# Questions tagged [infinite-impulse-response]

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

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### What is the numerical error of the signal.iirdesign methods in scipy?

How large are the numerical errors of the signal.iirdesign method from SciPy? I am trying to implement a digital filter on an FPGA, but at low frequencies, the filter is often unstable. I am not sure ...
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### Butterworth filter vs Elliptic filter - artefacts and huge transient

I'm working on a project involving digital filters and DFT. I want to use sampled ECG data to determine the heart rate using power spectral density. While filtering the ECG samples (samples are from ...
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### ECG analysis in MATLAB

I'm working on a little project involving digital filters and DFT, what I want to do is, given a sampled ECG, get the heart rate using power spectral density. I got the samples from this database. ...
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1 vote
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### How do you filter a signal, split in batches, using an IIR filter?

I have a signal that is measured by an optical sensor that is connected to an ESP-32. I am trying to apply a band pass filter "in real time" on this microcontroller. The signal is comming in ...
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### What is the sos simplification that octave does?

I am comparing sos (cascaded 2nd order IIR) coefficients from my own implementation of a textbook method versus the coefficients that octave generates. Here is an snip of the octave code: ...
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### How to handle non-causality when decomposing a 4th order IIR filter into a parallel bank of second order filters?

What I am trying to do I am trying to code a Gaussian smoothing filter using the 4th order IIR filter described in Van Vliet's paper "Recursive Gaussian derivative filters". My code works ...
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### Question about reducing phase delay in filters for microcontroller application

I am trying to design a filter to smooth out some of my sensor data. This is for a control systems application where I have limited phase margin. I am looking for a solution where I can maintain lower ...
1 vote
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### The discrete-time impulse response of an IIR filter

Suppose you begin with the following model of a discrete impulse response: $$h[n] = \begin{cases} \displaystyle\sum_{k=1}^K \alpha_k p_k^n & n \ge 0 \\ 0 & n < 0 \end{cases}$$ i.e. a linear ...
1 vote
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### Initial conditions for 2 IIR causal filters applied to the same time-series consecutively

I have a buffer of shape (n_samples, n_channels) in which new samples are coming in at regular intervals and old samples are discarded. In this example, the buffer array is called ...
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### Group delay equalization for second order IIR notch filter

A couple of second order notch filters seem to be appear regularly in the literature (see e.g., Tseng, Chien-Cheng, and Soo-Chang Pei. "Stable IIR notch filter design with optimal pole placement.&...
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### IIR filter design for "data-aided" least-squares filtering

Consider a discrete-time signal consisting of a desired signal component and noise, as follows. $$y_k=d_k + n_k, \qquad k\in\{0,1,\dots,K-1\}$$ This signal is applied to a linear time-invariant (LTI) ...
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### Symbol Sync blocks in GNU Radio seem to use PID (well, PI) for their clock sync feedback loops. Why not IIR/FIR?

E.g. the Symbol Sync block has a Loop Bandwidth, which (if I read the source right) ends up as a PI loop. I know what PID does mathematically, and what FIR and IIR ...
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### Best large gaussian filter for current SIMD instruction sets?

I'd like to make a faster version of the Gaussian blur for Inkscape. Here's what I found various open source projects use: librsvg: 3 box blurs when stdev > 2. Else, separable FIR filter. Krita:  ...
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### "Tone Control" IIR filter coefficients

The documentation for Analog Device's sigmastudio shows some of the formulas behind their biquad IIR filter coefficients. The usual suspects (HP, LP, peaking, ...) as described in RBJ's cookbook are ...
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### Why does an asymetric transfer function cause a non linear group delay?

I know that an IIR filter exhibits non linear group delay (so different frequencies can be delayed more) and that this is related to the fact that it is asymetric (due to considering previous outputs),...
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### Total delay of cascade FIR filters

I have a doubt regarding the total delay in terms of taps for cascade filters. Imagine that I have an SOS IIR Filter (2 delays) and an FIR filter of 10 taps (10 delays) and another of 20 taps (20 ...
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### Bilinear transformation with a high sampling rate (chebyshev filter)

I'm trying to design a digital Chebyshev filter of order 2. This gives the general transfer function If I transform this and simplify I get If I then expand the denominator and then normalize so ...
551 views

### Given two low-pass digital IIR filters, find bandpass coefficients

In the case of FIR filters it is easy to get a band-pass filter by subtracting the coefficients of two low-pass filter filters or by convolving a high-pass and a low-pass filter: ...
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### IIR/FIR equations for custom frequency response

Given a frequency response plot where gain is 0dB up to Fc and after Fc gain increases linearly by factor K (example chart below): I am seeking how to arrive at its IIR/FIR equations so it can be ...
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### Possible errata Proakis Digital Signal Processing Third Edition Figure 2.35c

I'm reading through the 3rd edition of John G. Proakis Digital Signal Processing and I came across a possible errata in Figure 2.35c on page 116. I couldn't find any errata sheet on the publisher's or ...
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### How to trade poles of All pole filter with zeroes?

I have filter of order 2000 IIR all-pole. I want to implement it via cascade IIR filter. Is there any way to reduces poles order and increase zeroes as its cost. To balance zero and poles. Since all ...
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### Converting transfer function to cascaded IIR filter [closed]

I have two function, But I don't know which one is correct to convert my Transfer Function(tf) to secound order sections(sos). I'm using GNU octave, and it have intrinsic ...
1 vote
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### Approximating fractional-octave Gaussian smoothing with non-causal variable-width IIR filters

I am trying to implement fractional-octave smoothing of amplitude response data with approximated Gaussian filters, as briefly discussed in this AES paper. Unfortunately, no implementation details are ...
1 vote
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### Is there a way to get this reverb effect working on something else than 44.1 kHz?

I have successfully implemented the Sony PlayStation 1 reverb effect, until I realized that it strictly works at a sample of 44.1 kHz. A quick web search shown that (as far as I understand), an IIR ...
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### Phase compensation using IIR allpass filters

As an exercise with IIR allpass filters, I am trying to compensate the phase of a lowpass Linkwitz-Riley filter using the Matlab integrated function iirgrpdelay. The code I am using is the following: <...
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### Why does scipy introduce its own convention for H(z) coefficients?

Conventionally, the definition of the system function for a IIR digital system is: $$H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+\cdots}{1-a_{1}z^{-1}-a_{2}z^{-2}-\cdots}$$ where coefficients are the ...
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### LCCDE filter classification

I am trying to figure out if $$y[n]-2.56y[n-1]+2.22y[n-2]-0.65y[n-3]=x[n]+x[n-3]$$ is either IIR or FIR, causal or non-causal, stable or unstable (BIBO). I got the transfer function from the ...
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### What order of FIR filter is equivalent to an IIR filter for same design specifications and to get same magnitude response

I have to design a bandpass filter with passband frequency [300Hz 500Hz] and sampling frequency is 16kHz.The stopband attenuation required is 60dB.I have used butterworth filter in MATLAB to design ...
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### Filter IIR, 1/3 Octave Corner with 2 Octave BW

I'm trying to design a new filter with IIR to filter out specific bands. Basically it's a bandpass filter with 2 Octave or 3 Octave bandwidth but the filter order should be equal to 1/3 Octave filter. ...