Hi, Suppose we have a signal y(t) that is composed of white noise of unknown variance n(t) and potentially a sinusoid of known power s(t) and known frequency F, so that y(t) = s(t) + n(t). The object is to detect the presence (or not) of s(t). Is it better to simply filter the signal y(t) as narrowly as possible and then set a detection threshold, or would it be better to compare the power in some off-band bandwidth of y(t) to the power about F and make a determination? --Randy
Question in Detection
Started by ●July 24, 2006
Reply by ●July 24, 20062006-07-24
Randy Yates wrote:> Hi, > > Suppose we have a signal y(t) that is composed > of white noise of unknown variance n(t) and potentially > a sinusoid of known power s(t) and known frequency > F, so that > > y(t) = s(t) + n(t). > > The object is to detect the presence (or not) of > s(t). > > Is it better to simply filter the signal y(t) as > narrowly as possible and then set a detection > threshold, or would it be better to compare > the power in some off-band bandwidth > of y(t) to the power about F and make > a determination? > > --Randy >The value of your detection threshold depends on the variance of the noise, so if it's unknown then you can't really set a detection threshold. So yes, I'd make an estimate of the variance and compare that to an estimate of the signal power around F. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●July 24, 20062006-07-24
Randy Yates wrote:> Hi, > > Suppose we have a signal y(t) that is composed > of white noise of unknown variance n(t) and potentially > a sinusoid of known power s(t) and known frequency > F, so that > > y(t) = s(t) + n(t). > > The object is to detect the presence (or not) of > s(t). > > Is it better to simply filter the signal y(t) as > narrowly as possible and then set a detection > threshold, or would it be better to compare > the power in some off-band bandwidth > of y(t) to the power about F and make > a determination? > > --Randy >The value of your detection threshold depends on the variance of the noise, so if it's unknown then you can't really set a detection threshold. So yes, I'd make an estimate of the variance and compare that to an estimate of the signal power around F. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●July 24, 20062006-07-24
Tim Wescott wrote:> Randy Yates wrote: > > Hi, > > > > Suppose we have a signal y(t) that is composed > > of white noise of unknown variance n(t) and potentially > > a sinusoid of known power s(t) and known frequency > > F, so that > > > > y(t) = s(t) + n(t). > > > > The object is to detect the presence (or not) of > > s(t). > > > > Is it better to simply filter the signal y(t) as > > narrowly as possible and then set a detection > > threshold, or would it be better to compare > > the power in some off-band bandwidth > > of y(t) to the power about F and make > > a determination? > > > > --Randy > >Tim, I would appreciate a greeting by name in your posts. When you omit it, you come across in a manner that does not encourage interaction.> The value of your detection threshold depends on the variance of the > noise, so if it's unknown then you can't really set a detection threshold.While this is true in theory, it's not really true in practice, because in practice we know (or expect most of the time) that the noise will be bounded by some upper limit. Even though this may have come across as a theory question, I'm really asking a combo theory/practice question.> So yes, I'd make an estimate of the variance and compare that to an > estimate of the signal power around F.In practice, you don't know for sure that there's not some other carrier in the band you choose to measure, so it's not at all clear that this is a better approach. If you still think so, then please state why. And please, no "yes/no" answers - give some thought (or even theory) behind it. --Randy
Reply by ●July 24, 20062006-07-24
Randy Yates wrote:> Tim Wescott wrote: > >>Randy Yates wrote: >> >>>Hi, >>> >>>Suppose we have a signal y(t) that is composed >>>of white noise of unknown variance n(t) and potentially >>>a sinusoid of known power s(t) and known frequency >>>F, so that >>> >>> y(t) = s(t) + n(t). >>> >>>The object is to detect the presence (or not) of >>>s(t). >>> >>>Is it better to simply filter the signal y(t) as >>>narrowly as possible and then set a detection >>>threshold, or would it be better to compare >>>the power in some off-band bandwidth >>>of y(t) to the power about F and make >>>a determination? >>> >>>--Randy >>> > > > Tim, > > I would appreciate a greeting by name in your posts. When you omit it, > you come across in a manner that does not encourage interaction. >Randy: You're getting a free answer and you're complaining about the wrapper?> >>The value of your detection threshold depends on the variance of the >>noise, so if it's unknown then you can't really set a detection threshold. > > > While this is true in theory, it's not really true in practice, because > in practice we know (or expect most of the time) that the noise will > be bounded by some upper limit.Then the variance isn't unknown -- it has a known upper bound.> > Even though this may have come across as a theory question, I'm really > asking a combo theory/practice question. >When I have such I try to state _all_ the constraints on the theoretical part, so I don't lead myself or others down the garden path.> >>So yes, I'd make an estimate of the variance and compare that to an >>estimate of the signal power around F. > > > In practice, you don't know for sure that there's not some other > carrier in the band you choose to measure, so it's not at all > clear that this is a better approach.Another carrier in your measurement bandwidth makes the noise significantly non white, as opposed to your statement that the noise is white in your problem description.> > If you still think so, then please state why. And please, no "yes/no" > answers - give some thought (or even theory) behind it. >I think I can't answer your questions. That's the yes/no part. Here's the why: 1. You want free information from me, but you criticize my manners if I don't follow your narrow rules of etiquette. Where I grew up one accepts freebies in the spirit that they're given, or one doesn't. It's considered bad form in this part of the world to take a freebie then berate the giver for their content or the manner in which they're given 2. You ask questions that you don't really mean, then jump on the respondent for answering them as asked. 3. You want me to watch for your name in posts, and change the way I answer questions just for you -- presumably so you have more things to pick apart. Have a nice life. Plonk -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●July 24, 20062006-07-24
Randy Yates wrote:> Suppose we have a signal y(t) that is composed > of white noise of unknown variance n(t) and potentially > a sinusoid of known power s(t) and known frequency > F, so that> y(t) = s(t) + n(t).> The object is to detect the presence (or not) of > s(t).This sounds like what people would use a PLL for. For audio frequencies the old favorite NE567. I worked with someone some years ago building a DTMF receiver with eight NE567's and appropriate gates. I believe it is on the data sheet for the 567. -- glen
Reply by ●July 24, 20062006-07-24
Tim Wescott wrote:> [...]Tim, I simply asked that you be respectful. If that causes you this much grief, then there must be something deeply wrong in your own heart. I encourage you to examine it. --Randy
Reply by ●July 24, 20062006-07-24
"Randy Yates" <yates@ieee.org> wrote in message news:1153764087.448643.174360@s13g2000cwa.googlegroups.com...> Hi, > > Suppose we have a signal y(t) that is composed > of white noise of unknown variance n(t) and potentially > a sinusoid of known power s(t) and known frequency > F, so that > > y(t) = s(t) + n(t). > > The object is to detect the presence (or not) of > s(t). > > Is it better to simply filter the signal y(t) as > narrowly as possible and then set a detection > threshold, or would it be better to compare > the power in some off-band bandwidth > of y(t) to the power about F and make > a determination? >I would say that it is better to estimate the ratio of the signal power to the noise power. I have recently created an "auto-squelch" function that does just that. I feed it a power spectrum (a set of squared-magnitude FFT coefficients) that include both your "signal band" and a larger "channel band". The first thing I do (convenience only) is convert the spectrum to dB. by computing 10*log(f_i) on each frequency component. Then I split the spectrum into two arrays, preserving the original ordering. The "noise" array gets the first third and the last third of the spectrum. The "signal" array gets the center third. To estimate the noise, I apply a median filter to the "noise" array and take the median value as the noise level. To estimate the signal, I convolve a FIR filter with the signal array, saving the result of each convolution if it's larger than any result previously seen. When I get done, I compare the largest estimated signal component with the noise level plus a threshold. If the signal component is larger, I open the squelch. The coefficients of the FIR filter are chosen to produce a Least-Mean-Squares estimate of the value at the center of a data window that can be represented by a 2nd-order polynomial. The size of the data window is chosen to insure that the Variance Reduction Factor of the filter is at least 10 dB.
Reply by ●July 24, 20062006-07-24
"Tim Wescott" <tim@seemywebsite.com> wrote in message news:9cednf0kr6-NvVjZnZ2dnUVZ_sOdnZ2d@web-ster.com...> Randy Yates wrote:>> [snip incredibly offensive, possibly drunken, rant >> attributed to Randy Yates]Tim, I have monitored this group for a long time--not as long as you have--but a long time. I don't think I have ever seen a similar post by Randy Yates. For that reason, I urge you to consider the possibility this post was a "Joe Job" by some fruitcake with whom Randy has had a disagreement. Granted, such festivities are much more common in the Badlands of sci.crypt than they are here, but USENET is full of creeps and their numbers seem to be exploding. Merely disagreeing with one of these brain-damaged cretins, no matter how mildly, is sufficient to trigger their wrath. None of the newsgroups in which I am a participant permits PKI-certified signed messages, so it's difficult to tell when some coward posts a message and attributes it to someone else. If, on the other hand, the post was genuine, I think your response was entirely reasonable. Just my two cents. -- jeh
Reply by ●July 24, 20062006-07-24
John E. Hadstate wrote:> "Tim Wescott" <tim@seemywebsite.com> wrote in message > news:9cednf0kr6-NvVjZnZ2dnUVZ_sOdnZ2d@web-ster.com... > >>Randy Yates wrote: > > >>>[snip incredibly offensive, possibly drunken, rant >>>attributed to Randy Yates] > > > Tim, > > I have monitored this group for a long time--not as long as > you have--but a long time. I don't think I have ever seen a > similar post by Randy Yates. For that reason, I urge you to > consider the possibility this post was a "Joe Job" by some > fruitcake with whom Randy has had a disagreement. Granted, > such festivities are much more common in the Badlands of > sci.crypt than they are here, but USENET is full of creeps > and their numbers seem to be exploding. Merely disagreeing > with one of these brain-damaged cretins, no matter how > mildly, is sufficient to trigger their wrath. None of the > newsgroups in which I am a participant permits PKI-certified > signed messages, so it's difficult to tell when some coward > posts a message and attributes it to someone else. > > If, on the other hand, the post was genuine, I think your > response was entirely reasonable. > > Just my two cents. > > -- > > jeh > >I was certainly surprised by it. I'll take your advise and de-plonk him, and see what happens. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html