Understanding Aliasing in Digital Down Sampling

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Iain Explains Signals, Systems, and Digital Comms

2 жыл бұрын

Explains a fundamental property of aliasing when discrete time signals are down sampled. Highlights the relationship between a low pass signal, and any other signal that has the same values at the sample times.
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For a full list of Videos and accompanying Summary Sheets, goto: www.iaincollings.com
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Пікірлер: 23

@frederikvanaverbeke8840 Жыл бұрын

This is incredibly well explained! THank you!

@iain_explains Жыл бұрын

Glad it was helpful!

@MusaYmc Жыл бұрын

Thanks for the clear explanation, extremely useful for dps courses.

@iain_explains Жыл бұрын

Glad it was helpful!

@Daniboy370 Жыл бұрын

As always, the best explanations ...

@iain_explains Жыл бұрын

Thanks for your nice comment. Glad you like the videos!

@SeyedAgent47 Жыл бұрын

Best Accent, Best Content, perfect dude... Thanks for the work. please keep posting ❤

@iain_explains Жыл бұрын

I'm so glad you like the videos, and the presentation style.

@MrSocialish Жыл бұрын

Thanks for the video! I see why we get repeats at the sampling rate and why we'd need to filter beforehand, but I'm confused on when it would be applicable to not "trash" the samples that were pushed to zero. My understanding was that when we downsampled, lets say by a factor of M=2, that we would only have half the number of samples from the original signal. Are there different applications for both scenarios (pushing to zero vs. trashing)?

@iain_explains Жыл бұрын

Yes, you're right, when sampling, you only really want to keep the "sampled" values, and remove the "zero-ed" indices, ... but it helps to view it in two steps in order to understand the process. In the "reverse direction" (ie. signal reconstruction) you definitely do need to consider the version that has the "zero-ed" indices, because you first need to "zero-pad" the compressed signal and then pass it through a reconstruction filter.

@MrSocialish Жыл бұрын

@@iain_explains Okay that makes sense I think. I always see decimators paired with LP filters. So if I am understanding correctly, that LP filter is strictly for out-of-band spectra before the downsampling, not for the images that are created FROM the downsampling. Is that correct? The process of filtering after upsampling makes sense to me. Although when I first saw it, it seemed like magic! It's a really cool, yet simple idea. Also, have you considered writing a book on all these topics? I would buy that in a heartbeat! You teach them very well; seemingly complex ideas become easily digestible.

@iain_explains Жыл бұрын

Yes, that's right. The low pass filter prior to sampling is called an anti-aliasing filter, as it removes all noise components so that they don't alias into the spectrum of interest. And yes, I have thought about writing a book, but at the moment I prefer putting my energy into making new videos instead.

@yasserothman4023 2 жыл бұрын

Thanks for sharing, may I know what it is the Min sampling frequency needed for a complex signal Of bandwidth B ? I know that from Nyquist this is 2*bandwidth of the signal if the signal is real but what if it is complex ?

@iain_explains 2 жыл бұрын

Well, I think the best way to think about it is to acknowledge that complex signals are not real. So what does it mean to "sample" a signal that is not real? "Complex signals" are simply a way to represent two orthogonal components of a real signal (ie. both components are real - they are just orthogonal), so rather than trying to sample a complex signal, it's better to think about sampling the real component and the "imaginary" component. You need to sample each at the respective Nyquist rate, so it results in twice the number of samples, compared to a "purely real signal".

@yasserothman4023 2 жыл бұрын

@@iain_explains thanks but what is the sampling rate in this case (complex signal) in terms of the bandwidth B ?

@user-iw1ty8sk1v 2 жыл бұрын

@@yasserothman4023 it's 4x BW and you should switch sign at each sample > The sampled data reflects the amplitude of the original RF signal sampled at intervals. If we define the first sample at as I, the next sample at is Q, the following sample at is -I, the next sample at is -Q, the following sample at is again I, and so on. The ADC output provides a data stream consisting of the repeating pattern of measurements of I, Q, -I, and -Q. The I and Q variables within this digital data stream are separated by a multiplexer that switches every other sample into two parallel digital paths. The sign inversion in each path is removed by multiplying each data stream by +1 and -1 alternately. The resulting outputs correspond to the measured I and Q of the input RF signal.

@yasserothman4023 2 жыл бұрын

@@user-iw1ty8sk1v can you please provide a reference for your answer ?

@user-iw1ty8sk1v 2 жыл бұрын

@@yasserothman4023 Digital I/Q Demodulator* C. Ziomek and P. Corredoura Quote taken from there.

@mofaelectronics1295 2 жыл бұрын

hi sometimes we have a rf signal that it's not repeatitive like a sound wave how can we downconvert this signals to sampling with low sample rate analog to digital converters? is there any way?

@iain_explains 2 жыл бұрын

I think perhaps you haven't understood that this whole video relates to signals that at not repetitive (like sound waves from music or speech). These are low-frequency baseband signals. Your question about down converting doesn't apply to signals that are already at baseband. I suspect you may be asking more about sampling, right? Perhaps this video might help: "Sampling Signals" kzfaq.info/get/bejne/d8mlhNF6vc--YnU.html

@mofaelectronics1295 2 жыл бұрын

@@iain_explains I want to sampling some nanosecond uwb signals with 1ns pulse width and prf 100khz in (real time) sampling... but as you know sampling this signals with this speed is hard because we need very high speed analog to digital converters very high accuracy timing circuits(optical technologies and....)and this is really expensive but if we can downconvert this signals it can be done with low cost parts too. and I'm trying to find a way to downconverting this short pulses and sampling in (real time)

@iain_explains 2 жыл бұрын

It sounds like you're talking about a different sampling task. The sampling I'm talking about in this video is sampling without loss of information. In other words, sampling in a way that would enable the complete analog signal to be regenerated _exactly_ from the discrete time samples. It sounds like you have a communications system, and you only want to "sample" the digital information contained in the analog waveform (whether the pulse was positive or negative, or whether it was present or absent). That's a different story. In that case you might like to watch these videos: "Sampling Bandlimited Signals: Why are the Samples "Complex"?" kzfaq.info/get/bejne/gM2chaqDzuDVd4E.html and "What is a Baseband Equivalent Signal in Communications?" kzfaq.info/get/bejne/m9qKdLWSsrSyYqc.html

@mofaelectronics1295 2 жыл бұрын

@@iain_explainsYes in fact I want to digitize non repeatitive ultrafast signals with cheap parts without losing signal information with some techniques....