How Fourier Synthesis is performed using Matlab ?

I have read about Fourier Synthesis

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?

Answer 1

[Youssef Khmou]

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;

[Ahmed Mujtaba]

Thanks.. Exactly what I was looking for. Simple and Compact.

Answer 2

[Image Analyst]

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.

[ramdas patil]

@Image Analyst thank for both of your code. But I am getting following errors in both of the code

A)For clouds.m file 1)How should I vary values of "h" ? also 2) when i run the code ,error is

v =

8.1.0.604 (R2013a)

Octave =

     0

Attempt to execute SCRIPT fft2 as a function: C:\Users\RK\Documents\MATLAB\fft2.m

Error in noiseonf (line 47) imfft = fft2(im); % Take fft of image.

Error in clouds (line 55) grayImage = noiseonf(rows, columns, h(index)); % The scale changes h with each new iteration.

>> B) noiseonf.m code, error is Error using noiseonf (line 44) Not enough input arguments.

>>

[Image Analyst]

You made your own script or function called fft2 and it looks like that is being used in preference to the real one. This is what you should see:

>> which fft2
C:\Program Files\MATLAB\R2015a\toolbox\matlab\datafun\fft2.m

Use a different name for your own version of it that you've placed in C:\Users\RK\Documents\MATLAB so that there is no conflict.

[ramdas patil]

@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]

Make sure that you're passing in an even number for rows and columns.