FFT Size
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Here comes an in depth article about FFT-size as used in Reaper
Contents |
In short
FFT (Fast Fourier Transform) is a algorithm used for
Theoretical understanding
"The FFT allows users to obtain the spectral makeup of an audio signal, obtain the decibels of its various frequencies, or obtain the intensity of its various frequencies. Spectral viewers, Equalizers, or VU-Meters may all use the FFT in order to display their results. The difference between them then depends upon one of a couple of equations that take the real and imaginary components of the FFT, and return either the intensity or decibel levels to be used in the graphed result." [1]
"The way the FFT works is fairly straightforward. It takes a chunk of time called a frame (a certain number of samples) and considers that chunk to be a single period of a repeating waveform. The reason that this works is that most sounds are "locally stationary," that is they look like envelopes (no, just kidding).What we mean is that over any short period of time, the sound really does look like a regularly repeating function. " [2]
DFT, FFT and IFFT
"The most common tools used to perform Fourier Analysis and Synthesis are called the Fast Fourier Transform (FFT) and the Inverse Fast Fourier Transform (IFFT). The FFT and IFFT are optimized (very fast) computer based algorithms that perform a generalized mathematical process called the Discrete Fourier Transform (DFT). The DFT is the actual mathematical transformation that the data go through when converted from one domain to another (time to frequency). Basically, the DFT is just a slow version of the FFT, too slow for our impatient ears and brains!
FFTs, IFFTs, and DFTs became really important to a lot of disciplines when engineers figured out how to take samples fast enough to generate enough (lots and lots!) data to recreate sound and other analog phenomena digitally. Remember, they don't just work on sounds, they work on any continuous signal (images, radio waves, seismographic data, heck, even the stock market — see, we told you this would be useful!)." [3]
"One of the main drawbacks of FFTs is that the frequency bins are linear. For example, if we have a bin width of 43Hz (which will be a result of dividing Nyquist frequency by the FFT frame size!), then we have bins from 0–43Hz, 43–86Hz, 86–129Hz, etc" [4]
Practical approach
"FFT processing always has a tradeoff between time resolution vs frequency resolution. i.e. either your transients get smeared, or your frequency control gets mangled. there's usually a happy medium, but it's almost always dependent on what you're working on (e.g. what works good for bass doesn't work so well for drums)." dub3000
"The FFT size should affect the performance (and dropouts), but it shouldn't affect how the sound actually sounds." Justin on FFT and ReaVerb
Reaper usage
External links
Music and Computers (book), toc: http://music.dartmouth.edu/~book/MATCpages/tableofcontents.html
