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

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What is the name of the following 1st order high-pass IIR filter?

What is the name/family behind the following high-pass IIR filter: $ T = 1/f_s \\ f_c = 5 \\ c_1 = \displaystyle \frac{1}{1 + \tan(\pi f_cT)}\\ c_2 = \displaystyle \frac{1 - \tan(\pi f_cT)}{1 + ...
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Check if a filter is IIR or FIR

I have the following equation: $$H(z) = \frac{z^3+5z^2+3z+1}{10z^3}$$ I want to find out whether if its IIR or FIR. Here is the steps I have gone so far: $$H(z) = ...
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Frequency response of a (rectangular) integrator

A very simple question which can't really figure out: I have a simple discrete time rectangular integrator with Z transform H(z) = 1/(1-Z^(-1)) Plotting the frequency response with Matlab using ...
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DSP Library IIR and FIR filters

Me and a coworker are currently in the process of making an audio dsp library. We are wondering what some good FIR and IIR filters to use were. I know ALOT of them but what do you guys think in ...
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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} = ...
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Spectral Factorization of Magnitude Squared IIR

Taking an IIR: $$ H(z) = \frac {A(z)} {B(z)} = \frac {\sum_{n=0}^{N} a_nz^{-n}} {\sum_{m=0}^{M} a_mz^{-m}} \qquad z=e^{iw} $$ The magnitude squared of the numerator $A(z)$ (the maths of the ...
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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?
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IIR filter and phase shift [closed]

I heard that an IIR filter has delay and phase shift effect, but not clearly what are they. For example, 1-pole Lowpass has 90 degree phase shift, 2-pole Lowpass has 180 degree? So does it mean two ...
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154 views

IIR Filter - calculating the phase response

Using formulae from Audio EQ Cookbook from here it was easy to implement biquad IIR filters in C++, i.e. to calculate coefficients b0, b1, b2, a0, a1, a2. Now, I want to calculate the phase response ...
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Z-plane/S-plane to time domain?

I'm working through the IIR chapter in Dick Lyons' Understanding DSP, and there's something I'm having a hard time wrapping my head around. He'll draw poles and zeros and then show the associated time ...
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Implementation of a cascaded IIR filter

I am attempting to implement a cascaded IIR filter in MATLAB. I used fdatool to design the filter and exported it as an object, Hd. In my script, I import a log file of data I captured and store my ...
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59 views

Why does the impulse response determine the transfer function of a system? [closed]

why does it describe the transfer function.. How come? Especially for LTI systems. I thinking about the theory about how come an impulse input can provide information about a complete system.. As it ...
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75 views

Zero-frequency response of an IIR transfer function

I have a question about the zero-frequency (DC) response of a IIR filter. The coefficients of the 3rd order IIR filter are as follows, ...
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52 views

Biquad high-pass filter - calculating filter slope

I have to design high-pass IIR Biquad filter with cutoff frequency of 80Hz, sampling frequency 24kHz, and filter slope of 24dB/oct @ 80Hz. I have used formula for HPF biquad coefficients from here. ...
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32 views

FIR/IIR approximation of known frequency response

I have two different sets of data from compatible signal sources but recorded off two different transmission line characteristics. I am trying to equalize out the transmission line in the two data ...
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91 views

Tricks for computing rapidly changing biquad coefficients

I have 5 'negative peaking' biquads that will change center frequency while maintaining a constant Q and A (amplitude reduction) on a realtime microcontroller (ARM cortex-m4) with a codec over i2s ...
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Closed-form responses for 2nd-order all-pass filter

Here is a Laplace transform for a 2nd-order all-pass filter: $$ f(s) = \frac{s^2 - \frac{\omega_0}{Q}s + \omega_0^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2} $$ The equation and a nice visualization ...
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Second-order sections from complex coefficients

I have an impulse response ir that I need to approximate with an iir because of realtime requirements. For stability I want to break down the 10th order IIR generated with Steiglitz-Mcbride to biquads ...
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54 views

Tradeoff between Filter Order and Sections

I have designed a bandpass IIR butterworth filter with desired response using the MATLAB FDAtool with the configuration shown in the figure below Since this is multistage implementation, when I ...
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66 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. fvtool() shows the ...
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41 views

How can slope of low-pass biquad be configured?

I have a biquad filter, configuread as a low-pass filter (using Zolzer's formulas, similar to these). It does not overshoot and decays nicely in what I assume is -40dB/dec. How can I device a ...
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271 views

How to compute magnitude and phase response from transfer function in Z-domain?

I have a transfer function $$H(z)=\frac{1+1.2z^{-1}+0.8z^{z^-2}}{1-0.9z^{-1}}$$ from which I'm supposed to sketch the magnitude and phase response. I know that you can transform $z=e^{j\omega}$ to get ...
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IIR filter implementation in Direct Form 2

I have implemented Direct Form 2 IIR filter. The input is the Kronecker delta function. I have written code for the response of the filter for Kronecker delta input. The code is: ...
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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 ...
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196 views

IIR low pass filter: floating point and fixed point

I have implemented an IIR low pass filter in direct form 2, the input to the filter is a unit impulse $\delta[n]$. I have calculated the output of the filter for the mentioned input using the ...
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sequence to perform filtering? which filter first?

Hi all Is there a generally accepted rule as to which order to perform filtering in? for example if I have three iir filters, a low pass filter a notch and a high pass filter, which sequence would ...
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83 views

How to concatenate IIR filter (Butterworth) with a Matlab function and evaluate the integral

I have a function of $j\Omega$ and $v$ (velocity), i.e.: $$A(j\Omega,v)=\frac{(j\Omega)^2}{p + \frac{j\Omega}{v}}$$ where $p$ is the pole. I want know how $A(j\Omega,v)$ modify its behavior, when I ...
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detect impact from digital audio

I've started a hobby project which is to detect and count the number of impacts (for example someone clapping, bouncing a ball or hitting a boxing bag). I've been reading and playing around (in java) ...
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464 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 ...
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Adaptive Line noise removal using IIR notch filters

I'm trying to filter out line noise(60Hz and 120Hz) from a EEG signals received over a bluetooth link. I'm proposing to use a IIR notch filter to filter out the line-noise which varies w.r.t to ...
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Changing the cutoff of an IIR lowpass filter with minimal transients?

I have a 1st order lowpass IIR filter of the form $ H(z) = \frac{b_{0} +b_{1} z^{-1}}{1+a_{1} z^{-1}} $ implemented using the direct method my code looks something like this ...
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Understanding Arrangement of second order sections

When splitting higher order recursive filters into more convenient 2nd order sections (biquads), in matlab, we usually use zp2sos to convert. In document, there's a ...
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257 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 ...
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79 views

Help on implementing an IIR filter

I am new to signal processing and and having difficulty understanding how to implement an IIR filter. The reference is athttp://www.dxatlas.com/rocky/Advanced.asp in the Band scope section. It ...
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112 views

Polyphase decomposition of IIR filter

Is there a way to decompose IIR filter into set of poly phase components, that are All pass. E.g. a an IIR filter of order M, can be decomposed into a cascade of All zero filter of order 2*M( which ...
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Is there a widely available implementation of an adaptive, recursive, numerically stable IIR filter?

I need to identify the coefficients of a linear, causal, time-invariant physical system that can be described by a classical state-space formulation. For the sake of the example, suppose that the ...
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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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298 views

Biquad Filter Transfer Function Frequency Response

$H(z) = G\cdot\displaystyle\frac{2b_0\left(1-z^{-2}\right)}{1-2a_1z^{-1}-2a_2z^{-2}} + 1$ I have a data sheet with the above transfer function, I need to calculate its frequency response in code. I ...
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115 views

FIR vs IIR complexity

IIR filters have feedback whereas FIR filters don't use feedback. Then why is it said that FIR filters sometimes have the disadvantage that they require more memory and/or calculation to achieve a ...
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79 views

Identify the system from input and output

I am using Excel. If I have an input and an output, and I know that a recursive band-pass filter produced the output, how can I can find the coefficients of that filter?
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Relationship between Difference equation and Impulse response

I'm having some difficulties understanding the relationship between the impulse response and the difference equation for IIR filters
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114 views

Realization of IIR resonator

The measure of a given frequency $\omega$ in a signal $x(t)$ is: $\frac{1}{N}\sum\limits^N_{t=0}x\left(t\right)e^{^{-i \omega t}}$ This is basically an average of the correlation between the signal ...
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Transient cancellation in non causal filtering

I am using the exponential moving average filter (IIR): $$y(n)=\alpha{}\cdot{}x(n)+(1-\alpha{})y(n-1)$$ in a foward-backward filtering scheme, in order to eliminate completely any phase response ...
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120 views

Difference Equation & Impulse Response of IIR filter - deconvolution

What i want to do is to design an IIR-filter that cancels the "echo", such that im only left with the delta[n]. To do so i ofcourse make an IIR-filter, where u take the z-trans of the impulse ...
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FIR / IIR and Wavelets

I am a self-learner of DSP by reading various books. I have accomplished basic understanding of Signals - CT and DT and a few transforms. I recently started to learn FIR / IIR Filters. The part that ...
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172 views

Filtering out unwanted square wave (Radio: DCS/DPL signal)

I've need to remove a DPL/DCS signal from a recording. Roughly speaking, a DCS signal is a low frequency (67.15Hz) square wave sent at the same time, over the same carrier, as speech. Because it is a ...
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Deriving finite impulse response for polylogarithm

As a part of my research i have to use the following z-transform in matlab 'filter' function so as to derive the convoluted signal from the original one. $$\frac{1}{{\rm Li}_{k}(z^{-1}e^{-b})}$$ ...
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212 views

How to find the frequency response of a communication channel from input and output symbols' functions in MATLAB?

I want to find the channel frequency response of a digital communications system. I have the functions of the input symbol (a triangle) and the output symbol - a distorted triangle: $$\dfrac{1}{1 + ...
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103 views

Understanding IIR , Low Pass, High Pass, Chebyshev, Elliptic Filter? [closed]

I see these terms everyday in every lecture, I do read stuff from wikipedia, follow lecture notes, study solved exercises. All in all I do have a rough idea about these, I know a little from ...
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152 views

linear-phase lowpass filters: frequency responses alignment

These two filters have very similar frequency responses, but those responses are not identical except at a single frequency ωo. I want to find ωo. One way I've seen that done is like this: ...