How to draw a spectrum of Pulse Amplitude Modulated signal?

I've know that Mathcad can do some sorts of Fourier Transforms, but I
can't really understand how these functions work. I'll be glad to use
them to verify my calculations...
There is a built-in function fft() (and there are ifft() for inverse
transform and dfft() for discrete transform) but I can't understant
what data should I give to it. In the Mathcad help there is written
fft() takes a vector (a one column matrix?) as input, but what should
this vector contain?

On May 7, 7:35 am, ivanat...@gmail.com wrote:
> Hello all!
>
> I have a school project to do about PAM (Pulse Amplitude Modulation),
> but these stuff aren't explained at all in our school class. I tried
> searching google about PAM spectrum, but I almost didn't find
> anything. Even in Wikipedia there was almost nothing useful about PAM.
> I'm given a triangle signal with period=T,amplitude=A and a pulse
> (square) carrier signal at 1MHz.
> I can write this signal in a mathematical way, but I don't know how to
> find its spectrum.
> I have 2 things to do:
> 1) Write down an algoritm to calculate the spectrum of the modulated
> signal.
> 2) Draw the spectrum of the modulated signal up to 6MHz.
>
> If you help me with 1) I'll be able to do 2)
>
> Thanks!


Let's start with the basics.  What is the definition of the spectrum
of a signal, say x(t)?

Julius

> Let's start with the basics.  What is the definition of the spectrum
> of a signal, say x(t)?
>
Lets say spectrum is when x(t) is discomosed to its simple composits -
we call them harmonics. So these all harmonics are plotted with their
amplitudes against frequency.
So drawing a spectrum is to show these harmonics (Amplitude-Frequency
Diagram).
Am I correct? :D

ivanatora@gmail.com wrote:
>> Let's start with the basics.  What is the definition of the spectrum
>> of a signal, say x(t)?
>>
> Lets say spectrum is when x(t) is discomosed to its simple composits -
> we call them harmonics. So these all harmonics are plotted with their
> amplitudes against frequency.
> So drawing a spectrum is to show these harmonics (Amplitude-Frequency
> Diagram).
> Am I correct? :D

Yes. That's what spectrum usually means. The amplitudes of the pulses 
vary depending on the data transmitted, so the harmonic amplitudes vary 
also from pulse to pulse. As a result, harmonics that would cancel when 
all pulses are the same will appear in the spectrum.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On May 8, 4:03 pm, ivanat...@gmail.com wrote:
> > Let's start with the basics.  What is the definition of the spectrum
> > of a signal, say x(t)?
>
> Lets say spectrum is when x(t) is discomosed to its simple composits -
> we call them harmonics. So these all harmonics are plotted with their
> amplitudes against frequency.
> So drawing a spectrum is to show these harmonics (Amplitude-Frequency
> Diagram).
> Am I correct? :D


No. Let's be formal here.  I think that's why you are having a hard
time finding the answer to your question.  Although I did cheat a
little
and abused the notation here.  Usually a PAM signal is taken to be
a signal determined by a sequence of random symbols.
In this case you are confusing "the spectrum of a signal" with
"the Fourier transform of a signal".  These are two different things.

Consider a *random* signal x(t) = \sum_n a_n g(t-nT), where a_n
is a sequence of random (PAM) symbols, and g(.) is the modulation
pulse shape.

The spectrum of this signal is the expected value of its square
magnitude in the frequency domain, also called its power spectral
density.

Are you still with me here?

You have the right intuition perhaps, but I think the problem is that
you
are being a little too quick in trying to jump to the answer.

If you're being impatient and want to jump to the answer, the best is
probably to lookup a digital communications textbook.  Where I
am trying to steer this discussion is almost always background
material reviewed in a digital comm text.

Julius