piecewise function Fourier seriers

I want use matlab help to derive the Fourier series of a piecewise function. I write code like following:

syms t Vin Vout Dp Ds D T

assume(t>0);
Vp = piecewise( ...
    t> 0 & t< Dp*T/2, Vin, ...
    t> (Dp*T/2) & t< T/2,0, ...
    t> T/2 & t< (1+Dp)*T/2, -Vin, ...
    t> (1+Dp)*T/2 & t< T, 0)


Vpf = fourier(Vp)
assume(t,'clear');

and result is :

fourier(piecewise(t < (Dp*T)/2, Vin, t < T/2&(Dp*T)/2 < t, 0, t < (T*(Dp + 1))/2&T/2 < t, -Vin, t < T&(T*(Dp + 1))/2 < t, 0), t, w)

The result does not helpful for me.

[Torsten]

Maybe assuming 0 < Dp < 1 can help.

[KUN]

Thank you for reminding me.

Answer 1

[Paul]

Hi KUN,

In the context of the Fourier transform, I'm not sure that the assumption on t makes sense, at least not in the context of fourier.

IIRC, fourier doesn't like piecewise. Instead, form Vp with terms using rectangularPulse and then find the Fourier transform.

[KUN]

Thank you for your answer. I will try rectangularPulse.

[Paul]

Feel free to post back here with updated code if you still have trouble after trying rectangularPulse.