I am quite new to signal processing so forgive me if I rant on a bit. I have download and installed FFTW for windows. The documentation is ok but I still have queries.
My overall aim is to capture raw audio data sampled at 44100 samps/sec from the sound card on the computer (this task is already implemented using libraries and my code), and then perform the DFT on blocks of this audio data.
I am only interested in finding a range of frequency components in the audio and I will not be performing any inverse DFT. In this case, is a real to real transformation all that is necessary, hence the fftw_plan_r2r_1d()
function?
My blocks of data to be transformed are 11025 samples long. My function is called as shown below. This will result in a spectrum array of 11025 bins. How do I know the maximum frequency component in the result?
I believe that the bin spacing is Fs/n , 44100/11025, so 4. Does it mean that I will have a frequency spectrum in the array from 0 Hz all the way up to 44100Hz in steps of 4, or up to half the nyquist frequency 22200?
This would be a problem for me as I only wish to search for frequencies from 60Hz up to 3000Hz. Is there some way to limit the transform range?
I don't see any arguments for the function, or maybe there is another way?
Many thanks in advance for any help with this.
p = fftw_plan_r2r_1d(11025, audioData, spectrum, FFTW_REDFT00, FFTW_ESTIMATE);
To answer some of your individual questions from the above:
- you need a real-to-complex transform, not real-to-real
- you will calculate the magnitude of the complex output bins at the frequencies of interest (
magnitude = sqrt(re*re + im*im)
) - the frequency resolution is indeed
Fs / N = 44100 / 11025 = 4 Hz
, i.e. the width of each output bin is 4 Hz - for a real-to-complex transform you get N/2 + 1 output bins giving you frequencies from
0
toFs / 2
- you just ignore frequencies in which you are not interested - the FFT is very efficient so you can afford to "waste" unwanted output bins (unless you are only interested in a relatively small number of output frequencies)
Additional notes:
- plan creation does not actually perform an FFT - typically you create a plan once and then use it many times (by calling
fftw_execute
) - for performance you probably want to use the single precision calls (e.g.
fftwf_execute
rather thanfftw_execute
, and similarly for plan creation etc)
Some useful related questions/answers on StackOverflow:
There are many more similar questions and answers which you might also want to read - search for the fft and fftw tags.
Also note that dsp.stackexchange.com is the preferred site for site for questions on DSP theory rather than actual specific programming problems.
来源:https://stackoverflow.com/questions/39839391/computing-the-discrete-fourier-transform-of-audio-data-with-fftw