hw2-2 - ECE130B Jan 10 2010 Home work 2 Due date Jan 20...

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ECE130B Jan. 10, 2010 Home work 2 Due date : Jan. 20, 2010 (Wednesday), by 5 p.m. at the home work box. Reading assignment . Chapter 3 of the text book, including both discrete and continuous Fourier series. Square wave . A square wave of period T is denoted by s ( t ) and is given by the formula, s ( t )= braceleftbigg 1 , if 0 lessorequalslant t mod T < T /2 , - 1 , if T /2 lessorequalslant t mod T < T , where t mod T is the unique number r between 0 and T that makes t - r exactly divisible by T ; that is, there exists some integer N , such that t = N T + r . Note that N can be a negative integer or even 0. Triangular wave . A triangular wave of period T is denoted by τ ( t ) , and is given by the for- mula, τ ( t )= 4 T t - 1 , if 0 lessorequalslant t < T /2 , 3 - 4 T t , if T /2 lessorequalslant t < T , where t = t mod T . Parabolic wave . A parabolic wave of period T is denoted by q ( t ) , and is given by the for- mula, q ( t )= 8 T 2 t ( T - 2 t ) , if 0 lessorequalslant t < T /2 , 8 T 2 ( T - 2 t )( T - t ) , if T /2 lessorequalslant t < T , where t = t mod T .
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