MATLAB: Area of a Spectrum

areasrs

What matlab command can give me the area of a spectrum. I have shock response spectrum but i need to find the area under the curve.

Best Answer

The area under your curve should just be:

N = numel(x);
dt = 1/fs;
df = fs/N;
y = fft(x)*dt;
area_y = sum(abs(y))*df; % which is also equal to: sum(abs(fft(x)))/N
energy_y = sum(abs(y).^2)*df;

If you really want "energy", then energy_y should be equal to energy_x:

energy_x = sum(x.^2)*dt;

Related Solutions

MATLAB: PSD question

Yes, it is dB/Hz.

psdest.Data are the power estimate, proportional to magnitude-squared of the DFT. So 10*log10() is in dB

MATLAB: Specter of a square signal(10Khz) at 10MHz frequency

hello

there is a much faster method to generate a square signal (using square )

see demo below for signal generation and fft analysis

NB your sampling freq is 100 kHz in the code, not 10 MHz as stated in the post

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% dummy data
Fs = 100e3;     % sampling freq
f0 = 10e3;     % signal freq
duration = 1;   % signal duration (s)
samples = Fs*duration;
t = (0:samples-1)*1/Fs;
% signal = square(2*pi*f0*t); % neg / pos symetrical square wave ( -1 / +1)
signal = 0.5*(square(2*pi*f0*t)+1); % 0 / pos  square wave ( 0 / +1)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 10000;    % 
Overlap = 0.75;
w = hanning(NFFT);     % Hanning window / Use the HANN function to get a Hanning window which has the first and last zero-weighted samples.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% display : averaged FFT spectrum 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[freq,fft_spectrum] = myfft_peak(signal, Fs, NFFT, Overlap);
sensor_spectrum_dB = 20*log10(fft_spectrum);% convert to dB scale (ref = 1)
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(' dB')
text(locs+.02,pks,num2str(freq(locs)))
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: PSD question

MATLAB: Specter of a square signal(10Khz) at 10MHz frequency

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