CODEWITHSUNDEEP
algorithmfftpcm
CmdrMoozy
CmdrMoozy

Reputation: 3931

Using PCM samples as input for DFT

I am writing an application which will compute the DFT (using a FFT algorithm) of a sound signal. The inputs I have for the FFT algorithm are PCM samples - namely, I have a large list of 16-bit unsigned integers.

I am aware of the fact that I will need to compute the DFT of several segments of the sound signal independently using a window function, and I have already written working code which decodes an input sound file to raw PCM samples.

My question is about the definition of the DFT given on Wikipedia:

The DFT is supposed to perform an invertible, linear transformation on the inputs x(0), x(1), ..., x(N-1), where each x(n) is a complex number. However, I do not understand how to take my decoded sample integers, and turn them into complex numbers suitable for the algorithm.

I have seen certain examples online where each sample is divided to obtain a floating-point value in the range [0, 1), and then the imaginary part is set to 0.

Is this scaling down to [0, 1) necessary? And is representing each sample as x + 0i where x is the sample value correct?

Upvotes: 3

Views: 872

Answers (1)

pentadecagon
pentadecagon

Reputation: 4847

Yes, you can create complex numbers by adding an imaginary part of 0 to each real value. Try that, it will work. However, you just doubled the amount of data to process and you created a lot of redundancy. You can notice the redundancy in the output: The resulting coefficients for the positive frequencies and for the negative frequencies will be identical, except for a different sign of the imaginary part. So to improve efficiency and reduce redundancy one typically uses a different transformation to turn N real values into N/2 complex values, and as a result you get (roughly) N/2 frequencies. I won't go into details here, but a nice implementation of both the complex FFT and the transformation for real input can be found here: http://sourceforge.net/projects/kissfft/

About your final question: No. You don't need to scale your input. The DFT is a linear transformation, so scaled input simply results in identically scaled output.

EDIT: BTW, are you sure it's a complex DFT what you want? For real data, in particular for PCM data, you should consider the Cosine Transform instead, which maps directly from real input data to real output.

Upvotes: 2

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