MATLAB: Extract a thin band of frequencies from entire spectrum using FFT

fftfrequencies

Hello,

I have following program:

fs=1e4;
x=randn(1,1e4); %gaussian dist random signal
x_fft=fft(x); %fft of the signal
N=length(x);
omega=fs*[(0:N/2) (-N/2+1:-1)]/N; %frequency axis(bins)
figure;
plot(omega(1:N/2),2*abs(x_fft(1:N/2))); %plot of one-sided spectrum

Now I want to extract only a thin band of frequencies(say 500-520Hz) from the spectrum,take its ifft store the obtained time-domain signal in a variable y. I know it is bandpass filtering in TD and there is function fdesign.bandpass() in matlab aswell for this purpose, but I want to do it in frequency domain (using FFT and IFFT) as in my case, the samples are very large and BPF is very time consuming.

At the end, I want to have a small function, where I only enter the frequency band of interest as my input and I get the corresponding TD signal extracted as my output.

Please help.

Best Answer

fs=1e4;pas=1/fs
x=randn(1,1e4); %gaussian dist random signal
x_fft=fft(x); %fft of the signal
N=length(x);
[wc,w0,a0,ak,bk,c0,ck]=get_harmonics(x_fft,pas,2)
fc=wc/(2*pi),

%to extract index frequencies from ck

idx=find(fc>=500 & fc<=520)

% corresponding temporel signal signal(t)

t=0:0.1:10000;
signal=zeros(1,numel(t));
for l=1:length(idx)
  k=idx(l);
  signal=signal+ck(k)*exp(j*k*w0*t);
end
plot(t,real(signal)); %more t is near inf more imag(signal) is near 0.

% download get_harmonics at http://www.mathworks.com/matlabcentral/fileexchange/37654-get-harmoniques-of-a-real-signal

Related Solutions

MATLAB: Calculate frequency band using Parseval

Hi, You can determine what percentage of power lies within a certain band. Here I determine the frequency with maximum power and then find the percentage of power lying in a band that is the maximum frequency plus or minus 2 DFT bins

     Fs = 1e3;
     t = 0:1/Fs:1-(1/Fs);
     x = cos(2*pi*100*t)+randn(size(t));
     psdest = psd(spectrum.periodogram,x,'Fs',1e3,'NFFT',length(x));
     [mx,I] = max(psdest.Data);
      relperc = ...
      100*avgpower(psdest,[psdest.Frequencies(I-2) psdest.Frequencies(I+2)])/avgpower(psdest,[0 Fs/2])

Or you could use cumsum() to get the cumulative percent power and figure out the power in a band with the appropriate subtraction.

    xdft = fft(x);
    xdft = xdft(1:length(x)/2+1);
    relpower = 100*cumsum(abs(xdft).^2)/norm(xdft,2)^2;
    plot(relpower);

The following gives you the percentage power at 100 Hz plus or minus two DFT bins.

   relpower(103)-relpower(99)

Note it's very close to the answer returned by the first method.

MATLAB: I get the peaks at the wrong frequency and with the wrong amplitude.

hello Anna

look at my fft function at the end of my code

clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% data
data = importdata('SFC5S_nov25_ST_1_1.txt');
dt = 1e-6; % 1 micro seconds
signal = data(:,1);
samples = length(signal);
Fs = 1/dt; % sampling frequency (Hz)
%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 1;
if decim>1
    signal = decimate(signal,decim);
    Fs = Fs/decim;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 512;    % 
OVERLAP = 0.95;
% spectrogram dB scale
spectrogram_dB_scale = 80;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% if you are dealing with acoustics, you may wish to have A weighted
% spectrums 
% option_w = 0 : linear spectrum (no weighting dB (L) )
% option_w = 1 : A weighted spectrum (dB (A) )
option_w = 0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% display 1 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[freq, sensor_spectrum] = myfft_peak(signal,Fs,NFFT,OVERLAP);
% convert to dB scale (ref = 1)
sensor_spectrum_dB = 20*log10(sensor_spectrum);
% apply A weigthing if needed

if option_w == 1
    pondA_dB = pondA_function(freq);
    sensor_spectrum_dB = sensor_spectrum_dB+pondA_dB;
    my_ylabel = ('Amplitude (dB (A))');
else
    my_ylabel = ('Amplitude (dB (L))');
end
figure(1),plot(freq,sensor_spectrum_dB,'b');grid
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']);
xlabel('Frequency (Hz)');ylabel(my_ylabel);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% display 2 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[sg,fsg,tsg] = specgram(signal,NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));  
% FFT normalisation and conversion amplitude from linear to dB (peak)
sg_dBpeak = 20*log10(abs(sg))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only
% apply A weigthing if needed
if option_w == 1
    pondA_dB = pondA_function(fsg);
    sg_dBpeak = sg_dBpeak+(pondA_dB*ones(1,size(sg_dBpeak,2)));
    my_title = ('Spectrogram (dB (A))');
else
    my_title = ('Spectrogram (dB (L))');
end
% saturation of the dB range : 
% saturation_dB = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
min_disp_dB = round(max(max(sg_dBpeak))) - spectrogram_dB_scale;
sg_dBpeak(sg_dBpeak<min_disp_dB) = min_disp_dB;
% plots spectrogram
figure(2);
imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([my_title ' / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');
function pondA_dB = pondA_function(f)
	% dB (A) weighting curve
	n = ((12200^2*f.^4)./((f.^2+20.6^2).*(f.^2+12200^2).*sqrt(f.^2+107.7^2).*sqrt(f.^2+737.9^2)));
	r = ((12200^2*1000.^4)./((1000.^2+20.6^2).*(1000.^2+12200^2).*sqrt(1000.^2+107.7^2).*sqrt(1000.^2+737.9^2))) * ones(size(f));
	pondA = n./r;
	pondA_dB = 20*log10(pondA(:));
end
function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer overlap % (between 0 and 0.95)
signal = signal(:);
samples = length(signal);
% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,1);
    s_tmp((1:samples)) = signal;
    signal = s_tmp;
    samples = nfft;
end
% window : hanning
window = hanning(nfft);
window = window(:);
%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows
    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft)).*window;
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling
% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select);
freq_vector = (select - 1)*Fs/nfft;
end

Best Answer

Related Solutions

MATLAB: Calculate frequency band using Parseval

MATLAB: I get the peaks at the wrong frequency and with the wrong amplitude.

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