Fourier series of real signals

Fourier series of real signals.
Written by Dr. Yoash Levron, January 2013.

This function computes the fourier series of a signal x(t). The amplitudes of the fourier series have the same dimension
of the original signal, so this function is useful for immediate computation of the actual frequency components, without
further processing.

for example, x(t) = 2 + 3*cos(2*pi*50*t) will result in :
dc value = 2
frequencies = [50 100 150 ...]
amplitudes = [3 0 0 ...]
phases = [0 0 0 ...]

x(t) is one cycle of an infinite cyclic signal. The function computes the fourier transform of that infinite signal.
The period of the signal (T) is determined by the length
of the input time vector, t.
x(t) must be real (no imaginary values).

The signal x(t) is represented as:
x(t) = Adc + A1*cos(w*t + ph1) + A2*cos(2*w*t + ph2) + ...

the function computes the amplitudes, Adc,A1,A2...
and the phases ph1,ph2,...

T = period of the signal = t(end) - t(1)
w = basic frequency = 2*pi/T

The function automatically interpolates the original signal to avoid aliasing. Likewise, the function automatically determines the number of fourier components, and truncates trailing zeros.

inputs:
t - [sec] time vector. Sample time may vary within the signal.
x - signal vector. same length as t.

outputs:
freq - [Hz] frequencies of the fourier series, not including zero.
amp - amplitudes vector. amp=[A1 A2 A3 ...], not including the DC component.
phase - [rad/sec] . phases, not including the DC component.
dc - the DC value (average of the signal).