Hi I'm new to DSP. I'm working on an ultrasonic project which involves measuring the time of flight of a 40khz pulse between 2 transducers. I think I understand how to use cross correlation to slide a stored version of the pulse shape across the received signal until a match is found. This seems to be called matched filtering. I have seen references to a technique called mismatched filtering, particularly in radar applications, but despite lots of Googling I haven't been able to find anything which explains the concept it in a non-mathematical way that I understand. I don't have access to a technical library. Can anybody help? Thanks Mike
What is a mismatched filter?
Started by ●December 9, 2008
Reply by ●December 9, 20082008-12-09
Mike J Smith wrote:> Hi > > I'm new to DSP. I'm working on an ultrasonic project which involves > measuring the time of flight of a 40khz pulse between 2 transducers. I > think I understand how to use cross correlation to slide a stored > version of the pulse shape across the received signal until a match > is found. This seems to be called matched filtering. > > I have seen references to a technique called mismatched filtering, > particularly in radar applications, but despite lots of Googling I > haven't been able to find anything which explains the concept it in a > non-mathematical way that I understand. I don't have access to a > technical library. > > Can anybody help? > > Thanks > > MikeIt occurs to me that "mismatched" filtering is simply filtering that isn't "matched". Matched filtering can be accomplished by convolving the received signal with a replica of the transmit signal - and using frequency-shifted replicas to deal with Doppler, etc. The objective is to get the best noise gain against white noise in a least-squares sense. So, if the reference signal for the convolution isn't exactly a replica then the filter might be said to be "not matched" or "mismatched". For example, a radar might simply use a passband filter that just filters away noise that's outside the entire band of interest - including Doppler. It's not optimum re: noise gain but it may work just fine. It's not "matched". But, it a heck of a lot easier to implement. Fred
Reply by ●December 9, 20082008-12-09
"Fred Marshall" <fmarshallx@remove_the_x.acm.org> writes:> Mike J Smith wrote: >> Hi >> >> I'm new to DSP. I'm working on an ultrasonic project which involves >> measuring the time of flight of a 40khz pulse between 2 transducers. I >> think I understand how to use cross correlation to slide a stored >> version of the pulse shape across the received signal until a match >> is found. This seems to be called matched filtering. >> >> I have seen references to a technique called mismatched filtering, >> particularly in radar applications, but despite lots of Googling I >> haven't been able to find anything which explains the concept it in a >> non-mathematical way that I understand. I don't have access to a >> technical library. >> >> Can anybody help? >> >> Thanks >> >> Mike > > It occurs to me that "mismatched" filtering is simply filtering that isn't > "matched". > > Matched filtering can be accomplished by convolving the received signal with > a replica of the transmit signal - and using frequency-shifted replicas to > deal with Doppler, etc. The objective is to get the best noise gain against > white noise in a least-squares sense. > > So, if the reference signal for the convolution isn't exactly a replica then > the filter might be said to be "not matched" or "mismatched". > > For example, a radar might simply use a passband filter that just filters > away noise that's outside the entire band of interest - including Doppler. > It's not optimum re: noise gain but it may work just fine. It's not > "matched". But, it a heck of a lot easier to implement.That sounds plausible. I was thinking that maybe it means a filter that was matched against a distorted form of the transmit waveform, assuming the distortion it undergoes in propagating from the tx to rx. -- % Randy Yates % "Watching all the days go by... %% Fuquay-Varina, NC % Who are you and who am I?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●December 9, 20082008-12-09
Fred Marshall wrote:> Mike J Smith wrote: >> Hi >> >> I'm new to DSP. I'm working on an ultrasonic project which involves >> measuring the time of flight of a 40khz pulse between 2 transducers. I >> think I understand how to use cross correlation to slide a stored >> version of the pulse shape across the received signal until a match >> is found. This seems to be called matched filtering. >> >> I have seen references to a technique called mismatched filtering, >> particularly in radar applications, but despite lots of Googling I >> haven't been able to find anything which explains the concept it in a >> non-mathematical way that I understand. I don't have access to a >> technical library. >> >> Can anybody help? >> >> Thanks >> >> Mike > > It occurs to me that "mismatched" filtering is simply filtering that isn't > "matched". > > Matched filtering can be accomplished by convolving the received signal with > a replica of the transmit signal - and using frequency-shifted replicas to > deal with Doppler, etc. The objective is to get the best noise gain against > white noise in a least-squares sense. > > So, if the reference signal for the convolution isn't exactly a replica then > the filter might be said to be "not matched" or "mismatched". > > For example, a radar might simply use a passband filter that just filters > away noise that's outside the entire band of interest - including Doppler. > It's not optimum re: noise gain but it may work just fine. It's not > "matched". But, it a heck of a lot easier to implement. > > Fred > >That sounds too easy -- but maybe that's it. Or it's a filter that minimizes some error metric in a more robust way than a matched filter would in the presence of colored noise or distortion or such. Dunno -- maybe we should have a contest to see what the most outrageous description we can hang onto the the name "mismatched filter". -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" gives you just what it says. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●December 9, 20082008-12-09
Tim Wescott wrote:> Fred Marshall wrote: >> Mike J Smith wrote: >>> Hi >>> >>> I'm new to DSP. I'm working on an ultrasonic project which involves >>> measuring the time of flight of a 40khz pulse between 2 >>> transducers. I think I understand how to use cross correlation to >>> slide a stored version of the pulse shape across the received >>> signal until a match is found. This seems to be called matched >>> filtering. I have seen references to a technique called mismatched >>> filtering, >>> particularly in radar applications, but despite lots of Googling I >>> haven't been able to find anything which explains the concept it in >>> a non-mathematical way that I understand. I don't have access to a >>> technical library. >>> >>> Can anybody help? >>> >>> Thanks >>> >>> Mike >> >> It occurs to me that "mismatched" filtering is simply filtering that >> isn't "matched". >> >> Matched filtering can be accomplished by convolving the received >> signal with a replica of the transmit signal - and using >> frequency-shifted replicas to deal with Doppler, etc. The objective >> is to get the best noise gain against white noise in a least-squares >> sense. So, if the reference signal for the convolution isn't exactly a >> replica then the filter might be said to be "not matched" or >> "mismatched". For example, a radar might simply use a passband filter >> that just >> filters away noise that's outside the entire band of interest - >> including Doppler. It's not optimum re: noise gain but it may work >> just fine. It's not "matched". But, it a heck of a lot easier to >> implement. Fred >> >> > That sounds too easy -- but maybe that's it. > > Or it's a filter that minimizes some error metric in a more robust way > than a matched filter would in the presence of colored noise or > distortion or such. > > Dunno -- maybe we should have a contest to see what the most > outrageous description we can hang onto the the name "mismatched > filter".First Google hit: http://home.earthlink.net/~loganscott53/temporal.htm Seems many hits are about sidelobe suppression in the filter output. OK. Probably not what I would have called it.. Fred
Reply by ●December 10, 20082008-12-10
On Dec 10, 9:38�am, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote:> Tim Wescott wrote: > > Fred Marshall wrote: > >> Mike J Smith wrote: > >>> Hi > > >>> I'm new to DSP. I'm working on an ultrasonic project which involves > >>> measuring the time of flight of a 40khz pulse between 2 > >>> transducers. I think I understand how to use cross correlation to > >>> slide a stored version of the pulse shape across the received > >>> signal until a match is found. This seems to be called matched > >>> filtering. I have seen references to a technique called mismatched > >>> filtering, > >>> particularly in radar applications, but despite lots of Googling I > >>> haven't been able to find anything which explains the concept it in > >>> a non-mathematical way that I understand. I don't have access to a > >>> technical library. > > >>> Can anybody help? > > >>> Thanks > > >>> Mike > > >> It occurs to me that "mismatched" filtering is simply filtering that > >> isn't "matched". > > >> Matched filtering can be accomplished by convolving the received > >> signal with a replica of the transmit signal - and using > >> frequency-shifted replicas to deal with Doppler, etc. �The objective > >> is to get the best noise gain against white noise in a least-squares > >> sense. So, if the reference signal for the convolution isn't exactly a > >> replica then the filter might be said to be "not matched" or > >> "mismatched". For example, a radar might simply use a passband filter > >> that just > >> filters away noise that's outside the entire band of interest - > >> including Doppler. It's not optimum re: noise gain but it may work > >> just fine. �It's not "matched". �But, it a heck of a lot easier to > >> implement. Fred > > > That sounds too easy -- but maybe that's it. > > > Or it's a filter that minimizes some error metric in a more robust way > > than a matched filter would in the presence of colored noise or > > distortion or such. > > > Dunno -- maybe we should have a contest to see what the most > > outrageous description we can hang onto the the name "mismatched > > filter". > > First Google hit: > > http://home.earthlink.net/~loganscott53/temporal.htm > > Seems many hits are about sidelobe suppression in the filter output. �OK. > Probably not what I would have called it.. > > Fred- Hide quoted text - > > - Show quoted text -Thanks to everyone for their input. Having done some more reading, it's beginning to seem to me that "mismatched filter" just means "not a matched filter"? Seems a bit like calling everything which isn't an elephant a "mismatched elephant"!! Thanks again. Regards Mike
Reply by ●December 11, 20082008-12-11
mikesspam@optusnet.com.au wrote:> On Dec 10, 9:38 am, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> > wrote: >> Tim Wescott wrote: >>> Fred Marshall wrote: >>>> Mike J Smith wrote: >>>>> Hi >> >>>>> I'm new to DSP. I'm working on an ultrasonic project which >>>>> involves measuring the time of flight of a 40khz pulse between 2 >>>>> transducers. I think I understand how to use cross correlation to >>>>> slide a stored version of the pulse shape across the received >>>>> signal until a match is found. This seems to be called matched >>>>> filtering. I have seen references to a technique called mismatched >>>>> filtering, >>>>> particularly in radar applications, but despite lots of Googling I >>>>> haven't been able to find anything which explains the concept it >>>>> in a non-mathematical way that I understand. I don't have access >>>>> to a technical library. >> >>>>> Can anybody help? >> >>>>> Thanks >> >>>>> Mike >> >>>> It occurs to me that "mismatched" filtering is simply filtering >>>> that isn't "matched". >> >>>> Matched filtering can be accomplished by convolving the received >>>> signal with a replica of the transmit signal - and using >>>> frequency-shifted replicas to deal with Doppler, etc. The objective >>>> is to get the best noise gain against white noise in a >>>> least-squares sense. So, if the reference signal for the >>>> convolution isn't exactly a replica then the filter might be said >>>> to be "not matched" or "mismatched". For example, a radar might >>>> simply use a passband filter that just >>>> filters away noise that's outside the entire band of interest - >>>> including Doppler. It's not optimum re: noise gain but it may work >>>> just fine. It's not "matched". But, it a heck of a lot easier to >>>> implement. Fred >> >>> That sounds too easy -- but maybe that's it. >> >>> Or it's a filter that minimizes some error metric in a more robust >>> way than a matched filter would in the presence of colored noise or >>> distortion or such. >> >>> Dunno -- maybe we should have a contest to see what the most >>> outrageous description we can hang onto the the name "mismatched >>> filter". >> >> First Google hit: >> >> http://home.earthlink.net/~loganscott53/temporal.htm >> >> Seems many hits are about sidelobe suppression in the filter output. >> OK. Probably not what I would have called it.. >> >> Fred- Hide quoted text - >> >> - Show quoted text - > > Thanks to everyone for their input. > > Having done some more reading, it's beginning to seem to me that > "mismatched filter" just means "not a matched filter"? > > Seems a bit like calling everything which isn't an elephant a > "mismatched elephant"!! >Well, that was the essence of my first post. But on Googling it seemed to mean something else to some. I didn't "dig" further. We surely agree. I like the elephant analogy. In this case it's like calling a tiger a non-elephant as you say. There must be better ways to refer to a tiger! But, to be fair, if one is totally focused on matched filters as the holy grail of receiver technology then I guess one might be motivated to say: "Hey! I found a "nonmatched" filter that does some good things!!" It suggests a rather narrow view doesn't it? A broader view might refer to a "good" filter according to its goodness measure. "least squares", "minimax/Chebyshev/equiripple", are examples of goodness measures we're all familiar with in a slightly different context. At least they are descriptive. If I were totally absorbed with FIR design using the Parks-McClellan program (which I often am) then I might call a slightly different approach "non-FIR" or "non-equiripple" because that's my point of departure. It wouldn't really help someone else understand that I'm leading up to a different measure for goodness. Fred
Reply by ●December 12, 20082008-12-12
On Dec 11, 9:47�am, mikess...@optusnet.com.au wrote:> On Dec 10, 9:38�am, "Fred Marshall" <fmarshallx@remove_the_x.acm.org> > wrote: > > > > > Tim Wescott wrote: > > > Fred Marshall wrote: > > >> Mike J Smith wrote: > > >>> Hi > > > >>> I'm new to DSP. I'm working on an ultrasonic project which involves > > >>> measuring the time of flight of a 40khz pulse between 2 > > >>> transducers. I think I understand how to use cross correlation to > > >>> slide a stored version of the pulse shape across the received > > >>> signal until a match is found. This seems to be called matched > > >>> filtering. I have seen references to a technique called mismatched > > >>> filtering, > > >>> particularly in radar applications, but despite lots of Googling I > > >>> haven't been able to find anything which explains the concept it in > > >>> a non-mathematical way that I understand. I don't have access to a > > >>> technical library. > > > >>> Can anybody help? > > > >>> Thanks > > > >>> Mike > > > >> It occurs to me that "mismatched" filtering is simply filtering that > > >> isn't "matched". > > > >> Matched filtering can be accomplished by convolving the received > > >> signal with a replica of the transmit signal - and using > > >> frequency-shifted replicas to deal with Doppler, etc. �The objective > > >> is to get the best noise gain against white noise in a least-squares > > >> sense. So, if the reference signal for the convolution isn't exactly a > > >> replica then the filter might be said to be "not matched" or > > >> "mismatched". For example, a radar might simply use a passband filter > > >> that just > > >> filters away noise that's outside the entire band of interest - > > >> including Doppler. It's not optimum re: noise gain but it may work > > >> just fine. �It's not "matched". �But, it a heck of a lot easier to > > >> implement. Fred > > > > That sounds too easy -- but maybe that's it. > > > > Or it's a filter that minimizes some error metric in a more robust way > > > than a matched filter would in the presence of colored noise or > > > distortion or such. > > > > Dunno -- maybe we should have a contest to see what the most > > > outrageous description we can hang onto the the name "mismatched > > > filter". > > > First Google hit: > > >http://home.earthlink.net/~loganscott53/temporal.htm > > > Seems many hits are about sidelobe suppression in the filter output. �OK. > > Probably not what I would have called it.. > > > Fred- Hide quoted text - > > > - Show quoted text - > > Thanks to everyone for their input. > > Having done some more reading, it's beginning to seem to me that > "mismatched filter" just means "not a matched filter"? > > Seems a bit like calling everything which isn't an elephant a > "mismatched elephant"!! > > Thanks again. > > Regards > > MikeUsually a mismatched filter will be optimal for some criteria. A matched filter maximizes SNR assuming a linear system with independent gaussian noise, but a mismatched filter might be preferred that is, for example, more robust to non-gaussian noise, more robust to signal distortions - e.g. the response should be of a certain nature when the received signal does not equal the reference matched signal - sidelobe reduction in radar range processing is one example of this. FFT windowing is another. -T
Reply by ●December 15, 20082008-12-15
Tom wrote:> Usually a mismatched filter will be optimal for some criteria. > A matched filter maximizes SNR assuming a linear system with > independent gaussian noise, but a mismatched filter might be preferred > that is, for example, more robust to non-gaussian noise, more robust > to signal distortions - e.g. the response should be of a certain > nature when the received signal does not equal the reference matched > signal - sidelobe reduction in radar range processing is one example > of this. FFT windowing is another.Just to be picky about it... I think one needs to say "the response would be of a certain nature *even* when the received signal *does* equal the reference matched signal" The trap is using a matched filter as the point of reference at all. Fred
