I'm trying to find the fourier series representation of the following periodic function: \(x(t)=cos(t)+sin(2t)+cos(3t-\frac{\pi}{3})\)
So I've found:
\(c_1 = c_{-1} = 1/2\)
\(c_2 = -\frac{j}{2}\)
\(c_{-2} = \frac{j}{2}\)
\(c_3 = \frac{1}{2}\times e^{-j\pi / 3}\)
\(c_{-3} =\frac{1}{2}\times e^{j\pi / 3}\)
According to the solutions the answer is supposed to be:
\(c_3 = c_{-3}= 1/2\)
Did I do something wrong?
So I've found:
\(c_1 = c_{-1} = 1/2\)
\(c_2 = -\frac{j}{2}\)
\(c_{-2} = \frac{j}{2}\)
\(c_3 = \frac{1}{2}\times e^{-j\pi / 3}\)
\(c_{-3} =\frac{1}{2}\times e^{j\pi / 3}\)
According to the solutions the answer is supposed to be:
\(c_3 = c_{-3}= 1/2\)
Did I do something wrong?