ECE 280/Fall 2021/HW5F21

This page will have clarifications and examples for HW 5.

Clarifications

• The value of $$A$$ for Exercise 5.4.11 is given as 20.
• For Part III, use $$N=51$$ in the code to get up to the 51st harmonic.
• For Part III.1, use $$T=1$$ and note that the width is half the period.

Examples

• To write code for a piecewise periodic function, note that in MATLAB mod(t,T) and in Python np.mod(t,T) will produce values that go from 0 to $$T$$ as $$t$$ goes from 0 to $$T$$ and will then repeat that periodically. That means for a periodic function $$g(t)$$, if you write the formula for the period from $$0$$ and $$T$$ as $$\hat{g}(t)$$, you can replace $$t$$ with mod(t, T) to get the periodic version. For example, the analytical version for $$x_3(t)$$ in III.1 could be:

  u = @(t) (t>=0)*1.0;
  vinr = @(t) 5*(u(mod(t,T))-2*u(mod(t,T)-T/2)+u(mod(t,T)-T));
  

  or

  u = lambda t: (t>=0)*1.0
  vinr = lambda t: 5*(u(np.mod(t,T))-2*u(np.mod(t,T)-T/2)+u(np.mod(t,T)-T));
  

  while the analytical version for $$f(t)$$ in Exercise 5.4.11 for III.2 could be:

  u = @(t) (t>=0)*1.0;
  vinr = @(t) 20*(u(mod(t,T)-1)-2*u(mod(t,T)-2)+2*u(mod(t,T)-3)-u(mod(t,T)-4));
  

  or

  u = lambda t: (t>=0)*1.0
  vinr = lambda t: 20*(u(np.mod(t,T)-1)-2*u(np.mod(t,T)-2)+2*u(np.mod(t,T)-3)-u(np.mod(t,T)-4))