Complex fourier series

1. What is meant by complex Fourier series?
2. How do you find the complex Fourier series?
3. What is complex Fourier transform?

What is meant by complex Fourier series?

Complex form of the Fourier series

Instead of trigonometric functions cosnx and sinnx we can use. complex exponential functions. einx = cosnx + i sinnx, e. −inx. = cosnx − i sinnx.

How do you find the complex Fourier series?

Assuming for the moment that the complex Fourier series "works," we can find a signal's complex Fourier coefficients, its spectrum, by exploiting the orthogonality properties of harmonically related complex exponentials. and integrate over the interval [0,T].

What is complex Fourier transform?

Fourier Transform of Complex Functions

Consider a complex function 𝑥(𝑡) that is represented as − x(t)=xr(t)+jxi(t) Where, 𝑥_𝑟 (𝑡) and 𝑥_𝑖 (𝑡) are the real and imaginary parts of the function respectively. Now, the Fourier transform of function 𝑥(𝑡) is given by, F[x(t)]=X(ω)=∫∞−∞x(t)e−jωtdt=∫∞−∞[xr(t)+jxi(t)]e−jωtdt.