Problem 6: (20 points)

¹Consider an FTIR interferogram signal is applied as an input to an FTIR spectrometer as a function of "z (cm)". MATLAB code which generates the signal has been attached. Add the script of fast fourier transform to this code to produce the output (spectrum) of the spectrometer as a function of wavenumber "k (cm^-1)".

(Visit the links below to understand FTIR spectroscopy)

MATLAB CODE FOR PROBLEM 6

clear all

clc

ko=5;

zo=5;

L=100;

ks=4*ko;

dz=1/ks;

z=0:dz:L-dz;

dk=ko/8;

f1=sin(2*pi*ko*(z-zo));

g1=exp(-((z-zo)*pi*dk).^2);

fun=f1.*g1+0.05*randn(size(z)); %Function in z domain domain

plot(z,fun);

axis([0 20 -1 1]);

xlabel('Distance (m)');

ylabel('f(z)');