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

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]

Is your theta in radians or degrees ?

Answer 1

[Star Strider]

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.

.

[Klaudjo Aliaj]

Thank you :)

[Star Strider]

As always, my pleasure!

Answer 2

[SHIVAM KUMAR]

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]

Thank you :)