FFT Analysis for Dummies Options

[Ethan Winer]

Folks,

I'd like to learn more about FFTs. I'm not a math guy, so I imagine I'll never fully understand all the nuances. But I'd like to try anyway. I understand the general concept, that an FFT shows how much energy is present at different frequencies. What I'd like to know is how to set the various parameters such as FFT Size and Overlap, when to use the different types of window smoothing and why, and so forth. Below is a list of settings in the Rightmark FFT analyzer with my associated questions, and hopefully this is a good place to start.

FFT Size: I understand that the higher the number, the better the frequency resolution. So why is this
even adjustable? Why not just use the highest resolution possible automatically?

Zero Padding: This ranges from None through 8x. What does this do?

FFT Overlap: What is this for, and when would you use higher or lower values?

FFT Window: I recognize some of the names, but have no idea when or why one would select these choices.

Kaiser Window beta: I have no idea what this does either.

I noticed that Sound Forge lets you pick the number of slices to show. What are slices and why is more than
one needed to analyze a Wave file?

I realize this is a lot to ask! If anyone knows of a good newbie-level tutorial that explains this in plain English with minimal math, I'd love to see it. Everything I've found through Google starts right in with math that's way over my head.

--Ethan

[benski]

Answering a bit more than your question asks, for anyone else who might be interested in this thread.

A transform is just a different way of representing the same set of data. If we have three samples, 4, 7 and 12, we could use a polynomial transform and use transformed coefficients of 4, 2, 1 and recreate the original samples through the equation a + b * x + c * x^2 by plugging in x for each sample (f(0) = 4, f(1) = 7, f(2) = 12). We havn't stored any less or any more data by using the transform rather than the samples, and we can change between them without loss.

A fourier transform is the same thing, but the equation to recreate the samples is a + b*sin(x) + c*cos(x) + d*sin(2x) + e*cos(2x) + ...
Taking the fourier transform is done by solving a giant system of equations to determine the correct coefficients to recreate the original samples out of this equation.
The fourier transform has the nice property that it it transforms the sample data into a representation that models the human ear (and other physical systems) very well.

When we take the FT (via FFT or DFT) of a large audio file, we are going to get coefficients representing different frequency bands. Unfortunately, this information gives us only the average energy of each frequency band, not the precise occurrence of the frequency within the song. If you had a weird high-pitch noise in some small section of the song, you could see it in the spectrograph, but would have no idea where it occurs. Just as looking at the streaming of audio samples gives you "time" data but no frequency information. The frequency coefficients of a fourier transform give you "frequency" data but no time information.

To work around this issue, we take the FT of sub-sections of the song called windows. A smaller window gives us less frequency bands, but if we see the weird high-pitched noise, at least we've narrowed it down to the current window. In the FT lingo, you can tradeoff "time resolution" and "frequency resolution" by using smaller or larger windows of audio. In Sound Forge, "FFT Size" corresponds to window size. At the extreme smaller end of window sizes, you have something called "Short Time Fourier Transform" which is often doing an FFT with windows of 4 samples. Wavelets are used when time and frequency resolution need to be adjusted more precisely, but that's a conversation for another day

When you see a spectrogram (2D spectrograph over time), it is a series of windowed FTs. Each vertical "strip" is one window.

Windowing the audio, however, causes an annoying artifact. If you were to play the sub-section of audio out of your speakers, you'd likely get a 'click' at the beginning and the end since they don't occur at zero crossings. It shows up as noise in the spectrograph just like it shows up as noise on the speakers. And because you can't tell "where" the noise occurs within the window, there's no way to isolate it out. You can see this phenomenon in low bitrate video as "blocking" artifacts - same reason. A windowing function is using to avoid these blocking artifacts. Conceptually, it fades in the start of the window and fades out the end of the window.

But as you can imagine, a windowing function is also destroying out data. This is where overlap comes in. If we let the windows overlap each other - e.g. first window is samples 0 through 1023 and the second window is samples 512 through 1535, we can avoid destroying the data. This is because the audio we "faded out" during the current window becomes part of the "fade in" of the next window. The downside of the windowing function is that the data has "smeared" itself across two windows. Different windowing functions change the amount of smear, allowing a trade-off between blocking artifacts and smear.

Hope that helps.

This post has been edited by benski: Mar 28 2010, 17:04

[Ethan Winer]

Okay, I have a few quick questions:

In Sound Forge I can select a portion of a Wave file for analysis, but I see no equivalent feature in the Rightmark analyzer. Is there a way to do that? If not, where in the file does Rightmark grab the specified number of samples to analyze?

Let's say I have a long wave file and I load it into Sound Forge and select a 5-second section. I understand that the FFT Size is the number of samples to analyze. But if my highlighted section is 5 seconds long, from where does Sound Forge take those samples? Are they contiguous? Does it skip every third sample so the total number (say, 65,536) starts at the beginning of the highlighted area and ends at the end? I realize the total number of samples dictates the lowest frequency that can be read, so that implies contiguous.

I have other questions, but I won't overload y'all for now. Also, assume that the two reasons I want to use FFT are:

1) To measure the frequency response of something, for example after passing white or pink noise through it.

2) To see the spectral content in a music file, as if I were to try to apply EQ in one audio file to match another as Harbal does. I'm not interested in doing such EQ matching! But I might want to know what frequencies are present in a music file and in what amounts.

--Ethan

[Arnold B. Kruege...]

Okay, I have a few quick questions:

In Sound Forge I can select a portion of a Wave file for analysis, but I see no equivalent feature in the Rightmark analyzer. Is there a way to do that? If not, where in the file does Rightmark grab the specified number of samples to analyze?

You'd need a waveform screen to do that. I see none in RMAA. The assmuption is that you edited the data before you ran the analysis.

Let's say I have a long wave file and I load it into Sound Forge and select a 5-second section. I understand that the FFT Size is the number of samples to analyze. But if my highlighted section is 5 seconds long, from where does Sound Forge take those samples?

If the sample is larger than the size of the FFT, then the program walks usually down the wave, repeating the FFT over and over again on each chunk, and averaging the spectral information.

Are they contiguous?

Not unless the chunks are overlapping. Soem programs let you specify overalp

Does it skip every third sample so the total number (say, 65,536) starts at the beginning of the highlighted area and ends at the end?

No. That would give you a FFT of a different wave. The dopped samples would have the effect of changing the frequency of the wave you were analyzing.

I have other questions, but I won't overload y'all for now. Also, assume that the two reasons I want to use FFT are:

1) To measure the frequency response of something, for example after passing white or pink noise through it.

Right. This only works easily if the test signal is in some sense flat. The good news is that white and pink noise are in some sense flat. This also works with multitones, if you are willing to look at a FR curve that is a series of peaks that are supposed to be the same height.

2) To see the spectral content in a music file, as if I were to try to apply EQ in one audio file to match another as Harbal does. I'm not interested in doing such EQ matching! But I might want to know what frequencies are present in a music file and in what amounts.

IME Eq is something you always apply by ear, unless you have some very special technical purpose.