Generate this curve within matlab using the following commands
fo = 4; %frequency of the sine wave
Fs = 100; %sampling rate
Ts = 1/Fs; %sampling time interval
t = 0:Ts:1-Ts; %sampling period
n = length(t); %number of samples
y = 2*sin(2*pi*fo*t); %the sine curve
%plot the cosine curve in the time domain
sinePlot = figure;
plot(t,y)
xlabel('time (seconds)')
ylabel('y(t)')
title('Sample Sine Wave')
grid
Matlab’s FFT Command
So now that we know what to expect, let’s use MATLAB’s built in fft command to try to recreate the frequency spectrum:
%plot the frequency spectrum using the MATLAB fft command
matlabFFT = figure; %create a new figure
YfreqDomain = fft(y); %take the fft of our sin wave, y(t)
stem(abs(YfreqDomain)); %use abs command to get the magnitude
%similary, we would use angle command to get the phase plot!
%we'll discuss phase in another post though!
xlabel('Sample Number')
ylabel('Amplitude')
title('Using the Matlab fft command')
grid
axis([0,100,0,120])
The x-axis gives us no information on the frequency.
The amplitude is all the way up to 100
The spectrum is not centered around zero
A Custom Function for fft to Obtain only the Positive Frequencies
function [X,freq]=positiveFFT(x,Fs)
N=length(x); %get the number of points
k=0:N-1; %create a vector from 0 to N-1
T=N/Fs; %get the frequency interval
freq=k/T; %create the frequency range
X=fft(x)/N; % normalize the data
%only want the first half of the FFT, since it is redundant
cutOff = ceil(N/2);
%take only the first half of the spectrum
X = X(1:cutOff);
freq = freq(1:cutOff);
end
