FFT calculation suitable, Wav File, Java

Question

If I have a wav file with this characteristics:

• 16bits (2 Bytes per Sample)
• 32000 Sampling Rate
• 60 Seconds
• 2 Channels

then I have:

Samples Per Channel: 32000*60 = 1920000
Samples Per File: 32000*60*2 = 3840000
Bytes Per File: 32000*60*2*2 = 7680000

It's a huge file!

If I change my file Characteristics to:

• 8bits (1 Byte per Sample)
• 8000 Sampling Rate
• 60 Seconds
• 1 Channel

then I have:

Samples Per Channel: 8000*60 = 480000
Samples Per File: 8000*60*1 = 480000
Bytes Per File: 8000*60*1*1 = 480000

If my FFT 2^12 = 4096 or 2^16 = 65536

Do I need to calculate the FFT 480000 times?

Does each how many samples I need to calculate the FFT? (480000 - 65536 = 414464?)

what is the suitable calculus?

How to do to show the spectrum?

Answer 1

To show only one spectrum then FFT of the whole sample could be done.But for better result you could take a window and take FFT. For taking windows of 4096 with 50% overlap then it is equivalent to doing FFT
no of times $$ \frac{480000}{4096*0.5} $$ times that is equivalent to $$ \frac{Total\hspace{1mm} sample\hspace{1mm} length}{(window \hspace{1mm}length)*(amount\hspace{1mm} of\hspace{1mm} overlap)} $$

Answer 2

If you want to see how the spectrum is changing over time, which is what it sounds like you want to do, then don't do it for every sample - it's too much information and too much calculation.

A rule of thumb I use is to calculate the Fourier Transform every 0.05 seconds, since this is roughly the human ear's temporal resolution. In your case, at a sampling frequency of 8kHz, that's a FT every 400 samples.

You also don't need to use the entire 60 seconds of data for each FT. A common technique here is to do a short-time FT - i.e. each point in time that you want to calculate the spectrum for you use a data 'window' of a certain sample size (e.g. 4096 samples). Also consider multiplying each 'window' of data by a window function to reduce spectral leakage.