# Question on PCM Sampling and Quantization order

I had a doubt in my mind regarding the orders of sampling and quantization in PCM. What is the impact if the order is reversed, that is, the continuous time signal is first quantized and then sampled? I find a source on the internet claiming that quantization noise will increase with the reversal (link given), but I'm not sure why. Personally, I feel it should be unaffected as we're simply quantizing as in allowing a finite set of amplitudes first and then sampling those amplitudes. Am I missing something?

Link which claims the same: (Question 16)

That link provides a very superficial Q & A on signals and systems.

It's not clear which kind of a sampler or quantizer they are referring to.

However, if sampling and quantization are defined as ideal mathematical operators then, you should get exactly the same result by altering their orders. Hence the sample values should be same (meaning that the same noise also).

May be they're referring to some unstated practical ADC schemes (that I cannot recall) which do not perform ideal operations and might create different results.

• Amplitude is a vector? Guess I’m an idiot. Commented Apr 6, 2021 at 1:30
• i think modeling the quantization error, as a signal component, before sampling is not as useful as modeling the quantization error after sampling. Commented Apr 6, 2021 at 2:03
• @DanSzabo yes it's said to be a vector there, they probably mean it has a sign compared to the always positive magnitude. May be in 3D wave mechanics they are using vector amplitudes? not sure. Commented Apr 6, 2021 at 11:36
• @robertbristow-johnson regarding your comment, in fact, now I think that if we quantize a bandlimited signal before sampling, it will become a non-bandlimited staircase signal (due to jumps in quantization values) and thus it should be further bandlimited before ideal bandlimited sampling, may be that further lowpass filtering alters the sample values? Commented Apr 6, 2021 at 11:39
• yes Fat, that is what i was seeing. but the end result (the values of the samples) is the same. so forget about using an anti-aliasing filter before sampling (put it before the quantizer); somehow all of that aliasing due to the high frequency content due to the sharp edges of the quantized continuous-time signal, somehow all that aliasing just cancels itself out and the net spectrum of the quantization (as long as the signal swing is much larger than the quantization step size) is flat. Commented Apr 6, 2021 at 15:59