# How to create a function as sum of some sine functions?

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Klaudjo Aliaj on 6 Jan 2021
Commented: Star Strider on 8 Jan 2021
I am trying to create a function which looks like:
,
but I am not finding the way how do it it. Can someone help me?
SHIVAM KUMAR on 6 Jan 2021

Star Strider on 6 Jan 2021
A loop is not necessary.
If you have R2016b or later, try this (using your own variable vectors):
t = linspace(0, 2, 750); % Time Vector
a = 1:10; % Amplitude Vector
f = linspace(1000, 2000, numel(a)); % Frequency Vector
th = linspace(-pi, pi, numel(a)); % Phase Vector
y = sum(a(:).*sin(2*pi*f(:)*t + th(:))); % Compute Function, Then Take Sum Of Rows
figure
plot(t, y)
grid
This uses automatic implicit expansion, introduced in R2016b. If you have an earlier version:
y = sum(bsxfun(@times, a(:), sin(2*pi*f(:)*t + th(:)))); % Compute Function, Then Take Sum Of Rows
produces the same result.
.
##### 2 CommentsShowHide 1 older comment
Star Strider on 8 Jan 2021
As always, my pleasure!

SHIVAM KUMAR on 6 Jan 2021
Edited: SHIVAM KUMAR on 6 Jan 2021
This can be done like
y=0; %necessary to add the other things
for i=1:length(a)
y=y+a(i).*sind(2*pi*f(i).*t+theta(i));
end
If this works accept this answer but
if this does not work tell the error/other requirements in comment
Klaudjo Aliaj on 8 Jan 2021
Thank you :)