FFT not giving the desired result

Hi all,

The code I have written I think is correct. I am comparing two sound sources and not getting the desired outcome, one of the sound sources has a higher frequency content when it should be lower! I think there is something wrong with my Fourier Transform?

I have attached the two files post audio read saved as Bolt and Squid.

My code is as follows, any help would be much appreciated:

read in the .wav file

[y,fs]= audioread('CD152DEP1_20170829_160000.wav');
% y=samples
% fs=sampling frequency
Starttime=0;
Endtime=30;
time= Endtime-Starttime;
Sample=time.*fs;
Starty=Starttime.*fs
Endy=Endtime.*fs
t=linspace(Starttime,Endtime,Sample); 
%linspace function that creates evenly spaced time vector
y2=y((Starty+1):Endy,:);
figure;
subplot(3,1,1)
plot(t,y2);
xlabel('Time (seconds)') 
ylabel('Amplitude')
title('Day 1 Bolt 16.00') 
hold on 
%a is normalised into seconds for plot
%xlim([0 350])
%b= 45/350
%X = [b, b];
%Y = [0.8,0.5];
%a = annotation('textarrow',X,Y,'String','Lander crossing');
%%frequnecy analysis
Nfft=2048;
f=linspace(0,fs,Nfft); 
%f is freq vector, 0 starting freq, fs is end freq, Nfft is length of
%vector
G=abs(fft(y2,Nfft));
%G is the fft of y in the same number of points as the sample
%calculating the phase
phase = unwrap(angle(fft(y,Nfft)));
%subplot of phase and freq
subplot(3,1,2),plot((f(1:Nfft/2)),(G(1:Nfft/2)))
xlabel('Frequency(Hz)')  
ylabel('Amplitude')
xlim([0 1000])
hold on 
subplot(3,1,3), plot((f(1:Nfft/2)),(phase(1:Nfft/2)))
xlabel('Frequency(Hz)') 
ylabel('Phase(radians)')
xlim([0 1000])

Answer 1

[Star Strider]

You did not state what your sampling frequencies are, or include them in your files, so I assume they is the same for both files. My code accommodates separate sampling frequencies for each signal. My code is reliable, based on this version of the fft (link) documentation (it works for all versions), and has worked successfully in the past. (I did not try to troubleshoot your code. I am simply posting mine. This is based on the files you attached to your previous Question.)

I cannot specifically reply to you statement about the frequencies, since I have no idea what you are doing.

Here is my Fourier transform analysis of your data.

DBolt = load('Edward Jones Bolt.mat');
DSquid = load('Edward Jones Squid.mat');
Bolt = DBolt.y2;
Squid = DSquid.y2;
FsB = 44100;                                                    % Assumed Sampling Frequency (Bolt)
FsS = 44100;                                                    % Assumed Sampling Frequency (Squid)
FnB = FsB/2;                                                    % Nyquist Frequency (Bolt)
FnS = FsB/2;                                                    % Nyquist Frequency (Squid)
LBolt = length(Bolt);
LSquid = length(Squid);

NFFTB = 2.^nextpow2(LBolt);
NFFTS = 2.^nextpow2(LSquid);

FT_B = fft(Bolt,NFFTB)/LBolt;
FT_S = fft(Squid,NFFTS)/LSquid;

FvB = linspace(0, 1, fix(length(FT_B)/2)+1)*FnB;                % Frequency Vector (Bolt)
IvB = 1:length(FvB);                                            % Index Vector (Bolt)
FvS = linspace(0, 1, fix(length(FT_B)/2)+1)*FnB;                % Frequency Vector (Squid)
IvS = 1:length(FvS);                                            % Index Vector (Squid)

figure(1)
subplot(2,1,1)
plot(FvB, abs(FT_B(IvB,:))*2)
title('Bolt')
set(gca, 'XLim',[0  5E+2])
grid
subplot(2,1,2)
plot(FvS, abs(FT_S(IvS,:))*2)
title('Squid')
set(gca, 'XLim',[0  5E+2])
grid

You can break out the subplot calls to plot the Fourier transform of each channel in your signals as well. I plotted both channels for each file in each subplot in my code.

[Edward Jones]

Thank you very much for the help! the only problem is the squid should have a frequency range that is higher then the Bolt, this does not seem to be the case!

[Star Strider]

My pleasure!

[Edward Jones]

Star strider, does the magnitude of the two plots not compare because i need to scale the output of the fft?

[Star Strider]

I’m not certain what you intend by ‘amplitude’. They seem to have the same essential amplitude range.

In my code, the amplitudes are scaled appropriately (by dividing by the length of the original signal in the fft calculation, and multiplying their absolute values by 2 in the plot, so the amplitudes display correctly). If you have other scaling that you need to do because of your experimental set-up, I would do that before doing the Fourier transform.

One option is to subtract the mean (d-c or constant offset value of each signal) before doing the fft. I doubt if this is an issue, since your two signals seem to have the same essential amplitude, and the d-c or 0 Hz component didn’t appear significant in either one.

[Edward Jones]

When I run the code the output of the Squid FFT is a factor of 10 lower then the Bolt, I don't think that should be the case? I was expecting the squid to have a much higher frequency content?

[Star Strider]

I have no idea what you’re doing. I would check the sampling frequency for the two records. That’s the only reason I can think of for they’re not being as you believe they should be.

I designed my code to accommodate different sampling frequencies for different vectors, so it should work with minimal changes, if your signals have different sampling frequencies. You can get the same frequency resolution for both signals by using the same ‘NFFT’ for both, even if they are not originally the same lengths.

[Edward Jones]

will the sampling frequency just be 44100 like all audio files?

[Star Strider]

It is whatever you set it to be when you set up your experiment. The sampling frequency should be recorded as ‘metadata’ in the same file that your recording equipment created when it saved the file.

Set the sampling frequency to at least 2 times the maximum expected frequency of your signal, if possible.

The 44100 Hz value is the standard CD audio sampling frequency, because the Nyquist frequency, 22050 Hz, spans normal the human hearing range, and being slightly oversampled, allows for effective digital signal processing.