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

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Differentials - Differences: Non causality in the system

I'm still learning DSP and referring to Oppenheim video lectures. In that lectures, differential difference equation is obtained for IIR filter design, in Lecture 14. $$\mathcal{L}[\frac{\mathrm ...
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IDFT of H(z) sampled in N values

If a have a causal IIR filter described by $H(z)$ and I sample it in $N$ equispaced values around the unit circle, I get a DFT of $N$ points. That DFT corresponds to $h[n]$ truncated in $n=N-1$ or to ...
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Decimating physics data

At work we run a physics simulator (video game) that operates in an inner loop at 360 Hz. Data from that inner loop is collected 60 times a second and sent out to hardware (a force feedback steering ...
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FIR estimator for IIR system

Suppose that we have a dynamical system of which the impulse responses are infinite (IIR). Now I found methods on papers (http://dx.doi.org/10.1109/9.839942) estimating states or outputs of such a ...
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How do I find the phase response of a filter from the filter equation?

I am new to this forum. I have been teaching myself DSP for the last two years, so my experience and knowledge has a long way to go. I am trying to find the phase response of a specific filter that I ...
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Calculating the product of discrete transfer functions

I'm trying to construct a higher order IIR from a biquad cascade, I know this is generally frowned upon, but it's necessary as the coefficients will be embedded into a larger formula used in a FDTD ...
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Filtering an audio file using IIR filter on Matlab

First of all, sorry for my English. I'm quite lost with Matlab, I'm not comfortable at all and I have to create an IIR filter using Matlab. The thing is I'd like to remove background noise from an ...
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Regarding BIQUAD IIR implementation in MATLAB

I want to implement a high pass filter (order 4) in MATLAB using cascade form. ...
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Zero-Phase Algorithm in Matlab

https://ccrma.stanford.edu/~jos/fp/Forward_Backward_Filtering.html from this document it's says 1.Filter the Data 2.Flip that 3.Filter again 4.and Flip that again ...
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Are all IIR filters unstable in nature?

I know this question has been asked here numerous times. But I am still unclear here :( My book says, A linear time-invariant system is stable if its impulse response is absolutely summable. ...
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Convolution by IIR filter, a case where circular convolution is allowed?

The question is, how to attain the frequency domain representation of any signal (which is finite, non-unit length) convolved with an IIR filter. The correct answer in my opinion is that there is in ...
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why difference between this example and matlab result

everyone fs=30 000 , fc=3000; when i code apply this in matlab result is very difference ...
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There is a mysterious factor when compute coeffiencts

everyone i m trying write higher order butterworth algorithm in c++.I can compute nominator and denominator second order. So i tell myself , i can cascade struct for higher order. But there is between ...
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Is the below filter linear phase

$$h(t) = \frac{1}{1 + t^2}$$ and is it IIR or FIR filter. I tried finding the Laplace transform of this filter to get the data flow diagram with 5 taps and T=2s, however, I am unable to solve this. ...
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35 views

What is the correct way to apply multiple IIR filters to a signal in MATLAB

I am attempting to apply multiple IIR filters (one band-pass, one high-pass, and one low-pass;each with Fs of 44.1 kHz ) to a signal in MATLAB by using the ...
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96 views

Why lattice-structured all-pole IIR filter becomes stable, if the k-coefficients satisfies $|k_i| < 1$? [closed]

Why the lattice-structured all-pole IIR filter becomes stable, if the k-coefficients satisfies $|k_i| < 1$? Anyone who can tell me the way how to prove it, would be so thankful for me :) ps. If ...
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May a causal system depend on future values of its own output

For example, let's assume a system given as y[n]-9y[n+2]=x[n] I convert the difference equation to y[n]=(y[n-2]-x[n-2])/9 ...
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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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Overlap/Chunk processing possible with Zero-phase?

I'm relatively new to DSP and I'm currently investigating FIR filter and IIR filters. From what I've found FIR filters can be implemented efficiently using the overlap-save method, but I was wondering ...
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Convert simple CT filter to DT with impulse invariance and bilinear transform

Can someone verify my work. Problem Question: Convert simple CT filter to DT with (A) impulse invariance and (B) bilinear transform $$ H_c(j \Omega) = \begin{cases} |\Omega|, & |\Omega| ...
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Lynn's integer filter has a linearly increasing trend

I have a PPG signal sampled at 50Hz and I want to filter the signal using Lynn's integer filter. I.e \begin{equation} H(z)=\frac{(1-1/z^m)^2}{(1-1/z)^2} \end{equation} Cutoff frequency is 5Hz, so ...
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How to compute DFT of IIR

This question pertains to frequency domain filtering. I'd like to multiply an IIR filter's frequency response by a buffer of samples that have been FFT'd. I get how I'd evaluate an FIR, I'd FFT and ...
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82 views

How to estimate filter coefficients of an all-pole system?

Suppose we have measured the frequency response of a system that is known to be all-pole; measuring impulse response is not possible. What are the methods available, if any, to estimate the ...
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How to shift the center frequency of an IIR filter

I have a pre-designed in-series 14th-order IIR filter in second-order sections. Problem is, when I simulate and measure the behavior in my codec, there is a frequency shift downward (as compared to ...
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45 views

equations to calculate coefficients of recursive IIR Gaussian blur filter

I am reading the implementation of IIR Gaussian blur filter from this link. In the source code, the coefficients are generated by the following code ...
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frequency response of Gaussian filter

In Matlab, the function freqz can produce frequency response in terms of transfer function and the function freqz2 can produce frequency response for FIR filter. It seems that I can's use the input ...
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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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174 views

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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68 views

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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190 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} = ...
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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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365 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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60 views

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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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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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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118 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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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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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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66 views

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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94 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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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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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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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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638 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 ...