Task description : Intro: Fourier series Orthogonal Representations of Signals S

Question

Task description :
Intro: Fourier series
Orthogonal Representations of Signals
Signals Space
Exponential form of FS
Task-specific training :
Write a Matlab code (or use any other software) to check the orthogonality of any two signals.
Additional documents: https://view.officeapps.live.com/op/view.aspx?src=http://env.dipseil.net/v3/rem_server/task_files/1617_Part9_221.pptx
Reference Information:
Books & Links:
oText Book
Signals, Systems and Transforms,
Prentice Hall, 4th Edition
Charles L. Philips et.al
oReferences:
Signals and Systems Analysis, second edition, By: Samir Soliman, et. al
Introduction to Comm. Systems, third edition, By: Ferril Stremler
Linear Systems and Signals, B.P second edition, By: Lathi Task description :
Intro: Fourier series
Orthogonal Representations of Signals
Signals Space
Exponential form of FS
Task-specific training :
Write a Matlab code (or use any other software) to check the orthogonality of any two signals.
Additional documents: https://view.officeapps.live.com/op/view.aspx?src=http://env.dipseil.net/v3/rem_server/task_files/1617_Part9_221.pptx
Reference Information:
Books & Links:
oText Book
Signals, Systems and Transforms,
Prentice Hall, 4th Edition
Charles L. Philips et.al
oReferences:
Signals and Systems Analysis, second edition, By: Samir Soliman, et. al
Introduction to Comm. Systems, third edition, By: Ferril Stremler
Linear Systems and Signals, B.P second edition, By: Lathi Task description :
Intro: Fourier series
Orthogonal Representations of Signals
Signals Space
Exponential form of FS
Task-specific training :
Write a Matlab code (or use any other software) to check the orthogonality of any two signals.
Additional documents: https://view.officeapps.live.com/op/view.aspx?src=http://env.dipseil.net/v3/rem_server/task_files/1617_Part9_221.pptx
Reference Information:
Books & Links:
oText Book
Signals, Systems and Transforms,
Prentice Hall, 4th Edition
Charles L. Philips et.al
oReferences:
Signals and Systems Analysis, second edition, By: Samir Soliman, et. al
Introduction to Comm. Systems, third edition, By: Ferril Stremler
Linear Systems and Signals, B.P second edition, By: Lathi

Explanation / Answer

If two signals are mutually independent then they are said to be orthogonal

Two signals are mutually independent if their inner product is zero

That is the integration of their product is zero which implies projection of one signal over the other is zero

MATLAB CODE

Clc;

Close all;

Syms t ; % declaring t as a variable

f1 = 200; % frequency of signal x

f2 = 400; % frequency of signal y

x= sin(2.*pi.*f1.*t);% I selected x as sin (2pif1t)

Sub plot(3,1,1);

Plot(x);

Title(' signal x');

Xlabel (' time period');

Ylabel (' Amplitude');

y= sin(8.*pi.*f2.*t);% I selected y as sin (8pif2t)

Sub plot(3,1,2);

Plot(y);

Title(' signal y');

Xlabel (' time period');

Ylabel (' Amplitude');

z = x.*y;

o= int(z, t, 0, inf)

If (o==0)

Disp (' two signals x and y are orthogonal);

Else

Disp (' two signals x and y are not orthogonal);

Other link that you have posted is not opening.

Thank you

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