Reply by julius May 8, 20072007-05-08
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
Reply by Jerry Avins May 8, 20072007-05-08
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. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by May 8, 20072007-05-08
> 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
Reply by julius May 8, 20072007-05-08
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
Reply by May 8, 20072007-05-08
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?

Reply by Jerry Avins May 8, 20072007-05-08
Clay wrote:

   ...

>> I don't think a PAM spectrum can be deduced in the abstract. One needs >> the modulating signal, just as for AM or FM. Adjacent pulses will have >> different amplitudes. (The duty cycle needs to be specified too, and in >> practice, the splatter filter will round the corners of the pulses. >> >> Jerry >> -- > > He just ends up with a summation where each term is weighted by the > corresponding PAM value. For special sets of PAM values, the summation > can be reduced.
Sure. There are even some interesting observations to be made about the overall statistical properties of the summation. There are some spectral effects that don't appear when all the pulses have the same amplitude. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by Clay May 7, 20072007-05-07
On May 7, 9:02 pm, Jerry Avins <j...@ieee.org> wrote:
> Clay wrote: > > On May 7, 11:53 am, ivanat...@gmail.com wrote: > >> I've read some reviews on that book and I want to find it. I checked > >> in some libraries but no one have it. I wish I had a CC to order it > >> from Amazon... > >> Do you have this book in some sort of e-book variant (PDF, html or > >> etc)? > > > I have the book in a quaint form - hardcover. I bought it in a > > bookstore (Barnes & Noble) last summer. I have other books by Nahin, > > so I was sure this would be a keeper, and it is. > > > Clay > > > On your original problem, find the FT of a solitary pulse. Then think > > about how you would find the FT of two pulses side by side using the > > Heaviside shifting theorem. Then extend the idea to an infinity of > > pulses. > > I don't think a PAM spectrum can be deduced in the abstract. One needs > the modulating signal, just as for AM or FM. Adjacent pulses will have > different amplitudes. (The duty cycle needs to be specified too, and in > practice, the splatter filter will round the corners of the pulses. > > Jerry > --
He just ends up with a summation where each term is weighted by the corresponding PAM value. For special sets of PAM values, the summation can be reduced. Clay
Reply by Jerry Avins May 7, 20072007-05-07
Clay wrote:
> On May 7, 11:53 am, ivanat...@gmail.com wrote: >> I've read some reviews on that book and I want to find it. I checked >> in some libraries but no one have it. I wish I had a CC to order it >> from Amazon... >> Do you have this book in some sort of e-book variant (PDF, html or >> etc)? > > I have the book in a quaint form - hardcover. I bought it in a > bookstore (Barnes & Noble) last summer. I have other books by Nahin, > so I was sure this would be a keeper, and it is. > > Clay > > On your original problem, find the FT of a solitary pulse. Then think > about how you would find the FT of two pulses side by side using the > Heaviside shifting theorem. Then extend the idea to an infinity of > pulses.
I don't think a PAM spectrum can be deduced in the abstract. One needs the modulating signal, just as for AM or FM. Adjacent pulses will have different amplitudes. (The duty cycle needs to be specified too, and in practice, the splatter filter will round the corners of the pulses. Jerry -- Engineering is the art of making what you want from things you can get. &macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
Reply by Clay May 7, 20072007-05-07
On May 7, 11:53 am, ivanat...@gmail.com wrote:
> I've read some reviews on that book and I want to find it. I checked > in some libraries but no one have it. I wish I had a CC to order it > from Amazon... > Do you have this book in some sort of e-book variant (PDF, html or > etc)?
I have the book in a quaint form - hardcover. I bought it in a bookstore (Barnes & Noble) last summer. I have other books by Nahin, so I was sure this would be a keeper, and it is. Clay On your original problem, find the FT of a solitary pulse. Then think about how you would find the FT of two pulses side by side using the Heaviside shifting theorem. Then extend the idea to an infinity of pulses.
Reply by Thomas Magma May 7, 20072007-05-07
<ivanatora@gmail.com> wrote in message 
news:1178541359.429108.295770@p77g2000hsh.googlegroups.com...
> 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! >
Well one way to do this is if you can write this signal in a mathematical way you can generate samples of that signal, that you can later subject to a frequency transform. If your interested in frequencies up to 6 MHz then Nyquist says you need a sample rate of at least 12MHz (I personally would go beyond just Nyquist). Then generate an array of samples with respect to time. i.e. t=0 t=8.3E-8 t=1.66E-7 t=2.5E-7 are the first four samples at Nyquist. Then you can do a DFT or FFT on the samples to get the spectrum. Whatever the required frequency resolution will determine how many samples are generated. Thomas Magma