How to write Malvar window/piecewise function?

I want to plot

I can use the piecewise function to get v(x) but I cannot figure out how to combine it into w_j(t).

 % Create array of a_j's
a = linspace(1, 4, 4);

 % Create array of alpha_j's
alpha = linspace(1/4, 7/4, 4);

 %Malvar window for each j
for j = 1:3 

    syms x
    v = piecewise(x<=0, 0, 0<x<=1, (sin(pi*x/2))^2, x> 1, 1);

    fplot(v)

    syms t
    w = piecewise(-sqrt(alpha(j)^2) + a(j)<=t<=sqrt(alpha(j)^2) + a(j), sin((pi/2)*v((t - a(j) + alpha(j))/(2*alpha(j)))), a(j) + alpha(j)<t<a(j+1) - alpha(j), 1, -sqrt(alpha(j+1)^2) + a(j+1)<=t<=sqrt(alpha(j+1)^2) + a(j+1), cos((pi/2)*v((t - a(j+1) + alpha(j+1))/(2*alpha(j)))), 0);
    fplot(w)
 end

I have tried using if-else statements and heaviside function instead of piecewise and they also did not work.

Thanks

Answer 1

[Walter Roberson]

You define v as a symbol (with a scalar value), but you use v(expression) . That is trying to index into the scalar symbol. You should define

   v(x) = piecewise(x<=0, 0, 0<x<=1, (sin(pi*x/2))^2, x> 1, 1);

Note by the way that the ability to use range expressions of the form A < t <= B is not documented, which means that it could go away without notice. You should be using A < t & t <= B