Homework 7 Problem 2
A periodic signal x(t) is expressed in the complex Fourier series form as
$$x(t) = \sum_{n=-\infty}^{\infty} C_n e^{jn\omega_0 t}$$,
where T = 1 second and
$$C_0 = 1$$
$$C_1 = (1 - 0.5j)$$,
$$C_{-1} = (1 + 0.5j)$$,
$$C_2 = \frac{\sqrt{2}}{4} (1 + j)$$,
$$C_{-2} = \frac{\sqrt{2}}{4} (1 - j)$$,
$$C_n = 0, |n| > 2$$.
1. Express x(t) in the trigonometric form
$$x(t) = a_0 + \sum_{n=1}^{\infty} [a_n cos(n\omega_0 t) + b_n sin(n\omega_0 t)]$$
What is the fundamental frequency $\omega_0$ in rad/s
1. What is $a_0$
2. What is $a_1$, $b_1$, $a_2$ and $b_2$
Script
1 % Enter the fundamental frequency Omega
2 Omega = [ ];
3 % Enter a0
4 a0 = [ ];
5 % Enter a1
6 a1 = [ ];
7 % Enter b1
8 b1 = [ ];
9 % Enter a2
10 a2 = [ ];
11 % Enter b2
12 b2 = [ ];
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