Hi, I am new to digital and analog filters. I tried to construct digital filter but I don't know how to measure the delay introduced by the filter. I have designed 4th order low pass butterworth filter having sampling frequency of 48kHz and cutoff frequency of 5kHz. I don't know how to measure the delay and how to reduce it. Please give me some solution to reduce the delay of filter as much as possible. Thank You.
Urgent: Need to reduce the delay of digital filer
Started by ●July 30, 2014
Reply by ●July 31, 20142014-07-31
On Wed, 30 Jul 2014 19:45:11 -0700, vishwajeet13243 wrote:> Hi, > > I am new to digital and analog filters. I tried to construct digital > filter but I don't know how to measure the delay introduced by the > filter. I have designed 4th order low pass butterworth filter having > sampling frequency of 48kHz and cutoff frequency of 5kHz. I don't know > how to measure the delay and how to reduce it. Please give me some > solution to reduce the delay of filter as much as possible.Starting with an IIR filter like a Butterworth is a good thing. There are a lot of different meanings to the word "delay", and each meaning has its own measurement. You need to tell us more about what you're doing before we can help you on the delay aspect. To some extent, however, the narrower you make the filter, the higher the delay will be. That's just an inescapable part of filter design. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●July 31, 20142014-07-31
Hi,
"group delay" is the key word. You can calculate it from the derivative of
the phase of the frequency response (see Wikipedia). It matters at
frequencies where signal energy is present. In other words, don't look at
it in the stopband, as no one cares by how much the rejected part of the
signal is delayed.
As Tim already wrote, the bandwidth of the filter is one lower bound (the
famous time-bandwidth product). The steepness of the filter also plays a
role here.
What you can do is design variants of Chebyshev filters with different
ripple and compare (it becomes Butterworth without ripple). Repeat for
multiple orders and check what trade-off results.
An alternative is to specify a nominal group delay and solve numerically.
But this is more advanced and rarely ever mentioned in textbooks ("brute
force - if it doesn't work, you aren't using enough of it...")
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Reply by ●July 31, 20142014-07-31
On 7/31/14 2:45 AM, mnentwig wrote:> > "group delay" is the key word. You can calculate it from the derivative of > the phase of the frequency response (see Wikipedia). It matters at > frequencies where signal energy is present. In other words, don't look at > it in the stopband, as no one cares by how much the rejected part of the > signal is delayed. > > As Tim already wrote, the bandwidth of the filter is one lower bound (the > famous time-bandwidth product). The steepness of the filter also plays a > role here. > > What you can do is design variants of Chebyshev filters with different > ripple and compare (it becomes Butterworth without ripple). Repeat for > multiple orders and check what trade-off results. > > An alternative is to specify a nominal group delay and solve numerically. > But this is more advanced and rarely ever mentioned in textbooks ("brute > force - if it doesn't work, you aren't using enough of it...")i'm not so sure why *group* delay is the key word. maybe the OP will be more interested in the phase delay. i dunno. but there are at least two different measures of delay through a filter, and i wouldn't assume one over the other until i know more about what is being sought. an example of where phase delay is the salient parameter is a digital filter with feedback. if you're trying to do something like the Barkhausen criterion and need to understand at what frequencies the loop phase shift is some multiple of 2*pi, it's *phase* delay that is more important than group delay. in an obscure music synthesis technique, the Karplus-Strong algorithm, it's *phase* delay that's the key word, but there may be other apps. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●July 31, 20142014-07-31
>> "group delay" is the key word. You can calculate it from the derivativeof>i'm not so sure why *group* delay is the key word. maybe the OP will be >more interested in the phase delay. i dunno.Right, it's a guess, assuming "signal" means information going through the filter. You are right, for stability at any given frequency it is the absolute phase that matters, but a physical interpretation of delay may easily get me into faster-than-light territory. Anyway, I think no one expects us to spend more time pondering the meaning of a question than it took the OP to write it. _____________________________ Posted through www.DSPRelated.com
Reply by ●July 31, 20142014-07-31
On Thu, 31 Jul 2014 08:04:54 -0400, robert bristow-johnson wrote:> On 7/31/14 2:45 AM, mnentwig wrote: >> >> "group delay" is the key word. You can calculate it from the derivative >> of the phase of the frequency response (see Wikipedia). It matters at >> frequencies where signal energy is present. In other words, don't look >> at it in the stopband, as no one cares by how much the rejected part of >> the signal is delayed. >> >> As Tim already wrote, the bandwidth of the filter is one lower bound >> (the famous time-bandwidth product). The steepness of the filter also >> plays a role here. >> >> What you can do is design variants of Chebyshev filters with different >> ripple and compare (it becomes Butterworth without ripple). Repeat for >> multiple orders and check what trade-off results. >> >> An alternative is to specify a nominal group delay and solve >> numerically. But this is more advanced and rarely ever mentioned in >> textbooks ("brute force - if it doesn't work, you aren't using enough >> of it...") > > > i'm not so sure why *group* delay is the key word. maybe the OP will be > more interested in the phase delay. i dunno. but there are at least > two different measures of delay through a filter, and i wouldn't assume > one over the other until i know more about what is being sought.I've seen beginners on this group whose only conception of "delay" is "I put a step into the filter, and I care about the 'delay' coming out". In that case they're probably closer to settling time -- but "delay" is the word used.> an example of where phase delay is the salient parameter is a digital > filter with feedback. if you're trying to do something like the > Barkhausen criterion and need to understand at what frequencies the loop > phase shift is some multiple of 2*pi, it's *phase* delay that is more > important than group delay. in an obscure music synthesis technique, > the Karplus-Strong algorithm, it's *phase* delay that's the key word, > but there may be other apps.Phase delay and the Barkhausen criterion really only applies in narrow- band systems. When it comes to the ability to close a control loop from DC up to some bandwidth, then group delay is probably more appropriate to think about (I haven't had to -- usually you only care up to a plant phase shift of 180 degrees or so, because at that point your loop is definitely getting dangerous and ridiculous at the same time. I think that under those circumstances phase delay and group delay are more or less equivalent, but I'd have to play a bit to see). -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●July 31, 20142014-07-31
On Wednesday, July 30, 2014 10:45:11 PM UTC-4, Vishwajitsinh Atodaria wrote:> Hi, > > > > I am new to digital and analog filters. I tried to construct digital filter but I don't know how to measure the delay introduced by the filter. I have designed 4th order low pass butterworth filter having sampling frequency of 48kHz and cutoff frequency of 5kHz. I don't know how to measure the delay and how to reduce it. Please give me some solution to reduce the delay of filter as much as possible. > > > > Thank You.Tim's first response was good. What is the application the filter is being used for? What are your specs? Why did you choose the filter you chose? Dirk Dirk
Reply by ●July 31, 20142014-07-31
On Wed, 30 Jul 2014 19:45:11 -0700 (PDT), vishwajeet13243@gmail.com wrote:>Hi, > >I am new to digital and analog filters. I tried to construct digital filter= > but I don't know how to measure the delay introduced by the filter. I have= > designed 4th order low pass butterworth filter having sampling frequency o= >f 48kHz and cutoff frequency of 5kHz. I don't know how to measure the delay= > and how to reduce it. Please give me some solution to reduce the delay of = >filter as much as possible. > >Thank You.In addition to the other responses, a practical working measure of the basic delay of a filter can be determined by putting an impulse in and seeing when the "impulse" comes out. The nuances come largely from defining the moment that the "impulse" comes out, since it will be spread and distorted by the response of the filter. The peak of the output often serves as a basic delay measurement, but it may be necessary to interpolate the peak location between output samples to get a fractional delay value when appropriate. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●July 31, 20142014-07-31
Hello Markus, Some weeks ago I sent you two private e-mails, but I did not receive any replies from you. (I tried two different e-mail addresses for you.) I'm wondering, did you receive my e-mails? Thanks Markus, [-Rick-]
Reply by ●August 1, 20142014-08-01
