IIR to find minimum, maximum enveloppe of a signal
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From: Tim Wescott on 24 Feb 2010 18:56 Michael Plante wrote: > Tim wrote: >> vectorizor wrote: >>> Now, I would also like to find the enveloppe of the signal, i.e. the >>> local minimum and maximum. I'm trying to find a way to do that using >>> IIR filters (because of the speed), but I cannot for the life of me >>> find a way forward. Does anybody have ideas on that? Note that it does >>> not necessarily need to be a IIR filter, we can keep the conversation >>> more general at first. I suggested them because of the level of >>> performance they enabled, which is important to my project. >> >> You can implement a _non_-linear recursive filter, that forces its >> output to the signal value if the signal value exceeds it's state, but >> otherwise implements a first order low-pass (which is DSP for the >> Economist's 'moving average' filter). For signals which hit their >> maxima often this works pretty well, but if you're looking for an >> infrequent but guaranteed maximum this will often be wrong. > > > Essentially an idealized diode envelope detector, right? It'd be > interesting to know what additional tricks can be played digitally, though > I imagine it's pretty dependent on prior knowledge about the signal. > Right, and subject to numerous problems if the signal isn't just right. I can't recall a specific instance where I've used something exactly as I describe here -- I generally end up doing things block by block -- but there has to be _some_ time that it's useful! -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
From: suren on 24 Feb 2010 22:59 On Feb 24, 9:16 pm, vectorizor <vectori...(a)googlemail.com> wrote: > Hi all, > > First of all, I'm a newbie in signal processing, so go easy :) > > I have used an IIR filter to computer the local average of a signal, > and it works well. It essentially is what they call in finance a > moving average, i.e. the output at a sample point is a fraction of > itself and (1-fraction) of its predecessor. Results fit my > requirements, and the speed is absolutely tremendous. > > Now, I would also like to find the enveloppe of the signal, i.e. the > local minimum and maximum. I'm trying to find a way to do that using > IIR filters (because of the speed), but I cannot for the life of me > find a way forward. Does anybody have ideas on that? Note that it does > not necessarily need to be a IIR filter, we can keep the conversation > more general at first. I suggested them because of the level of > performance they enabled, which is important to my project. > > Thanks in advance, > > A Hi, You could use a single pole IIR filter with time varying alpha (or 2 sets of alpha) to track the maxima. y[n]=alpha*x[n] +(1-alpha)*y[n-1]. Essentially, if the input x[n] is greater than the previous output y[n-1], use a faster alpha and if its smaller, use a smaller alpha. This is like a fast attack and slow decay kind of a filter. This can be used to track envelope efficiently. Hope this helps. regards suren
From: vectorizor on 25 Feb 2010 05:04 Thanks to all for all interesting answers. To refocus the conversation, the signals being processed are images, so I dont need to know the future :) , and a running min/max is not sufficient, as I'm more looking for a smooth enveloppe, rather than one looking like a step function. > Hi, > You could use a single pole IIR filter with time varying alpha (or 2 > sets of alpha) to track the maxima. > y[n]=alpha*x[n] +(1-alpha)*y[n-1]. > Essentially, if the input x[n] is greater than the previous output > y[n-1], use a faster alpha and if its smaller, use a smaller alpha. > This is like a fast attack and slow decay kind of a filter. This can > be used to track envelope efficiently. This is the most interesting answer IMHO. I can see how it could potentially give a smooth enveloppe. But how to control the alpha? Could you give me more clues/point me to some reference materials? Thanks again A
From: suren on 25 Feb 2010 05:18 On Feb 25, 3:04 pm, vectorizor <vectori...(a)googlemail.com> wrote: > Thanks to all for all interesting answers. To refocus the > conversation, the signals being processed are images, so I dont need > to know the future :) , and a running min/max is not sufficient, as > I'm more looking for a smooth enveloppe, rather than one looking like > a step function. > > > Hi, > > You could use a single pole IIR filter with time varying alpha (or 2 > > sets of alpha) to track the maxima. > > y[n]=alpha*x[n] +(1-alpha)*y[n-1]. > > Essentially, if the input x[n] is greater than the previous output > > y[n-1], use a faster alpha and if its smaller, use a smaller alpha. > > This is like a fast attack and slow decay kind of a filter. This can > > be used to track envelope efficiently. > > This is the most interesting answer IMHO. I can see how it could > potentially give a smooth enveloppe. But how to control the alpha? > Could you give me more clues/point me to some reference materials? > > Thanks again > > A Hi, That is quite simple. You need to use two parameters alpha_fast and alpha_slow. A quick pseudo code is give below. if (input>prev_output) { alpha = alpha_fast; } else { alpha = alpha_slow; } output = alpha*input + (1-alpha)*prev_output; prev_output = output; Hope this helps. suren
From: Jerry Avins on 25 Feb 2010 05:22
vectorizor wrote: > Thanks to all for all interesting answers. To refocus the > conversation, the signals being processed are images, so I dont need > to know the future :) , and a running min/max is not sufficient, as > I'm more looking for a smooth enveloppe, rather than one looking like > a step function. > >> Hi, >> You could use a single pole IIR filter with time varying alpha (or 2 >> sets of alpha) to track the maxima. >> y[n]=alpha*x[n] +(1-alpha)*y[n-1]. >> Essentially, if the input x[n] is greater than the previous output >> y[n-1], use a faster alpha and if its smaller, use a smaller alpha. >> This is like a fast attack and slow decay kind of a filter. This can >> be used to track envelope efficiently. > > This is the most interesting answer IMHO. I can see how it could > potentially give a smooth enveloppe. But how to control the alpha? > Could you give me more clues/point me to some reference materials? Before going off on a wild goose chase, define /precisely/ what you mean by "envelope". You can't compute what you can't define. Jerry -- Engineering is the art of making what you want from things you can get. ����������������������������������������������������������������������� |