Questions tagged [infinite-impulse-response]

Infinite impulse response (IIR) is a property of signal processing systems.

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33
votes
2answers
36k views

What is the advantage of MATLAB's filtfilt

MATLAB's filtfilt does a forward-backward filtering, i.e., filter, reverse the signal, filter again and then reverse again. Apparently this done to reduce phase ...
17
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1answer
6k views

Digital filter design basic principles (IIR/FIR)

Although I have a solid experience in designing audio engines and such, I am fairly new to the realm of Digital Filter Design, particularly IIR and FIR filters. In other words, I'm trying to learn as ...
26
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2answers
43k views

Applying filter in scipy.signal: Use lfilter or filtfilt?

I saw in a SO thread a suggestion to use filtfilt which performs backwards/forwards filtering instead of lfilter. What is the ...
6
votes
2answers
11k views

Single-pole IIR low-pass filter - which is the correct formula for the decay coefficient?

A single-pole IIR low-pass filter can be defined in discrete time as y += a * (x - y), where y is the output sample, ...
5
votes
1answer
4k views

Analytically designing a notch-filter for specified frequency 50 Hz

I tried to analytically construct a causal notch filter that stops frequencies at 50Hz and I thought if zeros are more than poles it will be non-causal so I chose equal amount of poles and zeros ...
4
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1answer
1k views

How does this "simple filter" work?

I'm new to DSP, and I'm using this basic "1-pole LPF" Param Smooth filter which "smooth" param when I change it. The code is pretty simple: ...
3
votes
3answers
1k views

Berchin's FDLS arbitrary filter design algorithm

I'm trying to use Berchin's FDLS methods (for those that don't know what it is, it's a way to design arbitrary magnitude and phase of an IIR Eq) I tried different things but neither gave me what i ...
28
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5answers
18k views

What Is the Best First Order IIR (AR Filter) Approximation to a Moving Average Filter (FIR Filter)?

Assume the following first order IIR Filter: $$ y[n] = \alpha x[n] + (1 - \alpha) y[n - 1] $$ How can I choose the parameter $ \alpha $ s.t. the IIR approximates as good as possible the FIR which is ...
13
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2answers
11k views

Filter Order Rule of Thumb

Is there a rule of thumb for calculating the approximate filter order of a FIR/IIR based on passband vs sample rate? I seem to remember reading about it once in Undergrad. I'd think you could make a ...
8
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6answers
5k views

Convert a FIR to an equivalent IIR

Is there a way to convert a FIR to an IIR filter with the most similar behavior?
6
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2answers
5k views

best implementation of a real-time, fixed-point iir filter with constant coefficients

I have implemented IIR filter in direct form, parallel form, and cascade form. The input in all the cases is a kronecker delta function. How to judge which implementation is better is in real time and ...
1
vote
1answer
445 views

Real-time modulated IIR filter

I've been learning to implement an IIR filter for a synthesizer project. It is now more or less stable when the parameters are constant, but ultimately I want the parameters to be arbitrarily ...
11
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2answers
2k views

What kind of filter is that? Is it IIR?

I am trying to answer the following question: Is the system described by equation: $$y[n]=0.5y[n-1]+x[n]-0.5x[n-1]$$ an IIR filter? My answer is yes. Thank you
4
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1answer
315 views

Advancing a causal IIR filter's impulse response

Given an infinite impulse response (IIR) filter as coefficients in a topology of your choice, what is a straightforward way to modify the filter so that the impulse response is shifted in time (...
3
votes
3answers
3k views

Is there a way to derive an FIR filter using an IIR filter?

I know there's a thread similar to this one here, but the OP is asking the reverse of what I'm trying to find here. I've done some research on the web with very few sources coming up with actual ...
2
votes
3answers
2k views

How to design very narrow, sharp lowpass filters - Only DC needed?

I asked exact the same here one year ago: One year ago question I asked this question again here, because after one year, I have learned more about DSP and am thinking ways to improve it. Filter ...
2
votes
2answers
192 views

Can I set a constraint on the first tap of an FIR filter such that its inverse is stable?

Let's say I have the following FIR filter $h[n]$, so the output $y[n]$ for an input $x[n]$ is $$ y[n] = \sum_{k=0}^{m-1}x[n-k]h[k] $$ The inverse of this filter is given by the IIR difference ...
4
votes
1answer
1k views

Design $ {L}_{2} $ Norm Optimal Infinite Impulse Response (IIR) Filters

It is widely known that matching a FIR filter of fixed length to a band model is an unconstrained QP-problem. The MATLAB function firls() implements a solution to ...
3
votes
2answers
888 views

Design a linear-phase FIR filter approximating the magnitude of a given IIR filter

I have a biquad IIR filter from which I want to get a linear-phase FIR. I saw that related question but the OP does not care much about phase. I have troubles getting the exact same magnitude curve ...
4
votes
2answers
2k views

Step response overshoot in IIR filters

Is there an analytic expression by which it is possible to calculate overshoot of step-response of second order IIR digital filter? I have tried to search through Mitra's signal processing book and ...
4
votes
1answer
639 views

Discrete-time Biquad filter: Relation between peak frequency and pole frequency

This question arose from a discussion in the comments to this question and its answer. The author of that question discussed a discrete-time second order filter described by the following difference ...
31
votes
2answers
47k views

Filter order vs number of taps vs number of coefficients

I'm learning DSP slowly and trying to wrap my head around some terminology: Question 1: Suppose I have the following filter difference equation: $$y[n] = 2 x[n] + 4 x[n-2] + 6 x[n-3] + 8 x[n-4]$$ ...
11
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1answer
2k views

What's the advantage of adaptive IIR filter against FIR?

Adaptive IIR filters is not straightforward, and may be unstable. Many people say that adaptive IIR filters use less coefficients than FIR filters. What I'm curious about is how many coefficients can ...
20
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3answers
11k views

How does cascading biquad sections for higher order filters work?

I'm trying to implement an 8th order IIR filter and every application note and textbook I've read says that it is best to implement any filter of order more than 2 as second order sections. I used <...
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vote
2answers
3k views

How to design a filter with custom group delay -- why is it an IIR?

Say I have an FIR filter with desired magnitude characteristics. I could imagine using an allpass IIR in series with the FIR to alter the group delay characteristic to provide both a 'magnitude ...
3
votes
2answers
1k views

Matlab `filtfilt` provides excessive transient

I observed that filtfilt suffers from an undesired behavior when I provide IIR bandpass filters having steep transition bands. Specifically, the output signal exhibits excessive transient response; ...
3
votes
2answers
12k views

How to produce a high-pass filter from a low-pass one?

I already have a low-pass filter and want to remove the DC offset of a signal with a high-pass one. I guess you can subtract a low-pass filtered signal from the original signal and the result is a ...
2
votes
1answer
508 views

Design Lowpass Filter With -7.5 dB/Octave Rolloff

I am working on a project that needs a lowpass filter with a -7.5 dB/Octave rolloff. This is somewhere between the rolloff of a one-pole and two-pole filter, so I wanted to ask what some standard ...
3
votes
1answer
1k views

Complex IIR to Real IIR

I have created an IIR design algorithm that generates complex coefficients (there is no symmetry in the poles and zeros). However, the IIRs will be used to filter a real signal. Is there a closed form ...
2
votes
2answers
561 views

Find reverse one pole lowpass filter

I need to find a filter that revert the one pole filter of the current signal, a function using Python (or MATLAB) scipy.signal.filtfilt or ...
1
vote
1answer
290 views

Shall a $1^{\rm st}$ order IIR filter include $x[n-1]$ term?

I have seen a $1^{\rm st}$ order IIR filter in the following form: $$y[n] = \alpha x[n] + (1 - \alpha) y[n - 1]$$ Such as: another post in this forum However, the filters generated by Matlab, such ...
1
vote
1answer
268 views

IIR filter relationship between number of poles, order and second order sections

I have ported Iowa Hills Code Kit to a mcu to calculate IIR filter coefficients. They are used to initialize the CMSIS Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure. Trying to ...
0
votes
3answers
172 views

What is the need of IIR filter? When FIR have generally good/desirable characteristics?

FIR filters are generally stable and have linear phase response. These two characteristics are often desired in dsp So why do we need and use IIR filters,despite the fact that IIR filters often have ...
0
votes
1answer
404 views

Custom nearly-linear-phase IIR filter computation gone wrong

I'm using the code in this book: Algorithms for the constrained design of digital filters with arbitrary phase and magnitude responses to compute nearly-linear-phase IIR EQs. ...
7
votes
6answers
3k views

Meaning of Phase response of a filter? In simple words?

What is meant by phase response of a filter? Often it is associated with restoration of signal shape,so if a filter has linear phase response, its output looks like input otherwise output is ...
5
votes
6answers
738 views

Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter

I would like to approximate a moving average filter with an IIR filter of much lower order than the tap-length of the moving average filter. Optimality shall refer to the $L_2$ norm of the impulse ...
17
votes
2answers
3k views

Are there any standard implementation forms for tunable Butterworth filters?

One of the standard ways to implement a Butterworth filter is with a cascade of second-order sections, each corresponding to a pair of complex-conjugate poles. For a fourth-order filter, for example, ...
15
votes
3answers
1k views

How can I design a very narrow filter?

Suppose I've got an audio signal sampled at $48000$ Hz, and I'd like to design a low-pass filter that isolates everything below ~$60$Hz. In the digital world, this is a low-pass filter with the ...
3
votes
2answers
4k views

Hilbert transform filter for audio applications: Using IIR half-band parallel all pass structure

Does anyone have any experience designing wideband IIR Hilbert transform filters with audio applications in mind? I am using the filter for single side band modulation audio effects discussed in this ...
3
votes
1answer
5k views

Cutoff frequency of a first order recursive filter

I've implemented a very simple first order recursive low pass filter in c using the algorithm: ...
1
vote
1answer
4k views

How to normalize predesigned IIR filter coefficients to have unity gain?

There is a low pass filter with difference equation already provided. $$ y_n = (x_n - 2x_{n-6} + x_{n-12}) - (-2y_{n-1} + y_{n-2}) $$ $$ a_0 = 1, a_1 = -2, a_2 = 1 $$ $$ b_0 = 1, b_6 = -2, b_{12} = ...
14
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2answers
1k views

What bandpass filter design will yield the shortest impulse response?

Designing a simple 2nd order IIR bandpass Buterworth filter with a centre frequency of 500 Hz and a 1 octave bandwidth gives me the following frequency response ... Now, if I take the impulse ...
8
votes
2answers
6k views

How does MATLAB handle IIR filters?

MATLAB has a butter, which constructs a Butterworth filter given an order and relative cutoff frequency. The filter created can be used to ...
7
votes
1answer
313 views

Designing an IIR to generate a specific data sequence

I know that it's possible to design an IIR with specific poles and zeroes to create specific frequency responses. Is it also possible to design an IIR such that when you give it an impulse, it ...
4
votes
1answer
4k views

Is it possible to design noncausal filters in Matlab?

I'm trying to design a lowpass IIR filter with 5Hz cutoff frequency (sample frequency is 200Hz). i know how to create it with fdatool, or with functions such as 'butter' or 'ellip'. However, i think ...
1
vote
1answer
83 views

What is the best way(In terms of speed) to implement a direct form type 2 IIR Filter in VHDL?

I am trying to implement a 4th order direct form type II IIR filter in VHDL(Specifically, in xilinx FPGA) and when i implement it i get correct output yet very low maximum clock rate(Around 80 Mhz). ...
9
votes
3answers
4k views

Downsampling lowpass filter for audio: FIR or IIR?

I'm working on a real-time audio processing project in which I have to downsample a 44.1 kHz to a yet-to-be-determined lower sampling rate essentially for reducing computational complexity. I'm ...
5
votes
7answers
5k views

Design of a digital A-weighting filter with arbitrary sample rate

I want to A-weight a time series with arbitrary sample rate. An analog A-weighting filter is defined exactly by IEC 61672-1. But there's no definition for a digital filter. One method is to use the ...
3
votes
2answers
3k views

Determining which Filter from a Z-Plane Plots?

How do i determine which FIR filter (LP, HP, BS, BP) it is from looking at it's z-plane plot?
3
votes
1answer
171 views

Jacobian Computation in Least Squares IIR Filter Design

Long time lurker and first time poster - but unfortunately I haven't had any joy untangling this on my own. I've been studying Mathias Lang's thesis, Algorithms for the Constrained Design of Digital ...