Syntax of the equation below

y= (1./k)*(sin(k'*t))

this equation was used to find the sum of odd harmonics of sine wave. Can someone explain how this equation works?

[Walter Roberson]

What are size(k) and size(t) ?

Answer 1

[KSSV]

t = 0:.01:10;
figure
hold on
for k = 1:2:10
    y = sin(k*t)/k;
    plot(t,y)      
end

Note that y = sin(f*t), f represents the frequency, here k (=f) takes only the odd frequencies. YOu can check that from the above plot.

[KSSV]

siva kumar commented:

Above equation which i have written worked.So please tell me what is the significance of . and '. Thank you

[KSSV]

It calculates 1/k*sin(k*t) for each k and sum's them. This is same as:

t = 0:.01:10;
k = 1:2:10 ;

% y= (1./k)*(sin(k'*t)) ;
% 
% plot(t,y) ;
yy = zeros(size(t)) ;
for i = 1:length(k)
    yy = yy+1/k(i)*sin(k(i)*t) ;
end
plot(t,yy)

.* stands for element by element multiplication; ' this stands for transpose.

[Walter Roberson]

This does not find the sum of the harmonics, only plots them individually.

. has no meaning of its own in the original code. ./ is the name of an operator that is different than the / operator. The / operator is formally named as mrdivide and it is algebraic matrix division with A/B being similar to A*pinv(B) where * is algebraic matrix multiplication. The ./ that was used is element-by-element division, so 1./[3 5 7] would give you [1/3 1/5 1/7]

' is complex conjugate transpose. In the special case of working with real values, that is equivalent to transpose . That is, it would switch between row vector and column vector, or column vector and row vector.