IIRs don't _have_ to have infinitely-long impulse responses. And CICS filters can have, if you start and end with an integrator. ;)
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
Yeah, you can do 1-bit correlators, but it costs you at least 3 dB in SNR compared with linear or multibit ones. Hanbury Brown tried it in the '60s, and it doubled the required measurement time.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
But, but, but, IIR means Infinite Impulse Response.
And CICS
I'm still perplexed by the sinc3 filter (commonly used for delta-sigma recovery) that is a string of integrators and differentiators. I of course wanted to use an IIR filter, but I'm just the boss so nobody listens to me.
We have an isolated delta-sigma measuring a current shunt in our PM alternator simulator, and it feeds into a programmable impedance algorithm, so it's in a pretty hairy feedback loop. An FIR was easier to Spice.
it is in the the name
IIR and recursive is not the same thing
Depends whom you ask. IIR (C) Oppenheim and Shafer don't use the term "IIR" on account of the terminological confusion.
Anyway, because your definition is inaccurate for any given filter. Because of limited resolution even an "IIR" filter doesn't really have an infinite impulse response even in theory, unless it exhibits a limit cycle. A simple 1-pole rolloff such as
y_N = 0.5 (x_N + y_N-1)
is an 'IIR' if that means recursive, but at N bit precision it goes to zero in at most N cycles after the input goes to 0. Even in IEEE quad precision with denormals, which has a 15-bit exponent and 112-bit significant, it'll go to zero after at most 64k + 112 cycles.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
then it becomes more philosophical like what is zero Hz
You are exactly right, but the Sonar folk were doing hideously large correlation windows (I sort-of recall that it was like a million bits), which could only be done with one-bit correlators with the hardware of the day. I think one application was beamforming. For detecting submarines, the correlation window width was more important than the 3 dB.
.Joe Gwinn
No, I meant IIR.
I suppose that one could Spice a FIR filter from a lot of tapped delay lines and some resistors.
Nice try. The filter output goes to zero exponentially with time, vs. frequency resolution increasing only linearly.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
That I believe.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
Depends on what the definition of IS is. :)
As I undersand it, the recursiveness of an IIR filter topology is what would allow it to be "infinite". It the total recursive gains are less than 1.0 and the input stops, the output will stop.
Kind of like the coronavirus
I seem to remember that some of the first audio Delta-Sigma A/D converters used an FIR filter for a flat group delay.
Hopefully not--lots of recursive filters have limit cycles, so the output never goes away. That's probably the reason for their bad reputation in some circles. Or maybe it's the likelihood of overflow of intermediate results, much like railing and slew limiting in poorly-designed active continuous-time filters.
A simple example of an IIR filter with a limit cycle is another one-pole lowpass implemented in integers, which can get stuck at a nonzero DC output if the decrement per cycle is less than 0.5. More complicated filters can exhibit AC limit cycles.
(Of course a limit cycle isn't an impulse response either.)
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
Not sure if I have heard of "limit cycles" in this context but I can certainly imagine a software failsafe.
So it can be implemented with a LPF eh ? Will have to look that up. I use IIR filters (type I II or whatever) but I haven't had a problem with unrestricted feedback. My filters are rather simple and haven't had any DC offset runaway so far.
It has been a very long time since I've used an FIR filter. Was used in a telephone hybrid around 1990. Worked great ! 128 taps as I remember
Not sure what you mean by that.
The offset doesn't run away in a stable filter, it just doesn't decay to
0 in general. For a toy example, consider a 1-pole IIR lowpass with a decrement of 1/256 per cycle, implemented in integers, i.e.y_n+1 = y_n + (x_n - y_n-1) >> 8.
It gets stuck at a value of 127 with correct rounding and 255 with truncation.
FIR filters have some really good properties, and can be implemented efficiently using FFTs if you don't mind the extra delay. Symmetrical FIR filters have exactly linear phase, which is sometimes a huge help.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
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