PWM and PPM are a constant frequency form of modulation, there is no frequency modulation. For the basics check Wikepedia for PWM and PPM.
The modulation sampling rate should be at least twice the highest modulation frequency. The higher the sampling rate, the easier it is to filter and recover the modulated signal.
I assume you want the frequency domain representation as the time domain representation is rather simple.
For a pulse that starts out at t=0 and stays high until t=Tau at which time it goes low and is periodic with period T (in other words a PWM pulse train) the frequency domain representation would be:
F(s)=Vo/s*(1-e^(-s*Tau))/(1-e^(-s*T))
where Vo is the amplitude of the pulses.
The above is derived from the more general form:
F(s)=F1(s)/(1-e^(-s*T))
where
F1(s)=Laplace{(u(t)-u(t-T))*f(t)}
and that F1(s) is the transform of the first period of f(t).
I am not really sure i understand your new questions, maybe you will have to restate them.
Maybe i did not understand your original question either because i am wondering why
you asked some of the new questions now. If the form was a surprise to you, then what
form of the equation did you expect to see here?
For example, to vary the PWM signal you would make Tau either shorter or longer (but
of course not longer than T). To vary PPM you would make T either shorter or longer
but not change Tau. I thought that was obvious as T and Tau specify the pulses.
hi suha, u can read the book"electronic communication systems" by kennedy or modern digital communication system by lathi. these contain detail information about pwm and ppm.
another thing, pwm and ppm are not belong to frequency modulation. in frequency modulation , frequency of carrier wave is varied with the amplitude of message signal. in pwm and ppm the frequency of carrier are kept constant.
and for effective modulation technique, sampling rate f(s)>= 2 fmax
before this, im bit confusing about the frequency carrier and sampling rate for PWM and PPM..
i've searching in journal and Google about it but most of them only explaining frequency modulation PAM...
thank you so much for explaining about the frequency of carrier and the sampling rate..