What is the best filter for a pulse in white noise? I remember in the depths of the past reading something about a filter with a reverse- time impulse response of the pulse which you convolve it with, but this is just an integrator. Hardy
Pulse in white noise
Started by ●June 7, 2012
Reply by ●June 7, 20122012-06-07
On Jun 7, 7:42�pm, HardySpicer <gyansor...@gmail.com> wrote:> What is the best filter for a pulse in white noise? I remember in the > depths of the past reading something about a filter with a reverse- > time impulse response of the pulse which you convolve it with, but > this is just an integrator. > > Hardyok it's a matched filter. How do you implement this - say in analogue? I imagine just a leaky integrator? Hardy
Reply by ●June 7, 20122012-06-07
On Thu, 07 Jun 2012 01:30:02 -0700, HardySpicer wrote:> On Jun 7, 7:42 pm, HardySpicer <gyansor...@gmail.com> wrote: >> What is the best filter for a pulse in white noise? I remember in the >> depths of the past reading something about a filter with a reverse- >> time impulse response of the pulse which you convolve it with, but this >> is just an integrator. >> >> Hardy > > ok it's a matched filter. How do you implement this - say in analogue? > I imagine just a leaky integrator? > > HardyDoes a leaky integrator's impulse response look like your pulse? Betcha could do better...
Reply by ●June 7, 20122012-06-07
On Jun 7, 4:30�am, HardySpicer <gyansor...@gmail.com> wrote:> On Jun 7, 7:42�pm, HardySpicer <gyansor...@gmail.com> wrote: > > > What is the best filter for a pulse in white noise? I remember in the > > depths of the past reading something about a filter with a reverse- > > time impulse response of the pulse which you convolve it with, but > > this is just an integrator. > > > Hardy > > ok it's a matched filter. How do you implement this - say in analogue? > I imagine just a leaky integrator? > > HardyMany matched filters are implemented as correlators, that is, active circuits with switches that are variations of integrate-and-dump circuits, and not as purely passive (linear time-invariant) circuits, whether in the analog or the digital domain. Dilip Sarwate
Reply by ●June 7, 20122012-06-07
On 6/7/12 7:50 AM, dvsarwate wrote:> On Jun 7, 4:30 am, HardySpicer<gyansor...@gmail.com> wrote: >> On Jun 7, 7:42 pm, HardySpicer<gyansor...@gmail.com> wrote: >> >>> What is the best filter for a pulse in white noise? I remember in the >>> depths of the past reading something about a filter with a reverse- >>> time impulse response of the pulse which you convolve it with, but >>> this is just an integrator. >> >> ok it's a matched filter. How do you implement this - say in analogue? >> I imagine just a leaky integrator? > > Many matched filters are implemented as correlators, > that is, active circuits with switches that are variations > of integrate-and-dump circuits, and not as purely passive > (linear time-invariant) circuits, whether in the analog or > the digital domain.Hardy, is there something that i'm missing about your question in your first post that isn't answered by two words (and not "leaky integrator") in your second post? -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●June 7, 20122012-06-07
robert bristow-johnson <rbj@audioimagination.com> writes:> Hardy, is there something that i'm missing about your question in your > first post that isn't answered by two words (and not "leaky > integrator") in your second post?"I imagine"?> "Imagination is more important than knowledge."-- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●June 7, 20122012-06-07
On Jun 8, 5:04�am, robert bristow-johnson <r...@audioimagination.com> wrote:> On 6/7/12 7:50 AM, dvsarwate wrote: > > > > > > > > > > > On Jun 7, 4:30 am, HardySpicer<gyansor...@gmail.com> �wrote: > >> On Jun 7, 7:42 pm, HardySpicer<gyansor...@gmail.com> �wrote: > > >>> What is the best filter for a pulse in white noise? I remember in the > >>> depths of the past reading something about a filter with a reverse- > >>> time impulse response of the pulse which you convolve it with, but > >>> this is just an integrator. > > >> ok it's a matched filter. How do you implement this - say in analogue? > >> I imagine just a leaky integrator? > > > Many matched filters are implemented as correlators, > > that is, active circuits with switches that are variations > > of integrate-and-dump circuits, and not as purely passive > > (linear time-invariant) circuits, whether in the analog or > > the digital domain. > > Hardy, is there something that i'm missing about your question in your > first post that isn't answered by two words (and not "leaky integrator") > in your second post? > > -- > > r b-j � � � � � � � � �r...@audioimagination.com > > "Imagination is more important than knowledge."Sorry, I remembered after I had posted it what the name of the filter was. I was unsure of the implementation. The literature just has block diagrams. For instance, is it commonplace in the digital domain to use FFTs for the convolution or just time-domain methods. For example, to work out cross-correlation you can convolve with the time-reversed impulse response which is what I need. To get this I could computed cross spectral density (cross-periodogram) and inverse FFT. I am wondering what the most common approach is since in the books they only seem to cover the theory and not implmentation issues. Hardy
Reply by ●June 7, 20122012-06-07
On 6/7/12 1:51 PM, Randy Yates wrote:> robert bristow-johnson<rbj@audioimagination.com> writes: > >> Hardy, is there something that i'm missing about your question in your >> first post that isn't answered by two words (and not "leaky >> integrator") in your second post? > > "I imagine"? > >> "Imagination is more important than knowledge."LOL! (after initial confusion) actually, now that you made me read it, Randy, he *did* ask another question in the second post about implementing a match filter in the analog[ue] world. i suppose, Hardy, to implement a matched filter in the analog world would be to first, F.T. (DFT, whatever) the pulse you're trying to pick out and design an analog filter with a frequency response that has about the same magnitude response and a phase response that is the negative of the phase component of the pulse spectrum with some necessary constant delay or linear phase term added. essentially, i never took a course in analog filters where we designed directly for a *specific* impulse response. sometimes given a prototype impulse response that is the sum of various decaying exponentials and damped sinusoids, i think we *have* designed for specific features in the impulse response (like its integral, the step response having a limited overshoot). in the digital world, we just use an FIR with impulse response that is proportional to the time-reversed copy of the pulse we're trying to detect. with simple additive white noise, that is pretty much the end result of what a matched filter is in the digital domain. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●June 7, 20122012-06-07
our most recent posts "crossed in the mail". On 6/7/12 2:49 PM, HardySpicer wrote:> > Sorry,none needed, but if i am confused, i start asking basic questions.> I remembered after I had posted it what the name of the filter > was. I was unsure of the implementation. The literature > just has block diagrams. For instance, is it commonplace in the > digital domain to use FFTs for the convolution or just time-domain > methods.if it's a really, really long pulse, lotsa samples, convolution in the frequency domain is the efficient way to do it. but if the pulse (or your approximation to it) is shorter than a few dozen samples, i think the matched filter is likely to be a simple FIR in the time-domain. one nifty use of truncated IIR filters (TIIR), which are a form of FIR filter but implemented using recursive means (a moving-sum or moving-average filter is maybe the simplest non-trivial example) is that if the pulse you're trying to detect is some damped sinusoid in time (which, seems to me, might be often found in nature or in physical systems), you can approximated that damped sinusoid with a finite-length replica and implement a finite-length time reversed copy (which has exponentially increasing amplitude, at least for a while) efficiently with a TIIR.> For example, to work out cross-correlation you can convolve > with the time-reversed impulse response which is what I need. To get > this I could computed cross spectral density (cross-periodogram)i think that's the F.T. of the cross-correlation, right?> and inverse FFT.then you get cross-correlation, then you look for peaks in that?> I am wondering what the most common approach is since in > the books they only seem to cover the theory and not implementation > issues.well, it's gonna depend on the shape and the length of the pulse you're trying to detect that's buried in white noise. probably, 90%+ of the time it's done with a simple FIR. i could be wrong about that percentage. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●June 7, 20122012-06-07
On Jun 8, 7:20�am, robert bristow-johnson <r...@audioimagination.com> wrote:> our most recent posts "crossed in the mail". > > On 6/7/12 2:49 PM, HardySpicer wrote: > > > > > Sorry, > > none needed, but if i am confused, i start asking basic questions. > > > I remembered after I had posted it what the name of the filter > > was. I was unsure of the implementation. The literature > > just has block diagrams. For instance, is it commonplace in the > > digital domain to use FFTs for the convolution or just time-domain > > methods. > > if it's a really, really long pulse, lotsa samples, convolution in the > frequency domain is the efficient way to do it. �but if the pulse (or > your approximation to it) is shorter than a few dozen samples, i think > the matched filter is likely to be a simple FIR in the time-domain. > > one nifty use of truncated IIR filters (TIIR), which are a form of FIR > filter but implemented using recursive means (a moving-sum or > moving-average filter is maybe the simplest non-trivial example) is that > if the pulse you're trying to detect is some damped sinusoid in time > (which, seems to me, might be often found in nature or in physical > systems), you can approximated that damped sinusoid with a finite-length > replica and implement a finite-length time reversed copy (which has > exponentially increasing amplitude, at least for a while) efficiently > with a TIIR. > > > For example, to work out cross-correlation you can convolve > > with the time-reversed impulse response which is what I need. To get > > this I could computed cross spectral density (cross-periodogram) > > i think that's the F.T. of the cross-correlation, right? > > > and inverse FFT. > > then you get cross-correlation, then you look for peaks in that? > > > I am wondering what the most common approach is since in > > the books they only seem to cover the theory and not implementation > > issues. > > well, it's gonna depend on the shape and the length of the pulse you're > trying to detect that's buried in white noise. �probably, 90%+ of the > time it's done with a simple FIR. �i could be wrong about that percentage. > > -- > > r b-j � � � � � � � � �r...@audioimagination.com > > "Imagination is more important than knowledge."ok thanks for that
