.e. calculating the FFT on $1024$ points. This will give you $f_s$ / $N_{FFT}$ $= 48000$ / $1024 = 46.875\,\texttt{Hz}$ of frequency resolution. This resolution is probably ok for your purposes, but if you want higher resolution, you can increase the size of each block FFT (to $2048$ for example).
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