How can I visualise the effects of EQ as a curvature represented on a graph?

Question

I have just started diving into the magic world of EQ. Basically, I can hear what the effects are, and see them via a freq-analyser, however, what i'd really like is a way I can represent any sound whose frequencies across the entire spectrum is represented as a flatline, with any curves occurring on the graph being the direct result of the effects that the EQ is having.

So basically, any troughs/peaks in the graphs are not the frequencies themselves, but the mathematical difference of the original frequency, the amplification/attenuation of any given frequency of that sound.

By the way, I got this idea off an article: http://www.soundonsound.com/sos/1995_articles/mar95/eq.html so the genius

So the genius idea doesn't belong to me ;)

Answer 1

The fun thing about working in the frequency domain is that the maths are really simple. For example, the effect of an equalizer is completely independent of the signal you're feeding it, it's just a simple multiplication of the signal (in frequency domain) with the equalizer frequency response.

What I'm getting at is that any visual equalizer already exactly shows what you want. So, if you have an equalizer that has settings for attenuating different frequencies (e.g., the one from windows media player), and you draw a nice smooth line through the settings, you already have the plot you want! Again, this is completely independent* of the signal you're feeding it.

Now what if you have an equalizer that has some vaguely named knobs like low, mid and high? Then you have a bit of a problem. Although it's possible to create the plot you want (divide the Fourier transform of the original and the equalized sound, and take the absolute value - i.e., what JCPedroza was getting at), chances are that it will be a very, very ugly plot. This is because, especially in music, many frequencies will not be present in the signal (if someone's singing an E, you won't have a lot of F in your signal), but above method will still try and get a frequency response at the frequency of a hypothetical F note. The result: a completely unreadable plot. The only 'easy' way to get a nice plot is to average a bunch of white noise fed through your equalizer.

*Completely independent in theory. In practice, there are always inaccuracies.

Answer 2

You want to plot the transfer function or the frequency response of your system (in this case an audio signal processed by an equalizer).

Googling around I found tools like VST Plugin Analyzer and Deconvolver. You can find both here, and there's a tutorial on the former here.

If you are into coding you should be able to implement one yourself with a plotting library and an audio library. I remember doing something similar in Python, but it was a long time ago and can't remember many of the details. We used matplotlib for plotting plus other library to handle audio.