Pulse Amplitude Modulation (PAM): The sampled signal.

[richard1991]

Hi. I'm referring to a signal that is the result of the sampling an audio analogue signal at a sampling rate that meets or bests the rate calculated by the Nyquist equation. I'm not referring to the modulation of a carrier.

My difficulty is not in grasping what I think is the theory, it's believing it.  So, I'm looking, in a way, for confirmation of what I think I'm understanding.

If we sample an analogue signal, by say using an electronic switch, which simply opens and closes, we are modulating the audio analogue signal.  This is shown by the fact that the spectrum of the output, of the sampling process, contains modulation products, that is new sidebands.   We then filter out all the new sidebands, by a low pass filter, we are left with a spectrum that matches the original analogue signal.

Imagine the sampling was a switch in series with one of the wires to a loudspeaker, and there is a low pass filter before the loudspeaker. OK. Now, this is what I think:

* If we analyze  the signal at the loudspeaker terminals, we see that it is a series of pulses of varying amplitudes.

* Speech or music is heard to the same quality as if we were feeding the speaker with the original (pre-sampled and filtered) analogue signal.

* That although modulation has been involved (PAM is involved), there is no need to demodulate the audio signal. (Unless the filtering is seen as demodulating process).

That's my understanding.  Am I correct? Thanks.

[Audioguru]

Yes you are correct. For years I worked with a very high quality and huge intercom system called Pamex. It sampled audio as you said and used a single path for up to 8 voice or music channels. Its audio fidelity was very good. It used some dead time between channel samples to avoid crosstalk.

[vk6zgo]

Hi. I'm referring to a signal that is the result of the sampling an audio analogue signal at a sampling rate that meets or bests the rate calculated by the Nyquist equation. I'm not referring to the modulation of a carrier.

My difficulty is not in grasping what I think is the theory, it's believing it.  So, I'm looking, in a way, for confirmation of what I think I'm understanding.

With respect, you don't quite understand the theory.
You are all around it, but not there yet.

If we sample an analogue signal, by say using an electronic switch, which simply opens and closes, we are modulating the audio analogue signal. 

Yes....., but the usual convention is that the lower frequency signal is modulating the higher frequency signal.

This is shown by the fact that the spectrum of the output, of the sampling process, contains modulation products, that is new sidebands.   We then filter out all the new sidebands, by a low pass filter, we are left with a spectrum that matches the original analogue signal.

Let's just for the moment, neglect the pulse side of things & look at a simple AM modulator, with a single modulating frequency.
We will call the Carrier frequency fc, & the Modulating frequency fm.
Appearing at the output of the modulator, are the two original frequencies, fc, & fm,as well as the sidebands, fc+fm,&  fc - fm

For instance, if the carrier is at 1.0MHz, & the modulating frequency is at 1.0kHz.
This results in a  lower sideband at 0.999MHz, & an upper sideband at 1.001MHz.

These sidebands, the original carrier, & the original modulating frequency will all appear at the modulator output.
Any of them, or any combination can be selected or rejected by the use of filters.

Imagine the sampling was a switch in series with one of the wires to a loudspeaker, and there is a low pass filter before the loudspeaker. OK. Now, this is what I think:

* If we analyze  the signal at the loudspeaker terminals, we see that it is a series of pulses of varying amplitudes.

* Speech or music is heard to the same quality as if we were feeding the speaker with the original (pre-sampled and filtered) analogue signal.

* That although modulation has been involved (PAM is involved), there is no need to demodulate the audio signal. (Unless the filtering is seen as demodulating process).

That's my understanding.  Am I correct? Thanks.


Imagine the sampling was a switch in series with one of the wires to a loudspeaker, and there is a low pass filter before the loudspeaker. OK. Now, this is what I think:

* If we analyze  the signal at the loudspeaker terminals, we see that it is a series of pulses of varying amplitudes.

* Speech or music is heard to the same quality as if we were feeding the speaker with the original (pre-sampled and filtered) analogue signal.

* That although modulation has been involved (PAM is involved), there is no need to demodulate the audio signal. (Unless the filtering is seen as demodulating process).

That's my understanding.  Am I correct? Thanks.

In your example, the speaker is, effectively, a Low Pass Filter.

[richard1991]

I see the PAM spectrum that results from sampling. Put that throgh a LPF and I see that the mixing products are removed by filtering. So, what is left is a spectrum that looks like the original audio analogue signal before it was sampled. But, never-the-less it consists of a series of pulses,because it's the result of sampling.

Now, it's said that this sampled/pulsed signal contains all (more or less) the information as the original analogue signal.  And if it were fed into say an audio amplifier the sound coming from the speaker would be a pretty faithful representation of the analogue signal,

Now, it's easy to go figure that the reason the PAM signal is akin to the original analogue signal, is because the sidebands have been removed from the spectrum.  But, is it correct to say, that it's not really the removal of the sidebands, that is responsible for the PAM signal rendering a signal that is very well faithful to the analogue signal?  Is it the action of a low pass filter, in terms of integration that is responsible for the PAM signal rendering such a faithful signal with respect to the originating analogue signal?

[Richard Crowley]

You are confusing yourself significantly by continuing to look at sampling as "PAM".  If anything, it is the opposite.

Yes,it is primarily the action of a low-pass filter to integrate the individual samples which renders a reproduction of the original waveform.
If you insist on comparing it to PAM, then the same low-pass filtering is "removing the sidebands".

Note that most modern digital audio equipment uses "oversampling" where 8, 16, 32, etc. extra samples are extrapolated between each real sample value.  This is trivial to do here in the 21st century with modern digital circuits.  The advantage being that the artifacts ("sidebands" if you wish to call them) are at super-sonic frequencies where it is easy to filter them with simple circuits without affecting the frequency or phase response down at audio frequencies (20Hz ~ 20KHz).  We are continuously evolving to where things are easier to do in the digital domain than in the analog domain.

[richard1991]

Okay, the results of sampling is a pulse amplitude modulated signal. And that is the type of signal that is under consideration. It's not the result of modulating a carrier.

Page 303 of ELECTRONIC COMMUNICATION TECHNIQUES by Paul H. Young says "Figure 11.1 shows an example of a sampler. The switch S₁ is closed instantaneously every Ts seconds to allow the instantaneous amplitude of V_A to appear at the output. The output is in fact, a pulse amplitude modulated signal."

So, I'm referring in my posts to a pulse amplitude modulated signal. And it is the result of something akin to modulation, because it has sidebands. One then thinks that sampling is a form of PAM. Because of the result, i.e, sidebands. But is it?

I am absolutely certain that modulating a sinusoidal carrier with pulses will be a form of modulation called PAM. Somewhat less certain whether chopping an analogue signal can be said to be PAM modulation (notice I did not sat PAM signal).

It seems then, that the result of sampling is a pulse amplitude modulated signal.   The result of pulse modulating a carrier is also a pulse amplitude modulated signal. However, what is being pointed out I think, is that only the latter involves PAM in the generation of the signal, that is by way of pulse modulation (of a carrier).  I guess then, that where a carrier is not involved, the method producing the pulse amplitude modulated signal is,  well - sampling.

Therefore there is a discrepancy in my title. The title should have been something like Pulse Amplitude Modulated signals: Sampled signals. Where PAM is involved, the title would be something like: Pulse Amplitude Modulated Signals: PAM signals.

[dmills]

That 'every Ts seconds' sure sounds like a carrier to me.

Regards, Dan.

[richard1991]

Actually, the caption for figure 11-3, which shows sampling says: "Pulse amplitude modulator, natural sampling."  Shows a circuit with a FET as a switch effectively chopping an analogue signal. That is I think saying sampling is PAM! Because the caption says "modulator" No carrier.

Figure 11-1, caption says "Impulse sampling of an analogue voltage". Shows, with graphs and a switch, production of a chopped signal.

I'm getting confused now. Off to bed, listen to football on the radio. Maybe all will be sorted out tomorrow. :-)

[Audioguru]

The sampling frequency is the carrier frequency and the momentary amplitudes of the lower frequency modulation signals are sampled. The momentary amplitudes are PAM and can be simply filtered.

[Richard Crowley]

This is one of the better discussions and explanations of audio ADC and DAC principles and practice:

https://youtu.be/cIQ9IXSUzuM