Digital Filter Elementary Question

[curious_mind]

I am new to digital filters and have a very basic question about IIR and FIR filters. I would like to know the essence and basis of these filters. There are tons of literature on web that details the design of these filters without directly providing the genesis. One fundamental question is that a signal can be considered as infinite (simple sine wave) then it must also contain infinite impulses which are scaled and shifted with respect to time. Therefore in the context of the input how do we understand infinite or finite impulse response of the system. In theory, if there is only one impulse as input, the systems output will eventually decay over time (like RC filter). Can we therefore call RC filter as FIR? but if input do exist like a continuous sine wave, the output of RC filter will also remain. In that case does RC filter behave as IIR filter ?. Please clarify

 

[KlausST]

I am new to digital filters and have a very basic question about IIR and FIR filters. I would like to know the essence and basis of these filters. There are tons of literature on web that details the design of these filters without directly providing the genesis. One fundamental question is that a signal can be considered as infinite (simple sine wave) then it must also contain infinite impulses which are scaled and shifted with respect to time. Therefore in the context of the input how do we understand infinite or finite impulse response of the system. In theory, if there is only one impulse as input, the systems output will eventually decay over time (like RC filter). Can we therefore call RC filter as FIR? but if input do exist like a continuous sine wave, the output of RC filter will also remain. In that case does RC filter behave as IIR filter ?. Please clarify

IIR vs FIR
Infinite impulse response vs finite impulse reponse.

But still "impulse response" ... finite/infinte is not about the input signal.

*****
Give an inpulse to a 5 tap FIR filter and the output will be stable after 5 samples.
Give an inpulse to an IIR filter and the output will change infinitely in time. It is only stopped by resolution.
(You can imagine an IIR response like an analog filter. Simplest: RC

Klaus

--- Updated Jan 30, 2024 ---

Added:

In theory, if there is only one impulse as input, the systems output will eventually decay over time (like RC filter). Can we therefore call RC filter as FIR?

"it will decay over time". True. But it will decay infinitely. Thus its like an IIR.

***
Again: sine input will result in sine output ... in (almost) any case. Independent of analog, digital, IIR FIR ...

Klaus

 

[danadakk]

There are also digital filters done via convolution, fourier transform, or wavelet based filters.
Even electrical filters done via mechanical methods.

All these methods have their own characteristics, good and bad, even when doing the "same" filter.


Regards, Dana.

 

[kaz1]

I am new to digital filters and have a very basic question about IIR and FIR filters. I would like to know the essence and basis of these filters. There are tons of literature on web that details the design of these filters without directly providing the genesis. One fundamental question is that a signal can be considered as infinite (simple sine wave) then it must also contain infinite impulses which are scaled and shifted with respect to time. Therefore in the context of the input how do we understand infinite or finite impulse response of the system. In theory, if there is only one impulse as input, the systems output will eventually decay over time (like RC filter). Can we therefore call RC filter as FIR? but if input do exist like a continuous sine wave, the output of RC filter will also remain. In that case does RC filter behave as IIR filter ?. Please clarify

The primary difference is that FIR has no feedback from its output but IIR does have feedback from its output as input. The only exception is that if the IIR feedback term cancels out inside filter then it behaves as FIR.

 

[danadakk]

https://ccrma.stanford.edu/courses/220a/static/lectures/digitalFilters/diffEquations.pdf

Difference between IIR and FIR filters: a practical design guide - ASN Home

What are the differences between a IIR filter and a FIR filter? And how do we choose the best type of digital filter for our application?

www.advsolned.com

Siemens DISW

Regards, Dana.

 

[D.A.(Tony)Stewart]

An RC filter in the analog domain can behave like a continuous-time system with a finite impulse response, it doesn't fit the strict definitions of FIR or IIR filters used in the digital signal processing context.

When moving to the digital domain, the choice of discretization method and implementation details will determine whether the digital representation resembles an FIR or IIR filter.

 

[KlausST]

HI,

I use FIR filters as well as IIR filters rather often.
But often they may not be ecogized as FIR filters.

Examples:
* FIR filter: Averaging n samples. Lets say I calculate the average of 8 samples. I add those 8 sample values up, then divide it by 8 (shift 3 bits right)
* IIR filter: low pass: (acting very similar to an RC)
LPF_out = LPF_fb + ((ADC_Value - LPF_fb) >> 3); LPF_fb = LPF_out;

Here " >> 3 " results in fc = f_sample / 7.45
" >> 8 " results in f_sample / 254

This is what I use for (small) microcontrollers without good arithmetics, like AVR.

But for sure the "biquad" is a classical IIR filter structure (2nd order) where frequency and filter characteristics can be adjusted more precisely.

Klaus

 

[curious_mind]

By reading the posts above, should I conclude that FIR and IIR is simply dependent on the coefficients that define the filter. FIR has finite coefficients and IIR has infinite

 

[KlausST]

By reading the posts above,

.. you could see that IIR has a feedback from the output, while IIR does not. (post #4)

And every textbook, internet search, operation chart, tutorial ... will show this.

*******
Just do a search for "what´s the difference between IIR and FIR" .. or simply "IIR vs FIR".
Select reliable and good sources like from: Semiconductor manufacturers, universities, reputable authors
Read through some of them. And for further questions please refer to them.

Klaus

 

[curious_mind]

I have seen several materials on the net. Yet I could not conclude the true meaning of IIR and FIR. Impulse responses will remain always remain infinite for Infinite inputs, which goes forever. Only coefficients could decide the distinction

 

[kaz1]

FIR has only forward coefficients, no feedback terms.
IIR has feedback (recursive) terms plus/minus forward coefficients.

The forward coefficients represent weight of contribution of input stages to final output sum.
The feedback coefficients represent weight of previous output stages to current output sum so output keeps contributing back (for ever if infinite bit width).

 

[KlausST]

I have seen several materials on the net.

I guess we all have.
Do you think it´s a good idea what exact material you have read? It just makes it impossible to discuss about.

Only coefficients could decide the distinction

Again: No.
A FIR topology will never generate an "infinite" reponse to a pulse input.No matter what coefficents you chose.

Yet I could not conclude the true meaning of IIR and FIR. Impulse responses will remain always remain infinite for Infinite inputs, which goes forever.

Don´t know what this means at all.
Why not take a pice of paper and a pencil and draw the
* input as a pulse
* the expected output .... to see/discuss whether it is "finite" or "infinte"

Klaus

 

[curious_mind]

OK, I get it. Confusion arose because, If we were to provide just the unit impulse to a system ( such as RC), eventually output would decay within certain time. In other words, the response to a unit impulse will be finite . Now I wanted to map this very concept with the definition of FIR and IIR. I understand now that in FIR the coefficients are restricted and hence we have a finite length filter.

 

[KlausST]

it would decay within certain time.

Again: Wrong. Where is this information from?
Didn´t you read our post before?

Klaus

 

[curious_mind]

Yes, Yes, the recursive feature makes IIR to generate infinite impulse response, whereas in FIR , it is limited due to finite coefficients (without feedback)

 

[danadakk]

FIR

As you can see there is no feedback anywhere in structure.
Notice transfer function only has pole terms at origin pole-zero plot.
Naturally produces linear phase types of response.

IIR filter, biquad

As you can see there is feedback in this structure.
Here pole terms complex, not constrained to (0,0) pole plot,
unlike FIR. Many work arounds to get linear phase types
of response. Structure can lead to unbounded arithmetic
problems.

Regards, Dana.

 

[FvM]

Notice transfer function only has pole terms at origin pole-zero plot.

I presume FIR Z-transfer function has no poles.

 

[kaz1]

I presume FIR Z-transfer function has no poles.

With FIR I have never seen any use of Z transforms. There are time domain or frequency based formulas and functions to get coefficients. a moderate FIR can have say 31 taps implying 31 Z stages...what for apart from modelling for fun?. Having said that I have seen Z based formulas to derive super-sampling FIR but the final structure seemed not working.

Moreover even IIR are dying away apart from first or second order filters.

 

[danadakk]

I presume FIR Z-transfer function has no poles.

Poles at 0 and infinity :

Why are FIR filters still stable even though they contain poles?

How come FIR filters are always stable? Since they contain poles, shouldn't they be more affected by stability issues than others?

dsp.stackexchange.com

Regards, Dana.