CODEWITHSUNDEEP
androidaudiofftwindowing
just_code_it
just_code_it

Reputation: 41

Correct way to apply window function in fft

I understand why I need to use window functions in fft,I record a sine wave (16 bit pcm format), I have the sine wave audio record which I would like to analyze,I have recorded the mic audio into a byte array, transformed it back to the sample array representing the sine wave with values from [-1,1] - values divided by 32768. Do I need to apply the window on the array with the values [-1,1](the divided one) or do I need tho apply it on the sample array without dividing it by 32768? I looked up for some answers on SO and google, couldn't find any explanation on what is the right way.

Upvotes: 0

Views: 212

Answers (1)

SleuthEye
SleuthEye

Reputation: 14577

One of the properties of linear-time-invariant is that the result of a cascade of multiple linear-time-invariant systems is the same regardless of the order in which the operations where done (at least in theory, in practice filters and such can have small non-linearities which can make the result slightly different depending on order).

From a theoretical perspective, applying a constant scaling factor to all samples can be seen as such a linear-time-invariant system. For a specific computer implementation, the scaling can also be considered approximately linear-time-invariant, provided the scaling does not introduce significant losses of precision (e.g. by scaling the number to values near the floating point smallest representable value), nor distortions resulting from scaling values outside the supported range. In your case, simply dividing by 32768 is most likely not going to introduce significant distortions, and as such could be considered to be an (approximately) linear-time-invariant system.

Similarly, applying a window which multiplies each samples by a different window value, can also be seen as another linear-time-invariant system.

Having established that you have such a cascade of linear-time-invariant systems, you can perform the scaling by 32768 either before or after applying the window.

P.S.: as Paul mentioned in comments, you'd probably want to perform the conversion from 16-bit words to floating point (whether scaled or not) first if you are going to work with floating point values afterward. Trying to perform scaling in fixed-point arithmetic might prove more complex than necessary, and may be subject to loss of precision I alluded to above if not done carefully.

Upvotes: 1

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