Return X coordinate of a fft plot where 80% of the total area under the curve is achieved

How to get X coordinate of a fft plot which covers 80% of the area of the total area covered by the whole plot.

Answer 1

[Star Strider]

Try this:

t = linspace(0, 10, 150);                                   % Create Data
y = sin(2*pi*t*3) .* cos(2*pi*t*2) + 0.01*randn(size(t));   % Create Data

L = numel(t);
Ts = mean(diff(t));                                         % Sampling Interval
Fs = 1/Ts;                                                  % Sampling Frequency
Fn = Fs/2;                                                  % Nyquist Frequency
FTy = fft(y)/L;                                             % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                         % Frequency Vector
Iv = 1:numel(Fv);                                           % Index Vector

areaFrac = 0.8;                                             % Desired Fraction Of Total Area
areaTot = trapz(Fv, abs(FTy(Iv)));                          % Total Area
areaCum = cumtrapz(Fv, abs(FTy(Iv)));                       % Cumulative Integral

Fv80 = interp1(areaCum, Fv, areaTot*areaFrac, 'spline')     % Frequency Corresponding To 80% Total Area
FTy80 = interp1(Fv, abs(FTy(Iv))*2, Fv80, 'spline')         % Value of Fourier Transform At ‘Fv80’

figure
plot(Fv, abs(FTy(Iv))*2, '-b')
hold on
plot(Fv, areaCum, '-k')
plot([0 max(Fv)], [1 1]*areaTot, '--k')
plot([0 max(Fv)], [1 1]*areaFrac*areaTot, ':k')
plot([1 1]*Fv80, [0 FTy80], '-r')
plot(Fv80, areaTot*areaFrac, 'r+')
hold off
legend('Fourier Transform', 'Cumulative Area', 'Maximum Area', '80% Maximum Area', 'Fourier Transform at 80% Maximum Area')

Experiment to get the result you want.

[Samyak Mohapatra]

I used these values, as given in Matlab manual

Fs =41670; % Sampling frequency

T = 1/Fs; % Sampling period

L = length(x); % Length of signal

t = (0:L-1)*T; % Time vector

p=nextpow2(L);

n=2^p;

f = Fs*(0:(L/2))/L;

Y = fft(X,n);

P2 = abs(Y/L);

P1 = P2(1:L/2+1);

P1(2:end-1) = 2*P1(2:end-1);

Also I want to draw a line on spectrum plot. I tried-

plot(f,P1) ;

title('Single-Sided Amplitude Spectrum of X(t)');

xlabel('f (Hz)');

ylabel('|P1(f)|');

hold on

line([Fv80 Fv80],[0 max(P1)],'color','r','linestyle','--');

but it's not coming right

[Star Strider]

I do not have your data, so I cannot comment on the reason your result is ‘not coming out right’.

Use my code with your data. It should run without error, and produce the correct result.

[Samyak Mohapatra]

EDIT:

I tweaked it. Is it right?

Ts = 1/Fs; % Sampling Interval

Fn = Fs/2; % Nyquist Frequency

FTy = P2; % Fourier Transform

Fv =f %linspace(0, 1, fix(L/2)+1)*Fn; % Frequency Vector

Iv = 1:numel(Fv); % Index Vector

areaFrac = 0.8; % Desired Fraction Of Total Area

areaTot = trapz(Fv, abs(FTy(Iv))); % Total Area

areaCum = cumtrapz(Fv, abs(FTy(Iv))); % Cumulative Integral

Fv80 = interp1(areaCum, Fv, areaTot*areaFrac, 'spline') % Frequency Corresponding To 80% Total

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

figure(1);

plot(x,X1);

title('Signal Acquired');

xlabel('Time(s)');

ylabel('Signal Amplitude (V)');

figure(2);

plot(f,P1) ;

title('Single-Sided Amplitude Spectrum of X(t)');

xlabel('f (Hz)');

ylabel('|P1(f)|');

hold on

line([Fv80 Fv80],[0 max(P1)],'color','r','linestyle','--');

[Samyak Mohapatra]

I think I am getting the right answer with my latest tweak. Thank you.

[Star Strider]

As always, my pleasure.

I have no idea what you tweaked or what your signals are. The code appears to be correct.