# Questions tagged [infinite-impulse-response]

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

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### 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: ...
893 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 ...
33k 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Convert a FIR to an equivalent IIR

Is there a way to convert a FIR to an IIR filter with the most similar behavior?
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### 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, ...
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### 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 ...
231 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 (...
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### 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 ...
939 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 ...
646 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 ...
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### 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 ...
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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 ...
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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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### 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 ...
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### 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 ...
443 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 ...
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### 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 ...
769 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 ...
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### 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; ...
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### 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 ...
350 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. ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### Zero-Phase Algorithm in Matlab

From this document it's says 1.Filter the Data 2.Flip that 3.Filter again 4.and Flip that again for zero-phase filter. but when i do this in matlab , i'm compare ...
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### Correcting Impulse Invariance Method

I'm trying to find out if the correction (Jackson, Nelatury, Mecklenbräuker) could improve the (IIM based) filter response near Nyqvist. Here's my c++ routine (which is used for to calculate various ...
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### DFT in IIR filters

To further summarize, I want to create a function in matlab that finds the time domain signal $y(n)$ and its $n$ time components ($n=0,1,2,...$) given the numerator and denominator of a transfer ...
987 views

### complementary IIR filters

I would like a pair of complementary IIR filters (lowpass/highpass). By complementary, I mean, when the output from the two filters is summed, the original signal is recovered. I thought I could build ...
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### DC blocking IIR filter clipping?

I'm processing audio data for voice input from a mic. The data arrives in 32 bit floats [-1 ~ +1]. My first filter is to remove DC: ...
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### Why does this parallel IIR filter have such a weird form?

Referring to "Parallel 1st-order IIR filters" on this wikipedia page, the structure of a 4-parallel IIR filter is discussed. However, the format in which it is implemented seems very odd. Why is it ...
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### How does parallel structure implementation of IIR speed up the process ? What happens in case of FIR?

I was learning about digital filter structures and there I came to know that parallel implementation of IIR filters speeds up the process and I understand that.But what I am not convinced of is that ...
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### How would I calculate the state-variables of digital biquad filter (direct form II transposed) at steady-state?

I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration For example, let assume the filter is fed a constant input of ...