Hi Guys, I am quite confused why he compares the incertitude of momentum and position of particle in quantum mechanics to frequency and amplitude in signal and system:

A waveform of infinite duration (infinite number of cycles) can be analyzed with absolute precision, but the less cycles available to the computer for analysis, the less precise the analysis. . . The fewer times that a wave cycles, the less certain its frequency is. Taking this concept to its logical extreme, a short pulse—a waveform that doesn’t even complete a cycle—actually has no frequency, but rather acts as an infinite range of frequencies. This principle is common to all wave-based phenomena, not just AC voltages and currents.

In order to precisely determine the amplitude of a varying signal, we must sample it over a very narrow span of time. However, doing this limits our view of the wave’s frequency. Conversely, to determine a wave’s frequency with great precision, we must sample it over many cycles, which means we lose view of its amplitude at any given moment. Thus, we cannot simultaneously know the instantaneous amplitude and the overall frequency of any wave with unlimited precision. Stranger yet, this uncertainty is much more than observer imprecision; it resides in the very nature of the wave. It is not as though it would be possible, given the proper technology, to obtain precise measurements of both instantaneous amplitude and frequency at once. Quite literally, a wave cannot have both a precise, instantaneous amplitude, and a precise frequency at the same time.
semiconductor

for my understanding when I sample a signal over many cycles, i do obtain the amplitude and frequency of the signal. so, why he is saying we loose the amplitude ?

 

Hi Guys, I am quite confused why he compares the incertitude of momentum and position of particle in quantum mechanics to frequency and amplitude in signal and system:

for my understanding when I sample a signal over many cycles, i do obtain the amplitude and frequency of the signal. so, why he is saying we loose the amplitude ?

You get ESTIMATES of both the amplitude and the frequency, but, for the same number of samples, you are trading off certainty of one for certainty of the other.

Say you have the ability to take 1000 samples at a controllable sampling rate. Let's further say that you have a waveform whose frequency content is known to be less than 500 Hz and is periodic.

By sampling at 1000 Sa/s, you can count the number of cycles and divide by the total time to get a good estimate of the frequency, but you have only the faintest idea of the amplitude.

On the other hand, if you sample at 500 kSa/s, you pack all of the samples into at most one cycle and can get a good estimate of the amplitude, but your knowledge of the frequency is not nearly as good.

If you want a better estimate of the amplitude, you can set a trigger threshold at your current best estimate and then take a burst samples at, say, 50 MSa/s, you are now taking a dense set of samples very close to the peak, so you your max sample value will be very close in time to the actual peak, but will still almost certain miss it. Even if it doesn't, you won't know with certainty that you didn't miss it. But now, with this burst of closely-spaced samples spanning only a small fraction of one cycle, you will have only the faintest idea of what the frequency is.

 

He is not saying that we loose the amplitude. He is saying that we lose the instantaneous amplitude of a varying signal if we sample it over many cycles. If you don't understand the difference, read this:

https://en.wikipedia.org/wiki/Fourier_transform

 

You get ESTIMATES of both the amplitude and the frequency, but, for the same number of samples, you are trading off certainty of one for certainty of the other.

Say you have the ability to take 1000 samples at a controllable sampling rate. Let's further say that you have a waveform whose frequency content is known to be less than 500 Hz and is periodic.

By sampling at 1000 Sa/s, you can count the number of cycles and divide by the total time to get a good estimate of the frequency, but you have only the faintest idea of the amplitude.

On the other hand, if you sample at 500 kSa/s, you pack all of the samples into at most one cycle and can get a good estimate of the amplitude, but your knowledge of the frequency is not nearly as good.

If you want a better estimate of the amplitude, you can set a trigger threshold at your current best estimate and then take a burst samples at, say, 50 MSa/s, you are now taking a dense set of samples very close to the peak, so you your max sample value will be very close in time to the actual peak, but will still almost certain miss it. Even if it doesn't, you won't know with certainty that you didn't miss it. But now, with this burst of closely-spaced samples spanning only a small fraction of one cycle, you will have only the faintest idea of what the frequency is.

now I understood what he meant. I was thinking, following your example, he could just sample more with higher frequencies(500Ks/s) and more than 3 cycles and not fixed to only 1000 samples.
Thank you

 

He is not saying that we loose the amplitude. He is saying that we lose the instantaneous amplitude of a varying signal if we sample it over many cycles. If you don't understand the difference, read this:

https://en.wikipedia.org/wiki/Fourier_transform

Yes, I got it now. Thanks