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

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Weighting function for output error IIR filter design

I noticed, when I try to fit filter coefficients to a given complex transfer function with the output error method, implemented for example in the MATLAB function ...
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Causal and Non-causal filtering. Strange behavior

I'm trying to understand the behavior of a causal filtering exemplified by figure below. This behavior is making LDA (Linear Discriminant Analysis) misclassify our data, by clearly reverse the ...
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Is there a method to calculate the maximum gain of a biquad?

Given an IIR expressed as a biquad: $$ H(z) = {b_0 + b_1 z^{-1} + b_2 z^{-2} \over 1 + a_1 z^{-1} + a_2 z^{-2}} $$ Is there a way to calculate the maximum gain the biquad attains over the range $0$ ...
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Difference equation when transfer function expressed as poles and zeros

The transfer function $H(z)$: $$ H(z) = \frac {b_0 + b_1 z^{-1} + b_2 z^{-2}} {1 + a_1 z^{-1} + a_2 z^{-2}} \tag{1} $$ Has difference equation: $$ y(n) = b_0 x(n) + b_1 x(n - 1) + b_2 x(n - 2) - ...
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Impulse response of a continuous time system

Question The impulse response of a continuous time system is $h(t) = e^{-t}u(t)$. When $x(t) = u(t - 1)$ is input to this system what is the value of the output signal $y(t)$ at $t = 2.34$. ...
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Formula for Bessel low-pass filter coefficients

When I am filtering a signal in python, it has a built in function to generate bessel filter coefficients given a cutoff ratio and a filter order (number of poles). I am trying to translate this to C ...
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60 views

Analytical way to generate an IIR that is the square root response of another IIR

For simplicity take the transfer function of a second order IIR in $z$-domain: $$ H(z) = \frac {b_0 + b_1 z^{-1} + b_2 z^{-2}} {a_0 + a_1 z^{-1} + a_2 z^{-2}} $$ Is it possible to generate a new ...
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Real Time Goertzel Algorithm

Why is Goertzel Algorithm considered a block algorithm? Given that my input is bounded, couldn't I just run it forever (taking every sample that comes out after some length N) given a big enough word ...
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How to use arm_biquad_casd_df1_f32 to implement a notch filter using DSP EQ cookbook coeffs

Goal: implement a notch IIR biquad filter 2nd order Direct Form I in floating point on a Cortex M4 using the Keil library with arm_biquad_casd_df1_f32 function (built into an audio chain for a ...
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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 ...
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Comparing with FIR, why does IIR always gives a bias error, when calculating signal DC?

I am trying the DC blocking function in matlab. The algorithm of DC blocking is to find DC of the signal first and then remove the DC value from the signals. Here are the codes I tried, which are ...
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When input data into a low pass filter, are the first several data unusable?

For example, I want to feed a DC into a low pass filter. The the filter's first several output will not have the same DC value I want. Does it mean that I need to dispose first several results? ...
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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 ...
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139 views

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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Unexpected behaviour when using lfilter with initial filter delay multiple times

I want to filter a very long signal in smaller parts, therefor I am currently using scipys lfilter with an initial filter delay doing multiple iterations of: <...
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Method for determining IIR filter stability

I have a function which takes some parameters for notch filters (gain, centre frequency, Q) and returns coefficients for a high-order IIR filter equivalent to placing the notch filters in series. It ...
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158 views

Fitting an IIR filter to a complex transfer function

anybody knows of better ways to fit an IIR filter to a complex transfer function than Matlab's invfreqz.m? I'm implementing a little transfer function fitting ...
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IIR filters with variable roll-off

I have a filter design problem in which lowpass filters have to be designed with varying roll-off. E.g: 2.7 db/ocatve or 1.4 db/ocave. See picture below. This is easy to achieve with a FIR filter, ...
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Phaser effect with feedback control IIR filter calculation

This question is possibly relevant to this one, but it's not duplicate as far as I'm aware. I'm trying to make phaser with feedback control as shown in the picture below: (Got it from here) First ...
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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 d}{\...
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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

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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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. (G....
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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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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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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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103 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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63 views

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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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 + \tan(\...
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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) = \frac{1}{10}\frac{z^3+5z^2+3z+1}{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 best/...
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370 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} = ...