# Confusions understanding frequency spectrum?

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

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 ?

• 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. Aug 11, 2022 at 14:59
• "kissing cousin" w@T Jun 11, 2023 at 17:04

• 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.
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).