Search code examples
iosaudiofftaccelerate-frameworkvdsp

What actually does the size of FFT mean

  1. While using FFT sample code from Apple documentation, what actually does the N, log2n, n and nOver2 mean?
  2. Does N refer to the window size of the fft or the whole number of samples in a given audio, and
  3. how do I calculate N from an audio file?
  4. how are they related to the audio sampling rate i.e. 44.1kHz?
  5. What would be the FFT frame size in this code?

Code:

/* Set the size of FFT. */
log2n = N;
n = 1 << log2n;

stride = 1;
nOver2 = n / 2;

printf("1D real FFT of length log2 ( %d ) = %d\n\n", n, log2n);

/* Allocate memory for the input operands and check its availability,
 * use the vector version to get 16-byte alignment. */
A.realp = (float *) malloc(nOver2 * sizeof(float));
A.imagp = (float *) malloc(nOver2 * sizeof(float));
originalReal = (float *) malloc(n * sizeof(float));
obtainedReal = (float *) malloc(n * sizeof(float));
Solution
    1. N or n typically refers to the number of elements. log2n is the base-two logarithm of n. (The base-two logarithm of 32 is 5.) nOver2 is n/2, n divided by two.
    2. In the context of an FFT, n is the number of samples being fed into the FFT.
    3. n is usually determined by a variety of constraints. You want more samples to provide a better quality result, but you do not want so many samples that processing takes up a lot of computer time or that the result is not available until so late that the user notices a lag. Usually, it is not the length of an audio file that determines the size. Rather, you design a “window” that you will use for processing, then you read samples from the audio file into a buffer big enough to hold your window, then you process the buffer, then you repeat with more samples from the file. Repetitions continue until the entire file is processed.
    4. A higher audio sampling rate means there will be more samples in a given period of time. E.g., if you want to keep your window under 1/30th of a second, then a 44.1 kHz sampling rate will have less than 44.1•1000/30 = 1470 samples. A higher sampling rate means you have more work to do, so you may need to adjust your window size to keep the processing within limits.
    5. That code uses N for log2n, which is unfortunate, since it may confuse people. Otherwise, the code is as I described above, and the FFT frame size is n.

    There can be some confusion about FFT size or length when a mix of real data and complex data is involved. Typically, for a real-to-complex FFT, the number of real elements is said to be the length. When doing a complex-to-complex FFT, the number of complex elements is the length.