Straightening amplitude-frequency response graph after FFT

Question

I have loaded a logarithmic swept sine (with some short fade in/fade out) into Matlab and run it through the fft function and plot it using semilog.

The input signal amplitude is almost constant in 10 ... 20000 Hz range. So to represent more accurately what is going on, I would like to see the graph as almost horizontal line.

What formula should I apply to make the AFR graph horizontal?

The Matlab script I used to plot the graph:

fid = fopen('sweepfaded.raw','rb');   %open file
data = fread(fid, inf, 'float32');  %read in the data
fclose(fid);   %close file

n = size(data,1);

n = 2^nextpow2(n); % Next power of 2 from length of audio - 2-powers are faster to calculate

p = fft(data, n); % take the fourier transform 

nUniquePts = ceil((n+1)/2); 
p = p(1:nUniquePts); % select just the first half since the second half 
                       % is a mirror image of the first
p = abs(p); % take the absolute value, or the magnitude 
p = p/n; % scale by the number of points so that
           % the magnitude does not depend on the length 
           % of the signal or on its sampling frequency  
p = p.^2;  % square it to get the power 

sampFreq = 44100;
freqArray = (0:nUniquePts-1) * (sampFreq / n); % create the frequency array 
semilogx(freqArray, 10*log10(p)) 

xlabel('Frequency (Hz)') 
ylabel('Power (dB)')

The resulting plot which I would like to be horizontal (like applying some rotation to it so the range 100...10000 Hz becomes a horizontal line):

Data from FFT

P.S. I am not good at audio signal processing, I am just a generic programmer, so do not waste your time trying to explain what is going on (although I guess, someday I'll have to read a good DSP book anyway). Just a correct formula to insert into my Matlab script will be good enough.

Paul R Paul R · Accepted Answer · 2011-10-17T12:00:09

Your spectrum will only be flat if you have the same amount of energy in each frequency bin - this means that your sine wave must be swept at a constant (linear) rate for the duration of the FFT sampling window.

Ideally you should also be applying a window function prior to the FFT to reduce the effect of spectral leakage, however this will affect the resulting magnitudes of the swept sine and you would need to compensate for this.

Straightening amplitude-frequency response graph after FFT

2 Answers