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The Discrete Fourier Transform (DFT) is a Fourier Transform that operates on a finite length, discrete signal (as opposed to a continuous signal, such as an analog signal) and is typically calculated using the Fast Fourier Transform (FFT) algorithm. What this means is that, just as the x-axis is time for a signal in the time-domain (namely 0sec, 1sec, 2sec.), the x-axis is frequency for a signal in the frequency-domain (namely 0Hz, 1Hz, 2Hz.). The Fourier Transform transforms the time-domain into the frequency-domain. The Fourier spectrum breaks down an audio wave into its frequency components, showing at what amplitude and at what phase each individual sine wave of a specific frequency must be in order to add up to the original audio wave. Just like any integer can be made by adding a different number of ones together, any audio signal can be made by adding sine waves with varying amplitudes, frequencies and phases together. If there are two of the same signals but they play at different times, then the difference in time is called the phase shift. If the frequency of the signal is high, then the pitch of the audio signal is high, and if the frequency is low, then the pitch is low. The frequency is equal to 1/period and is measured in cycles/second (Hertz). A sequence is periodic if it is composed of a repeating sub-sequence, with the length of the section called its period. The larger the number, the greater the amplitude, or loudness.
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A digital music signal is simply a changing value over time, stored as a sequence of numbers.