What is a Matched Filter?
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- čas přidán 21. 08. 2024
- Explains the Matched Filter from a signals perspective with a Digital Communications example.
* Note that in general (for complex valued waveforms) the impulse response of the MF is s*(T-t) . In this video I considered an example of a square pulse shape, which is a real-valued function (ie. zero phase). In this case s*(T-t) = s(T-t) .
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My brain hurts
for complex signals, h(t) = conj( s(-t) ) , matched filter weights = time reverse and conj s(t) s(t) being whatever the known pulse waveform is.
nothing but, perfect explanation
thank you! This is a million times more clear than my prof's explanation.
You're very welcome! I'm glad you like my approach to explaining things. Have you seen my webpage? It gives a full listing of all of my videos, in categories: iaincollings.com
Thanks so much Iain, your explanations are so clear and easy to understand.
Glad it was helpful!
After watch this, I understand match filter clearly. Thank you so much.❤
Glad it helped!
Great explanation again! Nice!
Thanks again!
You are the best
Best of all CZcams videos about matched filters
Thanks for the intuition!
You’re welcome
Thank you sir
Thanks Iain
you are really a gift, thanks a lot
So nice of you
Nicely explained... If we had a bank of signals that we wanted to match an input to, how is this any different than simply correlating the bank entries with our input? How does this differ from Logistic Regression in machine learning... seems like they must be very close cousins. Thanks for making the video.
Fundamentally, what's happening is that the signal is being projected onto the basis function (or a set of basis functions in the situation you've mentioned). Theses basis functions can be orthogonal (as is the case in digital communications with sin and cos), or they can be non-orthogonal (as is often the case in matching-based learning algorithms). Correlating and filtering are often equivalent. These videos may provide more insights: "How are Correlation and Convolution Related in Digital Communications?" czcams.com/video/We5q5FJcbcU/video.html and "Orthogonal Basis Functions in the Fourier Transform" czcams.com/video/n2kesLcPY7o/video.html
when I watch this I think of the raised cosine filter. My understanding is that the raised cosine filter eliminates ISI but by splitting it so that one is at the transmitter and the other at receiver (becomes root raised cosine filter), also means that it performs the function of a matched filter?
Yes, that's right. You might like to watch this other video on my channel for more details: "Pulse Shaping and Square Root Raised Cosine" czcams.com/video/Qe8NQx4ibE8/video.html
Great video!
Glad you liked it.
Sorry if this is obvious, but given the matched filter, how do we know that the sampling is only being performed when the energy is at a maximum, i.e. at the peak of the triangles?
The matched filter is designed such that the maximum output occurs at the sample time. That's part of the design constraint.
ECE 485, UofA.
How can we actually see match filter working in a real working communication system??? Or is there any such hardware model which may help in explaining Communication systems most abstract concepts in real systems?
Analog electronic filters are implemented with circuits involving passive components such as resistors, capacitors and inductors, and sometimes also involving active components such as individual transistors as well as more complex elements like OpAmps. A Matched Filter is just one of these circuits where it has been designed to have an impulse response that matches the impulse response of the transmit filter.
Thanks so much for your explanations, I am wondering how the digital signals become analog waveforms here(say square wave), is it because of the impulse response of the TX filter s(t) or say pulse shaping function by s(t)?
The short answer is "yes". Have you seen these videos? Hopefully they will help: "How are Signals Reconstructed from Digital Samples?" czcams.com/video/dD9HC1GThZY/video.html and "How are Complex Baseband Digital Signals Transmitted?" czcams.com/video/0lkRJgnywkg/video.html
Thank you very much
You are welcome
Is the matched filter same as inner product in vectors?
Also, are the correlation and the matched filtering same?
And also, what is the difference between convolution and correlation?
I have some idea, but asking to know your views and explanation.
Thank you sir.
Thanks for the questions Srikanth. I've just uploaded a new video that hopefully answers your questions. czcams.com/video/We5q5FJcbcU/video.html
Maybe for SNR calculation should be used expected value of noise sequence y_n instead of E[y_n(T)]?
I'm not sure what you're saying, sorry. The only thing that matters for the final decision, is the ratio of the component of the signal in the sampled output of the filter h(t), in relation to the component of the noise in the sampled output of the filter h(t). In other words, it is only the filter outputs at times T, 2T, 3T, 4T, ... that are available to the digital decision function.
@@iain_explains correct! Thanks for your channel Lain, I really like your explanation.
But my question was about yours definition of _expected value_ of noise.
For SNR calculation you took:
- value of output signal at time T (you noted it as y_s(T)) _correct!_
- expected value of noise ... at time T? (you noted it as E[y_n(T)])
From definition of _Expected Value_ only _sequence_ of noise (random variable) has an Expected Value or Weighted Arithmetic Mean and finding an expected value from one number doesn't make sense (since we will get the number itself).
So, maybe in the definition of SNR in the video should be _value_ of noise at time T instead of _Expected Value_ of noise at time T?
I think you're confused about random variables. You say "finding an expected value from one number doesn't make sense", but with respect, that statement doesn't make sense. What do you mean by "one number"? The variable y_n(T) is random! It is a random number. Of course you can take the expectation of it. It is the output of the filter, that results from the noise in the filter over the time between 0 and T (eg. the thermal noise in the receiver amplifier). Perhaps you might like to watch this video to understand more about the difference between a random number and a random process: "What is a Random Process?" czcams.com/video/W28-96AhF2s/video.html
Thanks
You're welcome
why do you even need a filter at the end with an impulse response? Why don't you just sample the incoming signal and get the positive value from the square for the first bit for example? So what do you gain by introducing an extra filter?
I think you're maybe not understanding what is required to "take a sample". It's not possible in the real world to simply "multiply by a delta impulse". Taking a sample, in the real world, requires integrating the signal for a period of time (to gather energy over the sample period) and then recording the output. This is exactly what we are doing with the Matched Filter (except it is doing it over the symbol period, so that the noise in the receiver is averaged out, and effects the received value as little as possible).
Can you maybe explain why we have to collect the energy of the signal to identify the symbol in the first place? Is there not an easier way of figuring out the transmitted symbol, how can I understand that? Thank you very much for the great work.
First it's important to understand that nothing happens instantaneously. Nothing can move faster than the speed of light. Even the electrons in an amplifier. Now let's think about the thermometers we use to take our temperatures when we're feeling sick. We need to put them under our tongue for a period of time, to allow enough heat energy from our mouth to warm them up to the temperature of our bodies. They don't heat up (or respond) instantaneously. The longer we leave them there, the more accurate the temperature reading. It's the same thing with amplifiers in digital communication receivers, except that the time scales are much shorter. We need to send a digital pulse (a symbol) for enough time, so that we can make a reliable reading at the receiver. If we try to send too quickly, or sample for to too short a time at the receiver, then we will make errors in our received data.
professor you are a magician your words are more powerful visualization tool than an animation 👍
Hi, where can I learn about the h(t)=S(T-t). I want to know how you came up with that.
It's a bit too mathematically involved to make a video about, but there's a good explanation in the book by Proakis called "Digital Communications", 4th Edition, pp. 237-239.
sir I have a doubt as you have said it's matched filter output energy has been added from 0 to T AND THEN it's sampled at time T AFTER THAT for 2nd symbol when again we are adding the energy from T to 2T and we are samling at 2T but my doubt is in duration from T to 2T the dying energy of first symbol is also being added which could give interference
Yes, they are being added together during the period T to 2T, but by the time it gets to 2T, the energy from the first symbol as completely died out, so sampling at 2T only contains energy from the second symbol.
@@iain_explains thanks sir got it now
hey lain i have watched the whole video mean while i have a doubt in mah mind , whether in case of matched filter there is no upconversion and down conversion here? mean if the same operation is done through the correlator receiver and in the correlator receiver case we are doing the down conversion by multiplying same set of rf frequency at the receiver then we are doing intigration and sampling , but in case of matched filter there is no such process of downconversion we are only convolving with the filter at the other end means every thing which is done is done with high frequency signal even sampling also if that is the case then it might be costlier to impliment i would rather prefer a correlator receiver
The Matched Filter doesn't require high frequency sampling. It's still just sampled at the symbol rate. In the case of wireless communications, the MF has an impulse response that is a sinusoidal wave at the carrier frequency. Hopefully this video helps: "How are Correlation and Convolution Related in Digital Communications?" czcams.com/video/We5q5FJcbcU/video.html
@@iain_explains thanks
Do you have a video about CIC filtering and its importance to decimation?
No, sorry. Thanks for the suggestion though. I'll add it to my "to do" list.
dear professor,in case match filtering how did the down conversion happens as we are not multiplying any carrier at the receiver end??
Everything in the video was shown at "base band". Note that I didn't show a carrier at the transmitter or the receiver. Hopefully these videos will help: "What is a Baseband Equivalent Signal in Communications?" czcams.com/video/etZARaMNN2s/video.html and "How are Complex Baseband Digital Signals Transmitted?" czcams.com/video/0lkRJgnywkg/video.html
Hey, I've learned that s(t)=h*(-t) and therefore h(t) is a matched filter when this is true. Where does your T come from? Thanks!
T is the time duration of the digital symbol waveform that is being sent to represent the digital data (eg. to represent a 0 or a 1 in the case of binary data). It is shown above the "s(t) box" in the signal flow diagram in the video.
Hi, thank you for the video! Any recommendations for a good book that related to this content?
My favourite digital comms book is: J.G. Proakis, “Digital Communications”
So in conclusion, matched filter helps make the received data (at the other side of the channel) be more observable, thus more detectable.
Not sure what you mean by "more observable". There needs to be something that "collects the energy" at the receiver, and "receives" the signal. The Matched Filter is the best thing to do this, in terms of maximising the signal to noise ratio.
@@iain_explains You used a word that describe what I said, more detectable means a better signal to noise ratio. BER should always be kept at the max.
I was taught the baseband and passband modulation schemes for digital data transmission and the respective receivers for decoding the transmitted signal (eg. Coherent detector for PSK). So, I'm wondering where the matched filter block is positioned in, say, a coherent detector for decoding PSK signal. I'd be extremely grateful if someone could explain this to me. Thanks :)
The matched filter is often implemented in the form of a correlator, which includes a mixer (in the passband case), which you may be familiar with. See this video for more explanation: czcams.com/video/We5q5FJcbcU/video.html
@@iain_explains The BPSK receiver I was taught had a Balanced modulator (or mixer) and the output of the BM was given to a LPF. I saw the video you referred to and was a bit confused at first but then concluded that the integrator in the correlation method must be same thing as the LPF. So basically, what I was taught was the correlation method and matched filter receiver is just an alternate design that gives the same output?
P.s : thanks for taking the time to reply to my query. I really appreciate it!
Yes, that's right.
Thank you, I understand all of the contents. But, we don't know the transmitted signal, so how can we adapt the filter to that signal?
Great question! In digital communications, you don't know the _actual_ signal that was sent in any given symbol period (because that depends on the data that's being sent), however you do know that it must be one of a finite set of signals (one for each of the digital symbols that could be sent). So you could have a parallel set of matched filters in your receiver - one for each of the possible 'data symbols'. Or you could have one filter matched to a sin wave, and one matched to a cos wave, and then match the pairs of outputs to the nearest constellation point in the 'symbol constellation space'. See these videos for more details: "What Does a Digital Detector Do?" czcams.com/video/XzoLe9ixAZs/video.html and "What is a Constellation Diagram?" czcams.com/video/kfJeL4LQ43s/video.html
Also, this video might also help: "How are Correlation and Convolution Related in Digital Communications?" czcams.com/video/We5q5FJcbcU/video.html
Being an asynchronous system, how do you phase synchronise your bit detection, especially at low SNRs.
Great question. Too hard to explain it all here sorry (maybe I'll try to make another video on this question). In summary though, there are multiple parts to it, including: Timing Recovery in the receiver (ie. tuning/calibrating T, and adjusting the sampling times so there's no offset), Frequency Locking (to make sure the oscillators in the transmitter and receiver are both at the exact same frequency), Phase Locking (to make sure the carrier sinusoid has zero phase drift), Equalization in the receiver (to recover from any phase offset in the channel and in the receiver).
And I've made a video on the Eye Diagram, which is used for Timing Recovery: czcams.com/video/ROhgIWBteQQ/video.html
thank you so much for this nice explanation, I have a confusion regarding the explanation in some of the books such as I am following "proakis_4th ed" and there they use an integrator which is followed by the projection of the received signal to the basis function in the case of a correlator demodulator and the product of the matched filter in the matched filter demodulator case. the integration takes place from (0 - T) and still, that is followed by a sampler at the time (t = T).
my question is wh are we using a sampler after the integrator?
It's to indicate that we only "measure" the output of the integrator at t=kT. ie. we don't constantly measure the output as it performs the integration between the sample times.
sir I have a doubt as you have said it's matched filter output energy has been added from 0 to T AND THEN it's sampled at time T AFTER THAT for 2nd symbol when again we are adding the energy from T to 2T and we are samling at 2T but my doubt is in duration from T to 2T the dying energy of first symbol is also being added which could give interference
Do you have a reference with a number of examples?
This is the textbook I like the most in this area: J.G. Proakis, “Digital Communications”
hello sir , greetings from india
i have a little qestion as you mentioned that we need to collect all of the enrgy at the receiver inorder to find out whaeather 0 or 1 was sent ,my question is that even if we had collected the energy for particular bit duration than also how can we differentiate between 0 and 1 as energy is always a positive quantity and we are sending our 0 bit as negative pulse which according to the video will be a negative enegy calculated for Tb duration
In order to collect all the energy, it is necessary to integrate over the full symbol period. It doesn't mean you are able to know what the energy is. That depends on what filter you use in the receiver. If you use an in-phase receive matched filter, then you will get the energy. If you use an out-of phase receive filter, then you will get a negative output. Whether it is in-phase or not depends on the digital data. So if you get a positive output, you will estimate a digital "1", and if you get a negative output, you will estimate a digital "0".
@@iain_explains Hi Ian. If we are considering single bit (0 or 1) the analogy explained here will work.. What happens if it is symbols with multiple bits representation?
@@malini50 hello i will try to answer your question
first part I think you are considering ASK modulation scheme here so for this scheme you are required only one filter that is inphase matched filter here if you will get output (any how you will get +ve output ) if you have sent +1 bit
otherwise you will receive some energy which will be the energy of the noise when you have sent 0 bit means you have not sent any of the waveform and the only received energy of the noise .
Your Signals and Systems with Communication (S&S&C) theory YT video tutorials are great. But two things are bugging me being the lone RF guy in a SERDES group. 1. How do Matched Filters deal with ISI. 2. is there a good book showing how S&S&C come into play in the real world of RF S parameter measurements. Mostly I just see Design-con things here and there looking at eye diagrams from sending a signal through measured S-parameters. But there has got to be a text out there showing things like how the S11 and S22 like terms affect the Tx and Rx side semi-independently due to VSWR. As while as clear analysis of S12 like terms group delay showing how to find the frequency components of the transmitted signal that are going to cause the most ISI. Sorry about being a little irate about this but it's just really disconcerting how separated S&S&C theory is from the RF physical implementation theory and I have been searching for over a year now if you got any leads it would be much appreciated, thanks.
Great comments, thanks. Yes, I agree there is a real tendency in digital communications research to assume the RF implementation is power efficient, linear, and immediately responsive. More can be done to integrate RF characteristics into the digital models. In answer to your questions: 1. The MF is always "matched" to the transmitted symbols. This implicitly assumes that the front-end hardware can't be adapted on a time-scale that would be necessary to "match" to the time varying ISI channel as well as the transmitted symbols (ie. matched to the entire RF chain and channel). Apart from anything else, you would need to know the channel in order to do this. In many cases this doesn't really matter, as the MF provides sufficient statistics for digital decision making. In other words, information is not lost by performing the MF matched to the symbols. 2. I have used the following books, which you may find useful: "Radio Receiver Design", Robert C. Dixon, published by Marcel Dekker, 1998; and "Advanced Techniques for Digital Receivers", Phillip E. Pace, published by Artech House 2000; and "Wireless Communication Technology", Roy Blake, published by Delmar Thomson Learning 2001. I'm not sure if they cover all of what you are looking for, but they might be worth a look.
@@iain_explainsThanks for the references I will check them out. For the MF would it be correct to say that in today's SERDES that the MF is embodied by the CTLE and DFE?
Also, one resource on the subject of communication is www.gaussianwaves.com/digital-modulations-using-python/
Sometimes, yes, but not necessarily. The MF is (most) often implemented as a correlator (mixer, integrator, and sampler) which can be part of the CTLE and DFE implementation. See czcams.com/video/We5q5FJcbcU/video.html for more details on the correlator receiver.
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