Can an IIR filter be applied by convoluting a signal with its impulse response?

  • Thread starter Thread starter sdfzz
  • Start date Start date
  • Tags Tags
    Filter
Click For Summary

Discussion Overview

The discussion revolves around the application of IIR filters, specifically whether an IIR filter can be effectively applied by convoluting a signal with its impulse response. Participants explore the distinctions between FIR and IIR filters, the implications of using convolution with IIR impulse responses, and the characteristics of specific filter types like Butterworth and Chebyshev.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that FIR filters use convolution and have a finite impulse response, while IIR filters are recursive with an infinite impulse response.
  • Another participant suggests that convoluting an IIR filter's impulse response with a signal effectively creates an FIR approximation, which can be accurate but is theoretically incorrect.
  • A participant questions whether a specific low pass filter's transfer function represents an IIR or FIR filter, leading to a clarification that it is neither in its discrete-time form.
  • Concerns are raised about the implications of using convolution with an impulse response, suggesting that it may limit the use of IIR filters like Butterworth or Chebyshev.
  • It is stated that linear phase cannot be achieved from an IIR filter, and that FIR filters are required if convolution is a necessity.
  • Participants discuss the potential advantages of using an FIR approximation of IIR filters, though the specifics of these advantages are not fully explored.

Areas of Agreement / Disagreement

Participants express differing views on the validity of using convolution with IIR impulse responses, with some arguing it leads to FIR approximations while others maintain that it is theoretically incorrect. There is no consensus on whether the approach can be considered a valid application of IIR filtering.

Contextual Notes

Participants mention that the accuracy of FIR approximations can vary based on the method of digitization used for the analog filter, indicating that assumptions about the filter's characteristics may depend on specific contexts.

sdfzz
Messages
6
Reaction score
0
Hi all..

I'm a new to filters and I need some help understanding filters (I'm in mechanical engineering)

So far, I've found out that FIR filters use convolution and has a finite impulse response.

On the other hand, IIR filters are recursive and have an infinite impulse response.

But, what if I get the impulse response of an IIR filter (Butterworth, for example) and convolute the response with a signal? (given that I use only a part of the infinite signal).

Does this still count as an IIR filtering? Can I apply an IIR filter this way?

Any help would be appreciated.

Thank you
 
Engineering news on Phys.org
Well - taking the convolution sum and truncating it to some finite range is effectively taking an FIR approximation of a given IIR filter, which is actually one of the techniques to design FIR filters.
As a practical way to model a system, it's ok, it can even be pretty accurate - eventually any IIR impulse response decreases to a certain level bellow which the quantization makes it effectively zero, but theoretically it is wrong, and off course using the recursive way to calculate the response is always more accurate than approximating with FIR.
 
Thank you for your reply :)
 
Can I ask one more question?

If I have a low pass filter, whose transfer function is

H(s) = a/(a+s),

It it an IIR filter or FIR filter?
 
It is neither.

The discrete-time versions are an approximation to the continuous transfer function.

The FIR approximation will come as close as you want to analog. The IIR version is very good but not exactly the same.

The IIR version of that filter includes a zero in the numerator at the nyquist frequency.

It's roughly y(n+1) = b*y(n) + c*(x(n)-x(n-1)).
 
Thank you for your reply and sorry for keep asking...

The equation I'm dealing with contains a convolution, like A = f*B, where B is the input signal and f is the impulse response of a filter.

Does this mean that I am forced to use FIR filtering and no Butterworth or Chebyshev for me? (man... they look so attractive)

Also, Butterworth has a nonlinear phase, but FIR filters have a linear phase. However, if I use the impulse response of the Butterworth to do convolution (which is FIR filtering), do I still get a linear phase?

Thank you
 
If you must convolve then yes FIR is required. Are you sure you must convolve?

You cannot get linear phase from an IIR.
 
Sadly, yes. I must convolve...

Will there be any advantages of taking FIR approximation of IIR filters?
 
Antiphon said:
The IIR version of that filter includes a zero in the numerator at the nyquist frequency.

not necessarily. if the analog filter was digitized using the bilinear transform, then it's true. but not necessarily if it was converted from analog to digital by other means (like Impulse Invariant).
 
  • #10
Thank you all for your help :)
 

Similar threads

IIR Filters: Questions & Answers
  • · Replies 1 ·
Replies
1
Views
4K
Taps for simple IIR Filter in GNU Radio
  • · Replies 1 ·
Replies
1
Views
3K
Output as the convolution of the Impulse response and input
  • · Replies 5 ·
Replies
5
Views
5K
Is Spline Interpolation an FIR Filter
  • · Replies 2 ·
Replies
2
Views
2K
How Do I Design an EMI Filter for a Converter with Only Voltage and Power Specs?
  • · Replies 8 ·
Replies
8
Views
2K
Engineering Recursive implementation of an FIR Filter
  • · Replies 2 ·
Replies
2
Views
2K
(Finite Impulse Response)FIR filter math by hand example
  • · Replies 2 ·
Replies
2
Views
4K
Is my understanding of the Nyquist theorem correct?
  • · Replies 4 ·
Replies
4
Views
2K
Designing butterworth filter of Nth order
  • · Replies 1 ·
Replies
1
Views
3K
Engineering Linear Filters for Removing Impulsive noise
  • · Replies 2 ·
Replies
2
Views
1K