With MATLAB calculate a number of sinusoids inside a for-loop and then plot them.

Question

I do the following in MATLAB and it works well. However I need to calculate 20 sinusoids instead of 3 and then plot them all.

x=sin(1*w*t)*(2/(pi*1));
y=sin(3*w*t)*(2/(pi*3));
z=sin(6*w*t)*(2/(pi*6));

plot(t,x,t,y,t,z)

I figure it should be possible to make a for-loop and then plot but I'm not sure how that's done and need some help.

Answer 1

Consider this example:

w = 2;
t = (0:0.05:pi)';              %'# time axis
p = [1 3:3:12];                %# parameters you loop over

%# sinusoids over all possible parameters
x = bsxfun(@times, sin(w*bsxfun(@times,p,t)), (2./(pi*p)));
plot(t,x)                      %# plot all of them at one
legend( cellstr(num2str(p')) )

You can simply change the vector p to your specific values

Answer 2

The function BSXFUN is one way to solve your problem, as illustrated by Amro. However, if you are a newer MATLAB user a simpler for-loop solution may be easier to understand and a little less intimidating:

w = 1;     %# Choose the value of w
k = 1:20;  %# Your 20 values to compute a sinusoid for
N = 100;   %# The number of time points in each sinusoid

t = linspace(0,2*pi,N).';  %'# A column vector with N values from 0 to 2*pi
X = zeros(N,numel(k));      %# A matrix to store the sinusoids, one per column

for iLoop = 1:numel(k)      %# Loop over all the values in k
  X(:,iLoop) = sin(k(iLoop)*w*t)*(2/(pi*k(iLoop)));  %# Compute the sinusoid
                                                     %#   and add it to X
end

plot(t,X);  %# Plot all the sinusoids in one call to plot

Here are some links to the documentation that should be helpful in fully understanding how the above solution works: LINSPACE, NUMEL, ZEROS, PLOT, For loops, Preallocating arrays to improve performance.