# How Fourier Synthesis is performed using Matlab ?

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ramdas patil am 18 Mai 2015
Kommentiert: Ahmed Mujtaba am 16 Nov. 2016
http://whatis.techtarget.com/definition/Fourier-synthesisFourier-synthesis I want to clear my concept about Fourier Synthesis using Matlab .But don't know how to do this.
So can anybody show me how Fourier Synthesis is performed using Matlab?
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### Antworten (2)

Youssef Khmou am 18 Mai 2015
Bearbeitet: Youssef Khmou am 18 Mai 2015
Fourier synthesis is simple application of coefficients summation either numerically or symbolically, Fourier decomposition requires certain conditions of the input function, you can start with a simple example which is an approximation of a square wave of 2 Hz, using 11 terms :
Fs=150;
t=0:1/Fs:4-1/Fs;
f=2;
x=square(2*pi*f*t);
figure;
plot(t,x);
axis([0 1 -2 2]);
% Approximation with Fourier decomposition
y=0;
N=11;
for r=1:2:N
y=y+sin(2*pi*f*t*r)/r;
end
hold on;
plot(t,y,'r');
xlabel('t');
ylabel('magnitude');
hold off;
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Ahmed Mujtaba am 16 Nov. 2016
Thanks.. Exactly what I was looking for. Simple and Compact.

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Image Analyst am 18 Mai 2015
There is nothing at that link. I don't know what Fourier Synthesis might be synthesizing. I don't think computing the Fourier spectrum of a signal or image is called "synthesizing", at least not by anyone I know, so I'm not really sure. You can synthesize things though, such as the attached demo where I synthesize clouds by manipulating the Fourier Spectrum.
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ramdas patil am 19 Mai 2015
@Image Analyst sorry but when I run clouds.m file and click on "CONSTANT H ", I am still getting the following error
Attempted to access radius(346.5,615.5); index must be a positive integer or logical.
Error in noiseonf (line 59) radius(rows/2+1,columns/2+1) = 1; % .. avoid division by zero.
Error in clouds (line 53) grayImage = noiseonf(rows, columns, 1.7); % 1.7 is a good value.
>>
Image Analyst am 19 Mai 2015
Make sure that you're passing in an even number for rows and columns.

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