Basic 2D Signals

Contents

• Start
• Define Important Variables
• Rectangular Function
• Take Fourier Transform
• Pyramid Function
• Fourier Transform of pyramid
• Cylinder
• Fourier Transform of Cylinder
• Cone
• Fourier Transform of Cone
• Airy PSF
• Fourier Transform of Airy PSF
• Gaussian
• Fourier Transform of Gaussian
• Peak
• Fourier Transform of Peak
• Exponential Decay
• Fourier Transform of Exponential Dacay

Start

close all;
clear all;
clc;

Define Important Variables

N = 64;         % Size of a sunction
D = N/2;        % to indicate origin at the center of the function
a = 8;          % radius for cylindrical function
w = 0.4;        % decay rate for exponential function
y = repmat(1:N,N,1);
x = y';
r = sqrt((D-x).^2+(D-y).^2);    % definition of radius
sig = 5;                        % Variance for gaussian function

Rectangular Function

re = zeros(N);
re(D-a:D+a-1,D-a:D+a-1) = w*ones(2*a);
mesh(re); title('2D Rectangular Function');

Take Fourier Transform

R = fft2(re);
R = fftshift(R);
figure;mesh(abs(R)); title('Fourier Transform of Rectangular function');

Pyramid Function

p = conv2(re,re,'same');
figure; mesh(p); title('2D Pyramidal Function');

Fourier Transform of pyramid

P = fft2(p);
P = fftshift(P);
figure; mesh(abs(P));title('Fourier Transform of pyramidal function');

Cylinder

c = w*double((r.^2)<a^2);
figure; mesh(c); title('2D Cylindrical Function');

Fourier Transform of Cylinder

C = fft2(c);
C = fftshift(C);
figure; mesh(abs(C));title('Fourier Transform of Cylindrical function');

Cone

co = conv2(c,c,'same');
figure; mesh(co); title('2D Conical Function');

Fourier Transform of Cone

CO = fft2(co);
CO = fftshift(CO);
figure; mesh(abs(CO)); title('Fourier Transform of Conical function');

Airy PSF

psf = (airy(w*r/2).^2)/pi;
figure; mesh(psf); title('2D Point Spread Function');

Fourier Transform of Airy PSF

PSF = fft2(psf);
PSF = fftshift(PSF);
figure; mesh(abs(PSF)); title('Fourier Transform of airy PSF function');

Gaussian

g = (2*pi*sig^2)*exp(-((r.^2))./(2*sig^2));
figure;mesh(g); title('2D Gaussian Function');

Fourier Transform of Gaussian

G = fft2(g);
G = fftshift(G);
figure; mesh(abs(G)); title('Fourier Transform of Gaussian function');

Peak

pk = 1./r;
pk(isinf(pk)) = 1;
figure; mesh(pk); title('2D Peak Function');

Fourier Transform of Peak

Pk = fft2(pk);
Pk = fftshift(Pk);
figure; mesh(abs(Pk)); title('Fourier Transform of peak function');

Exponential Decay

exd = exp(-w*r);
figure; mesh(exd); title('2D Exponential Decay Function');

Fourier Transform of Exponential Dacay

EXD = fft2(exd);
EXD = fftshift(EXD);
figure; mesh(abs(EXD));
title('Fourier Transform of Exponential Dacay function');

Published with MATLAB® 7.8