How to draw a frequency spectrum from a Fourier transform

Question

I want to plot the frequency spectrum of a music file (like they do for example in Audacity). Hence I want the frequency in Hertz on the x-axis and the amplitude (or desibel) on the y-axis.

I devide the song (about 20 million samples) into blocks of 4096 samples at a time. These blocks will result in 2049 (N/2 + 1) complex numbers (sine and cosine -> real and imaginary part). So now I have these thousands of individual 2049-arrays, how do I combine them?

Lets say I do the FFT 5000 times resulting in 5000 2049-arrays of complex numbers. Do I plus all the values of the 5000 arrays and then take the magnitude of the combined 2049-array? Do I then sacle the x-axis with the songs sample rate / 2 (eg: 22050 for a 44100hz file)?

Any information will be appriciated

Answer 1

What application are you using for this? I assume you are not doing this by hand, so here is a Matlab example:

>> fbins = fs/N * (0:(N/2 - 1)); % Where N is the number of fft samples

now you can perform

>> plot(fbins, abs(fftOfSignal(1:N/2)))

Stolen

edit: check this out http://www.codeproject.com/Articles/9388/How-to-implement-the-FFT-algorithm