Spectrum graph from sinusoidal signal in wavelength

Hello everybody:

I need to plot in Matlab an intensity modulation from and optical source. First, I need to calculate FFT of the sinusoidal signal of the source but instead of using an x-frequency axis I need to use and x-wavelength axis.

How can I do that?

[Ameer Hamza]

But frequency in fft() starts from 0. That will translates to a wavelength of infinity. Which range do you want to use?

[Joel Ruiz]

From 700 nm to 1560 nm

Answer 1

[Ameer Hamza]

This is a modified version of the example on MATLAB fft() documentation page. For this example, I assume wavelength = 1/f. And I restrict the wavelength in range 0.003 to 1.

Fs = 1000;            % Sampling frequency                    
T = 1/Fs;             % Sampling period       
L = 1500;             % Length of signal
t = (0:L-1)*T;        % Time vector

S = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);

X = S + 2*randn(size(t));

Y = fft(X);

P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);

f = Fs*(0:(L/2))/L;
lambda = 1./f;

idx = (lambda > 0.003) & (lambda < 0.1);

lambda = lambda(idx);
P1 = P1(idx);

plot(lambda, P1);
xlabel('wavelength');
ylabel('amplitude')