real vs complex fourier series

The complex Fourier series is presented first with pe- riod 2π, then with general period The connection with the real-valued Fourier series is explained and 

E1 10 Fourier Series and Transforms (2014-5543) Complex of cosθ and sinθ The Complex Fourier Series is the Fourier Series but written using eiθ In these lectures, we are assuming that u(t) is a periodic real-valued function of time

This is the forward transform, calculating the frequency domain from the time domain In spite of using the names: real part and imaginary part, these equations

Fourier Transform - Symmetry properties Fourier Series and Transform - Comparison Fourier Transform example - non-periodic function Complex Fourier 

The complex Fourier series is in some ways a superior product, at least for those people Equation (4) is also true for x = L and for x = −L if we interpret f(−L−) 

The complex Fourier series expresses the signal as a superposition The real and imaginary parts of the Fourier coefficients ck are written in this unusual way

It turns out this is always true whenever we rotate one complicated set of arrows by another It means that the angle of the resulting direction is the sum of the 

In this section we will learn how Fourier series (real and complex) can be used to represent functions and sum series We will also see what happens when we use  

Fourier coefficients an and bn into a complex coefficient cn through cn = 1 2 where a and b are real numbers and i2 = −1, can be written in polar form as