Evaluating a complex equation

Hi,

I'm trying to evaluate the following equation. Is there a way of doing it? I keep getting the following "Unable to perform assignment because the left and right sides have a different number of elements." Do I need to break it down further?

clc;

clear all;

close all;

N=8;

% for n=1:N

fc = 20; %CARRIER FREQUENCY

fs = 2000; %SAMPLING FREQUENCY

fm = 1; %MESSAGE FREQUENCY

tau = 0.2;

m=6;

T=1/fs;

t=0:1/fs:((2/fm)-(1/fs));

Y=0;

for n=1:8

Y(n)=(tau/T).*(1+m*sin(2*pi*fm*t))+(2/n*pi).*sin(n*2*pi*fs).*[tau/2+(m*tau/2).*sin(2*pi*fm*t)].*cos(n*2*pi*fs*t);

end

plot(Y)

Many thanks,

Andy

Answer 1

[Star Strider]

Preallocate ‘Y’ as:

Y=zeros(8,numel(t));

add a second dimension to ‘Y’ in the assignment to it:

Y(n,:) = ...

and add ‘t’ to the plot call, and it works.

Try this —

N=8;
% for n=1:N
fc = 20;        %CARRIER FREQUENCY
fs = 2000;      %SAMPLING FREQUENCY
fm = 1;         %MESSAGE FREQUENCY
tau = 0.2;
m=6;
T=1/fs;
t=0:1/fs:((2/fm)-(1/fs));
Y=zeros(8,numel(t));
for n=1:8
    Y(n,:)=(tau/T).*(1+m*sin(2*pi*fm*t))+(2/n*pi).*sin(n*2*pi*fs).*[tau/2+(m*tau/2).*sin(2*pi*fm*t)].*cos(n*2*pi*fs*t);
end

figure
plot(t,Y)

EDIT — (23 Aug 2023 at 14:55)

Another option is to use surf to plot the matrix —

figure
surf(t, (1:8), Y, 'EdgeColor','none')
colormap(turbo)
xlabel('t')
ylabel('n')
zlabel('Y')

.

[Andy]

Thank you for your help, it makes sense now.

[Star Strider]

As always, my pleasure!

Answer 2

[Voss]

Y(n)=(tau/T).*(1+m*sin(2*pi*fm*t))+(2/n*pi).*sin(n*2*pi*fs).*[tau/2+(m*tau/2).*sin(2*pi*fm*t)].*cos(n*2*pi*fs*t);

The left side Y(n) is a single element of Y. The right side is a vector the size of t. t has more than one element, so that assignment is not going to work because you can't put multiple elements into a slot that's only big enough for one element.

You need to change how the results are stored in Y. You need a way to store mutiple vectors together. Since all the vectors are the same size (the size of t), you can store them in a matrix.

Say you want to store each vector as a column of Y (instead of trying to force them into a single element). Then you can do something like this:

clc;
clear all;
close all;
N=8;
% for n=1:N
fc = 20;        %CARRIER FREQUENCY
fs = 2000;      %SAMPLING FREQUENCY
fm = 1;         %MESSAGE FREQUENCY
tau = 0.2;
m=6;
T=1/fs;
t=0:1/fs:((2/fm)-(1/fs));

n_max = 8;
Y = zeros(numel(t),n_max);
for n=1:n_max
    Y(:,n)=(tau/T).*(1+m*sin(2*pi*fm*t))+(2/n*pi).*sin(n*2*pi*fs).*(tau/2+(m*tau/2).*sin(2*pi*fm*t)).*cos(n*2*pi*fs*t);
end
plot(Y)

[Andy]

Thank you for your help, it makes sense now.

[Voss]

You're welcome!