# Recognizing different pulse shaping forms (16-QAM modulation)

I have three versions of a 16-QAM modulated signal, each showing the time curve of the real and imaginary parts, the spectrum and the symbol constellation. These three versions differ by the respective pulse shaping method (sinc, rect, raised-cosine or root-raised-cosine).

Is there any possibility to assign the corresponding pulse shaping method to each of these three versions and determine the parameters bandwith $$B$$, symbol duration $$T$$ and roll-off factor $$\beta\:$$?

The respective diagrams: The constellation diagram of the second signal looks exactly the same as the constellation diagram of the first one.

[![enter image description here][6]][6]

• This is a typical homework assignment or quiz/test question so we can’t bypass the learning opportunity here. All three are easy to recognize. Please clarify where you are stuck and what you’ve already done and we’ll see if we can help without simply providing the answer. Commented Jul 16, 2023 at 11:01
• @DanBoschen It's an exercise I would like to understand to prepare myself for an exam. I wasn't sure if I should mention this because I was under the impression that this site wasn't the best place for questions like this und maybe long 'explanation dialogues' between me and a potential helper. However, I couldn't find any other suitable forum and so I at least tried it here because I don't have any similar examples with solutions. I also tried to find some information in the internet or in books but it seems like I don't have a sufficient
– lyx
Commented Jul 16, 2023 at 13:01
• overview at the moment. Before I try do depict my current knowledge I would like to mention that I have to understand this exercise in the course of an relatively broad-ranging introduction course concerning communication technology. The focus wasn't on (digital) modulation and pulse shaping and especially not on a detailed mathematical analysis of these methods. I know that the bandwith of the spectrum of the 16-QAM modulated signal isn't limited and that an appropriate pulse shaping filter can limit the bandwidth so that it can be transmitted over a bandwith-limited channel for example.
– lyx
Commented Jul 16, 2023 at 13:03
• Moreover, pulse shaping is necessary to prevent ISI since mere rectangle signals are susceptible to due to their spectrum when they are transmitted over a low-pass channel. We talked about the sinc-, the raised-cosine- and the root-raised-cosine-pulse as possible pulses for pulse-shaping but I'm not sure how to recognise which one was used and how to determine the parameters $B$, $T$ and $\alpha$. I see that the first signal doesn't have a bandwith-limited spectrum. So I would suppose that there wasn't used a raised-cosine- or a root-raised-cosine-pulse but a rectangle-pulse.
– lyx
Commented Jul 16, 2023 at 13:03
• So I have todetermine the bandwith now. However, the whole spectrum looks more or less arbitrary to me and not as specific as the spectrum of a bandpass for example. I'm also not sure what the bandwith in this context is. I know the x dB bandwith but how am I supposed to read something from this diagram which looks like noise to me? Additionally, I'm not sure how I'm supposed to know about the spectrum for $f>50~\mathrm{Hz}$ or $f<-50~\mathrm{Hz}$. I also tried to read the symbol duration of the first signal from the first diagram. But I don't see clear ones and zeros.
– lyx
Commented Jul 16, 2023 at 13:04