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This might be a naïve question, are these correct statements?

  • Both amplitude and frequency modulated radio signals nowadays use quadrature modulation and demodulation as a mean to transfer and receive radio signals.

  • Whenever quadrature modulation is used the sampling rate should be equal to bandwidth.

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Both amplitude and frequency modulated radio signals nowadays use quadrature modulation and demodulation as a mean to transfer and receive radio signals.

This question is ill-defined – a signal doesn't use quadrature modulation/demodulation, transmitters/receivers do.

So, your question is, if we try to "rescue" it, is

Do modern FM receivers/transmitters use quadrature modulators

No, not generally. When I receive FM audio with my USRP, I might do that, but usually, I will use a trick and actually do a low-IF sampling.

When a car radio receives signals, it definitely doesn't – simply because IF receivers typically still have technological advantages over direct conversion /IQ receivers, mainly due to lack of DC offset, and because you can get high-Q analog bandpass filters easily. The bandwidths used for FM audio are so laughably small that any modern 16 or 32 bit microcontroller can usually deal with the IF sampling rate.

Now, assuming this is about FM audio broadcasts only: I'd suspect that you'll actually see the different components of the signal first being generated digitally, then digitally mixed to different IFs, and then generated using IQ DACs and mixed up using a Quadrature modulator. But: Broadcasting equipment often has seen quite a few winters, so this might not always be true!

Whenever quadrature modulation is used the sampling rate should be equal to bandwidth.

No, not generally. Nyquist says that in the complex sampling case, it is sufficient to sample with nothing more than the signal bandwidth, but in fact, you rarely do that, because you then wouldn't have the chance to suppress noise due to oversampling, or to have "spare" bandwidth to do frequency correction. Also, there might be simple technical problems ("can't get an oscillator running at 13.13131313 MHz") that make it impossible to sample at exactly the bandwidth. And, there's also applications where undersampling is employed.

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  • $\begingroup$ Thank you, so USRP receiver uses quadrature demodulation because it is done in software? $\endgroup$ – Jack Aug 17 '16 at 16:07
  • $\begingroup$ @MaryannEthan No! $\endgroup$ – Marcus Müller Aug 17 '16 at 16:08
  • $\begingroup$ @MaryannEthan don't mix hardware aspects, namely IQ modulation/demodulation, which is a mixer architecture, with the question whether a signal is processed digitally or with analog circuitry. There's no direct causality here. There's plenty direct sampling SDR architectures, plenty IQ mod/demod architectures, plenty IF/superhet SDR architectures, and combinations of these. $\endgroup$ – Marcus Müller Aug 17 '16 at 16:09
  • $\begingroup$ There is a Michael Ossmon's radio tutorial on imaginary numbers and he explains how it is easier to get the information out of a modulated signal when we have a real part and imaginary part. Basically I assumed we use it to makes the math part easier. $\endgroup$ – Jack Aug 17 '16 at 16:13
  • $\begingroup$ the engineer's job is not to make math easier, but to build better devices. It's nice when a technical implementation makes the math easier, but unless that simplification allows us to make statements we couldn't make before and therefore were able to do things we couldn't, there's no reason why we should chose an architecture "just because the math is easier". $\endgroup$ – Marcus Müller Aug 17 '16 at 16:27
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Both amplitude and frequency modulated radio signals nowadays use quadrature modulation and demodulation as a mean to transfer and receive radio signals.

The use of a quadrature transmitter / receiver is not needed unless you are using a quadrature signal. A simple car radio would likely use something much simpler. Radios that are capable of quadrature modulations would already have the I and Q receive paths so they could still just use that. There may be some benefits to using an IQ modulator for FM or AM, but I'm not sure what they would be.

Whenever quadrature modulation is used the sampling rate should be equal to bandwidth.

The frequency of complex samples does not need to be double the bandwidth, (but you need the same overall number of samples/second (I and Q) (unless aliasing is desired, and it sometimes is). Further, the signal is often over sampled to allow flexibility in later processing.

Your confusion may stem from the fact that QPSK can ideally support twice the data bandwidth for a given spectrum bandwidth, or the same data rate for half the bandwidth. In general, quadrature modulation schemes can be more or less complex/efficient than QPSK.

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    $\begingroup$ The second part of your answer is wrong; the "twice the highest frequency" sampling rate statement is a misconception of Nyquist, in two ways: 1. Nyquist's sampling theory states something about the bandwidth, not the highest contained frequency, and 2. the factor of two applies to real-valued sampling, not IQ sampling. $\endgroup$ – Marcus Müller Aug 17 '16 at 16:03
  • $\begingroup$ @MarcusMüller GAH, you're right. I edited my response to indicate complex samples vs real samples, bandwidth vs frequency. $\endgroup$ – Andrew W. Aug 17 '16 at 16:33
  • $\begingroup$ Not enough coffee this morning I guess _(ツ)_/¯ $\endgroup$ – Andrew W. Aug 17 '16 at 16:41

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