Sinusoïdal

Square

Triangular

Pulse

- Time domain : It is simply an algebraic expression written as v(t). In practice we use an
**oscilloscope**to view the signal in the time domain. - Frequency domain : The mathematical representation is more complex, we use Fourier analysis for periodic signals to find their frequency components. Fourier analysis stipulates that all periodic signals
can be replaced by a sum of sines and cosines functions with different amplitudes as it is shown by the following equation :

With a_{0}, a_{N}and b_{N}called the Fourier series coefficient and they can be found by using the following equations :

Our objective is to use the results of the calculations of the coefficients and apply it in the spectral analysis of periodic signals.In practice we use a**spectrum analyser**to view the signal in the frequency domain where the horizontal axis will represent the frequency f and the vertical one the voltage in Volts or the power in dBm as it is the case in telecommunications.

The fourier coefficients of the wave are given by the following expressions :

Note that the order of the harmonics can be both even and odd depending on the value of the duty cycle of the wave.