# Full-wave rectification of a cosine wave

#### furiousphil

Joined Dec 29, 2011
1
Hi I'm really struggling to make a start on a maths assignment i've been given and I hope somebody on here could help to get me going. The assignment is construct a full-wave rectified cosine wave on mathcad then pass it through a series of filters to see how the waveform changes. I just don't know how to determine a Fourier series for the waveform when all I have to start with is frequency=1500Hz. Any help would be appreciated.

#### Georacer

Joined Nov 25, 2009
5,182
Do you need the fourrier description of simply the function?

If it is the second, you can specify it as y(t)=abs(V*cos(wt))-2*0.6, with a V such that y(t)>0.

Maybe you can then do a fourrier transformation to that signal, for a period of T.

#### t_n_k

Joined Mar 6, 2009
5,455
If one assumes the rectification is ideal it presents one with a simpler problem.

In fact just adding two diode drops (0.6V?) to the absolute function doesn't equate with the real rectified function since the conduction angle per half cycle isn't exactly 180°.

The following link might be of some help wrt visualizing the ideal case of abs(cos(x))

http://www.wolframalpha.com/input/?i=fourier+series+abs(cos(x))&lk=3

In the link one can visualize several terms in the Fourier series to note how the waveform approaches the ideal case as the number of terms increases.

It appears only the even order terms in the series have a non-zero value.