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What is a FFT?
FFT stands for Fast Fourier Transform. Most computer software that measures noise and distortion or other properties of signals is based on the Fast Fourier Transform. Equipment or programs based on the Fast Fourier transform are called FFT's.
A famous Napoleanic-era French mathematician and public administrator named Joseph Fourier (1769-1830) invented the Fourier Transform. Engineers later realized that it was useful for the purpose of converting data taken in the form of a series of instantaneous signal intensities, taken at sucessive points in time; into a listing of the intensities of the various tones or frequencies that are contained in that data.
In other words, the Fourier Transform is a way to convert information about a signal, taken in the time domain, into data about the same signal, in the frequency domain. The Fourier Transform has an inverse, and the Inverse Fourier Transform takes data from the frequency domain to the time domain. The Fourier transform is also useful in optics because it transforms the spatial properties of images into to frequencies.
Fourier's Transform is a valuable analytical tool because it allows breaking a complex signal down into a collection of simple signals. When applied to two complex signals, comparing the properties of the two resulting collections of simple signals is a useful way to analyse the similarities and differences between the two signals.
For example, distortion adds erronious tone(s) related to the input signal, and changes the relative size and timing of the tone(s) that are already present in the input signal. The Fourier transform of the input signal is a list of pure tones and their timing and intensity as they appear in the input signal. The Fourier transform of the output signal is a list of pure tones and their intensity and timing, as they appear in the output signal. By comparing the two lists of the intensities of the pure tones in the input and output signals, the kind and size of errors can be determined, and put into a list of differences.
Because the list of differences includes information about the frequencies at which any errors occur, it can give insights into the physical causes of errors. For example, if an input signal at a high frequency creates more distortion than one at a low frequency, this is probably because the circuit is physically less efficient at handling high frequencies. The corrective action would probably involve selecting parts or parameters to improve the circuit's efficiency at high frequencies.
Fourier's transform is defined as a an infinite sum or mathematical Integral. Infinite sums are a little difficult to apply to real world data because real world data is finite. Infinite sums can be estimated, mathematically, for real world data, but this is a more time consuming process.
In the late 50's and early 60's mathematicians and engineers began to write about something they called the Discrete Fourier Transform that was far easier and quicker to compute. The Discrete Fourier Transform was called the Fast Fourier Transform and the latter name for it is far more popular.
Many poorly-informed popular writers have wrongly claimed that using pure tones is not a reasonable way to judge the performance of audio equipment. Today, music is broken down into information about pure tones, and then reconstructed back into music, from this information; often with very pleasing and recognizable results. This process is called Perceptual Coding.
All music is just a collection of pure tones. The size of some of these tones may be small, and their duration may be short. But, by the standards of modern computers, they are very manageable. Therefore, pure tones used properly, can be used to accurately judge the ability of equipment to reproduce music.
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