How are Signals Reconstructed from Digital Samples?

[@MikoPLG]

Thank you, professor. Very intuitive show of how it really happens that signals are reconstructed using LPF. Often it is said so, but unfortunately not shown what really happens beyond these words.

[@iain_explains]

Thanks for your comment. I'm glad you found the video helpful.

[@prabhurc3]

Very underrated channel, a rare gem. This is how an education should be. Thank you so much, can't express my gratitude enough...

[@iain_explains]

Thanks for your nice comment. I'm glad you like the channel.

[@speedsystem4582]

Conscise and clear! I feel like crying cause... (most of )my professors manage to overemphasize on simple things and avoid telling all the subtleties invovled in the more convoluted topics... if they are not passionate about teaching, why do itt ?? It's hella annoying... Sorry to rant out here... but I feel like it's taking a heavy toll on me !🥺 Thank you so much for making such good content available for free 🥹 !

[@iain_explains]

I'm so glad you found the video helpful. One of my motivations for making these videos is that I know that many students are confused by the topics, and that many lecturers find it difficult to explain the concepts clearly. I'm glad you found my explanation helpful.

[@speedsystem4582]

Thank youu so muchh 🥰

[@KallePihlajasaari]

Some interesting insights into DAC reconstruction filters can be seen in the two application notes by Analogue devices AN-823 and AN-837 for Direct digital synthesis applications but theory is similar.

[@Digiphex]

What do you think is the basic operation of the latest AK4499 flagship DAC? You think that chip is performing a sinc function on the signal?

[@iain_explains]

I'm not a hardware expert or an audio processing expert but looking at the specs it says it can play out sampled signals with up to 1.536 MHz sample rate with 64-bit PCM. That's very high for audio, which is in the range 0-20kHz or so, but it does allow for overcoming the practical problem of not being able to generate the theoretically optimal sinc pulse reconstruction filter for signals sampled at only the Nyquist rate. Over-sampling is how most ADC/DACs work. Here's a video on the extreme case of having only a 1-bit DAC: "What is a 1-Bit DAC and How Does it Work?" kzbin.info/www/bejne/aYObmqOKfcdsrrM

[@sdrnovice2000]

Is there a difference between reconstructing with a near perfect sync and reconstructing with a simple first order hold and a very steep analog LPF? I know mathematically a perfect LPF is a sync. But with filters I think of coils and capacitors

[@hariharannair3281]

These are gold dusts sir. May god bless u. With live from India

[@edmundkemper1625]

are you live oh you mean love ! haha

[@iain_explains]

I'm really glad the videos are helping you. I love India. I've only been there once, but hopefully after Covid settles down I can visit again.

[@hariharannair3281]

@@iain_explains sir please do visit us again.

[@emadibnalyaman8073]

Thank you very much sir for your efforts, every lesson is really useful for us.

[@iain_explains]

It's my pleasure. Glad they're helping.

[@ibrahimshikdaher7551]

Thank you professor, it's a short and clear video that can save the time of reading tens of pages of a text book. I also like this traditional way of description.

[@iain_explains]

Glad it was helpful!

[@power-max]

First time I've seen it done with just convolutions/Fourier transforms! In the past I've heard of signal reconstruction in terms of interpolation, such as sample and hold, linear interpolation, cubic interpolation, or sinx/x. Its cool to see it shown in a different way!

[@iain_explains]

Well it's not really a "different way". All of those methods you mention need to be implemented in some way. If the other explanations you've seen didn't refer to the filters that would implement the approaches, then they were only telling half the story.

[@GeraltOfRivia69]

Thanks for this amazing explanation.(from Kashmir, Indian side)

[@iain_explains]

Glad it was helpful!

[@AleksandarDjurovic90]

Hi Iain. Many thanks for one more amazing video. Just one question out of curiosity. Do you have insight which approach is in use in mobile communication, especially in 4G and 5G? If I have to bet on one, I will say some kind of sinc approximation.

[@iain_explains]

Mobile communications involves a number of different sampling operations. So there's not one single answer to your question. In the case of sampling voice signals, they are sampled in a way that involves compressing the data stream, and the reconstruction needs to be done in a way that matches the way they were sampled. It's complicated (and interesting too), and I've got it on my "to do" list as a topic for a future video.

[@AleksandarDjurovic90]

@@iain_explains thanks a lot. I can imagine it is not simple story. Looking forward to understand it in more details from your videos. Wish you all the best!

[@wooshylooshy]

very nice super thanks :)

[@iain_explains]

Glad you liked it.

[@VasanthP-yl9co]

prof can you give us the circuit to generate sinc signal?

[@iain_explains]

Sorry, but circuits are not my specialty.

[@codingmarco]

You can't generate a true sinc signal since it's infinite and acausal, but all real circuits are causal. To generate a truncated version you would need an arbitrary waveform generator since a sinc is a rather complex signal. If you want more information on how signals from a DAC are reconstructed in practice with real filters, you can google "Keysight AWG primer". Look for section "Reconstruction Filter" - there you'll find that in practice, a bessel filter is used for optimal time domain response (minimal overshoot and ringing) and an elliptic filter for optimal frequency response (faster roll-off near the nyquist frequency). The document describes the topic in the context of arbitrary waveform generators / high-speed DACs. You can google possible circuits for these filters.

[@muhammadahmedtariq2357]

Sir. May I ask that what is the relationship between spectrum of digital signal (discrete value) and that of sampled signal( discrete time but continuous value) ? In your video, you took the discrete numbers as samples of digital signal but you showed the spectrum of sampled signal assuming that both spectra of digital and sampled signals are one and the same. May you please highlight the difference between two if it exists from your practical insight ?

[@iain_explains]

I think this video should help: "Continuous Time and Discrete Time Fourier Transforms" kzbin.info/www/bejne/on3UZHdjq5mehrc

[@zhou6486]

Concise and understandable wireless topic channel, my favorite absolutely！Thanks so much for sharing, Professor Iain.

[@iain_explains]

My pleasure! I'm so glad you like the channel.

[@pierreschmidt271]

Thanks a lot. I would be very glad if you could provide similar video about ADPCM (Adaptive Differential Pulse Code Modulation) as it's still not clear to me why the need for prediction...

[@iain_explains]

Thanks for the suggestion. I've added it to my "to do" list.

[@gregalee]

This is an excellent visualization of why digital doesn't actually sound like the overly simplified stair-step that laypeople often imagine it does. Thank you for taking the time to put together such a clear explanation. I was able to use your video to help a non-technical friend understand digital audio better. Next, please consider a tutorial of how the different types of output filters we commonly see in audio work: linear phase, minimum phase, butterworth, brick wall, (and others?). The problem with actual circuits in the D/A stage of real world gear is that they either impose a single filter choice or they give a range of choices with very little explanation of the trade offs of each. Are there pieces of gear that offer the ideal linear pass filter or is that an impossibility to create economically in real world circuit applications? I'd love to know! Apodization! So confusing.

[@iain_explains]

I'm so glad to hear that the video has been helpful. And thanks for the topic suggestion. I've put it on my "to do" list.

[@gill6335]

Is the filter mentioned [H(t)] same as the analog LPF after the DAC in the transmitter or is it some digital filter in/before the DAC?

[@iain_explains]

It is the filter in the DAC that produces the continuous time output signal.

[@satheeshsimhachalam7563]

OMG !! What a fantastic explanation to have the intuition . Superb

[@iain_explains]

I'm so glad you found it helpful.

[@andrespasca4329]

Amazing explanation! Thank you!

[@iain_explains]

Glad it was helpful!

[@shawonaoschu9211]

Just Super. I have learned a lot from you professor.

[@iain_explains]

That's great to hear. I'm so glad the videos have helped.

[@hotmultimedia]

Great videos. But one thing confuses me: if you look at the fourier transform of the signal with delta functions, you see fairly narrow bandwidth peak in frequency domain. But when you "reconstruct" the signal with zero order hold or first order hold, the peaks get much wider (all the way to Fs) - is this result of some aliasing or just a quirk in the drawing?

[@hotmultimedia]

ah i might have got it partially: those peaks are not the same peaks visible in the first plot, but instead the later cycles of the sinc function. but still i don't understand how they become so wide. shouldn't atleast the baseband peak be about the same width as in the first plot?

[@iain_explains]

Ah, that is an excellent question. I guess I didn't make it clear enough in the video. The top frequency plot is the Fourier transform of the sequence of delta functions shown in the top time-domain plot (ie. the "sampled signal"). But the three frequency domain plots underneath it are the Fourier transforms of _just_ the impulse responses of the three "reconstruction filters" shown in the middle column of time-domain plots. In order to find the Fourier transform of the three reconstructed signals (shown in the left column of time-domain plots), you need to multiply the top frequency plot, with the respective reconstruction filter's frequency plot (since they are convolved in the time domain, which is equivalent to multiplication in the frequency domain). For example, with the bottom filter, it zeros-out all the higher frequency aliased copies, in the top frequency plot, and perfectly keeps the central component, around f=0.

[@andrus3125]

Thanks for the explanation

[@iain_explains]

You're welcome

[@ksa-1419]

Thanks Prof. so much, but can you tell us devices use these models?

[@iain_explains]

One example is the one-bit DAC that uses the first-order hold filter. These first became popular in portable CD players - like the one I had when I was at uni back in 1991 - because they are very cheap and easy to implement. They are now being proposed for use in mm-wave massive MIMO systems. The trick is that they are run at a much higher clock (sample) rate, so the overall waveform can look smooth. Perhaps I'll make a video on this to explain more.

[@ksa-1419]

@@iain_explains Thank you very much Prof.