Fourier Series`of an Even function

Why is a0 a value if pi when It shouldn't be?

%% Problem 17.5

display('Problem 17.5')

syms n t

Wo = 1;

T = 2*pi;

n = 1:10;

a0 = (1/T)*[int(-14,t,-pi,0) + int(7,t,0,pi)]

an = (2/T)*[int(-14*cos(n*Wo*t),-pi,0) + int(7*cos(n*Wo*t),0,pi)]

bn = (2/T)*[int(-14*sin(n*Wo*t),-pi,0) + int(7*sin(n*Wo*t),0,pi)]

[Utkarsh Belwal]

I am not understanding your issue, can you please tell your query again ?

[Salik Mallick]

Hello Mr.Belwal,

I meant why does ao have pi in it? I did the hand calculation and there shouldn't be a pi for the DC coefficent.

[Star Strider]

See also an apparent duplicate: Fourier Series of Rectified Cosine Function

Answer 1

[Utkarsh Belwal]

Hello Salik,

You are right, there should be no pi in the DC coefficient and the value should be 3.5. According to me as a0 is a symbolic variable so it has the pi symbol included in it for better precision. I calculated the value of a0 that MATLAB is displaying, and it is coming 3.5. If you want to use the numeric value, then you can do a symbolic to numeric conversion as follows:

A0_numeric = double(a0);

DISCLAIMER: These are my own views and in no way depict those of MathWorks.

[Salik Mallick]

Hello Mr. Belwal,

Would you know why this script isn't running?

%% Problem 17.9

display('Problem 17.9')

% Determine the Fourier coefficients an and bn of the

% first three harmonic terms of the rectified cosine

% wave

syms n t

T = 8;

Wo=2*pi/T;

n = 1:3;

an = (2/T)*[int(2.5*cos(n*Wo*t)*cos(n*Wo*t),-2,2)]

AN_numeric = double(an)