# Matlab FFT ref

[原文](ttp://www.mbfys.ru.nl/~robvdw/DGCN22/PRACTICUM_2011/LABS_2011/LAB_ASSIGNMENTS/LAB02_CN04/_MYOWN/ANSWERS/introFFT.pdf)

## 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
```

![](https://i.imgur.com/iYmbwvE.png)

## 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])
```

![](https://i.imgur.com/wauVolr.png)

* 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
```

```
[YfreqDomain,frequencyRange] = positiveFFT(y,Fs);
positiveFFT = figure;
stem(frequencyRange,abs(YfreqDomain));
set(positiveFFT,'Position',[500,500,500,300])
xlabel('Freq (Hz)')
ylabel('Amplitude')
title('Using the positiveFFT function')
grid
axis([0,20,0,1.5])
```

![](https://i.imgur.com/j9hiUME.png) ![](https://i.imgur.com/K6JS2y3.png)


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