Dimensions do not match error during integration
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Hi,
I was trying to implement Fourier series by creating a function. The function was created successfully but when i try to integrate the function, it is giving error of dimension mismatch. I'm not able to understand why this issue is happening. Could you please help me on this?
Thanks in advance
clear all
close all
clc
points = 201;
t3 = linspace(-10,10,points);
%taking mod of t3
t2 = 5*mod(t3, 2);
%figure
%plot(t3,t2)
%creating a periodic function
y(t2 <= 3) = t2(t2 <= 3 );
y(and((t2>3),(t2<=4))) = 3;
y(and((t2>4),(t2<=5))) = t2(and((t2>4),(t2<=5)));
This is the periodic signal y created w.rt to t3
%time period
T0 = 2;
%angular frequency
w0 = (2*pi)/T0;
syms t ;
%used to get number of harmonics
N=input("enter the harmonics count");
%take only integer value for n
n=1:N;
%Fourier series coefficient calculation
a0 = (1/T0)*(int(y,t,0,2));
an = (2/T0)*(int(y*cos(n*w0*t),t,0,2));
bn = (2/T0)*(int(y*sin(n*w0*t),t,0,2)) ;
%Fourier representation
figure
hold on
plot(t3,y)
F = a0;
for i=1:N
F = F + an(i)*cos(i*w0*t3) + bn(i)*sin(i*w0*t3);
plot (t3,F)
end
grid on
hold off
回答（1 个）
Walter Roberson
2023-1-22
0 个投票
your y is a numeric vector. You cannot use int() or integrate() with numeric vectors.
You have y*cos() of something involving y. That is an attempt to use the "inner product" operation between two row vectors. Element by element multiplication is the .* operator not the * operator
5 个评论
NAKUL
2023-1-22
T0 = 3;
fs = @(t) t.*(t>0 & t<=T0/3) + t.^2.*(t>T0/3 & t<=T0/2) + 0*(t>T0/2 & t<=T0);
f = @(t) fs(mod(t,T0));
t = -5:0.01:5;
plot(t,f(t))
NAKUL
2023-1-23
Walter Roberson
2023-1-23
is f(t) real valued? I would not expect it to be. You need to plot real() or imag() or abs() of it.
Furthermore, the fourier transform of time is frequency. That is, you should not be plotting the fourier transform with time as your independent axes
With below code I was able to generate the waveform, but after generating i see some alternate waveforms are not reconstructed. Any idea why this happens?
syms x
T0 = pi;
sum= 0;
y = @(x) x.*(x>=0 & x<=pi/4) + 3*(x>pi/4 & x<=pi/2) + 0*(x>pi/2 & x<=pi); %function you want
%ys is periodic function of y;
ys = @(x) y(mod(x,T0));
%calculating Fourier co-efficients
a0 = (1/pi)*(int(x,x,0,pi/4)+ int(3,x,pi/4,pi/2));
sum = a0;
% 5 harmonics
n=1:5
an=(1/pi)*(int(x*cos(n*x),x,0,pi/4)+ int(3*cos(n*x),x,pi/4,pi/2) + int(0*cos(n*x),x,pi/2,pi)) ;
bn=(1/pi)*(int(x*sin(n*x),x,0,pi/4)+ int(3*sin(n*x),x,pi/4,pi/2) + int(0*sin(n*x),x,pi/2,pi)) ;
%plotting from -4pi to 4pi
x= -4*pi:0.01*pi:4*pi;
hold on;
fplot(ys);
%FOurier series representation
for i=1:5
sum= sum+ (an(i)*cos(i*x)+bn(i)*sin(i*x));
plot(x,sum);
end
hold off
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