Questions tagged [infinite-impulse-response]

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

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Fixed Point, Time Domain and Freq Domain Filter Difference

I am trying to compare my IIR filter in time domain and freq domain, but i am getting different results which i dont understand why ?. So please help me out in understanding the issue. My code is : <...
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How do I prepare a input signal that consists continuous sinusoidal signals of two frequencies?

As the title suggests, how do I prepare a input signal that consists continuous sinusoidal signals of two frequencies in MATLAB?
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Resources for learning about filters from scratch?

Topic of filters is very important in signal processing So i want to learn about filters from scratch and then eventually reaching FIR and IIR filters I have some idea about low pass,high pass,band ...
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42 views

Calculating IIR Filter gain at given frequency

Let's consider an IIR filter with transfer function: $H(z)$. Given the sampling frequency $F_s$ how can I calculate gain at say $F$ ? When I was dealing with analog systems when I wanted to calculate ...
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what rule has coefficients to follow for an IIR filter to be stable? [duplicate]

I'd like to play with IIR filters, but not by designing them with algorithm but rather play with the coefficients directly. i got a stability problem though, because of course IIR filters are ...
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60 views

Trouble showing Time Invariance of recursive system

The system is described with the following recursive differences equation: $$y[n]-4y[n-1]+4y[n-2]=20x[n]+10x[n-1]$$ now lets say the input is delayed by k, then: $$y[n]-4y[n-1]+4y[n-2]=20x[n-k]+10x[...
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Realtime fixed point IIR filter implementation in C

I would like to implement a fourth order fixed point low-pass IIR filter in C (with Q15 arithmetic), and I will prepare this filter by using two stages cascaded direct form-II bi-quad filters. I have ...
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3 dB cut-off frequency of first-order IIR high-pass filter

As descipbed in this great answer (thank you Matt L.), the suggested exact formula was very precise. I need a first order high-pass with similar precision. EDIT: (clarification) The low-pass filter ...
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Direct form 1 filter equation for a biquad filter

In general, we all know that the direct form 1 equation for a biquad filter is given by $$y(n) = b_0x(n) + b_1x(n-1) + b_2x(n-2) - a_1y(n-1) - a_2y(n-2)$$ But when it comes to practical applications ...
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changing filtering “speed” (cutoff frequency) of an IIR filter knowing only its coefficients

i got an IIR filter bu I have only the coefficients. now i'd like to be able to change the filter characteristics of the low pass filter (the "cutoff" frequency) but all i got are a and b ...
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207 views

How to use the iircomb filter in matlab

I have a sound file that needs filtering which looks like this: Hence I think that I have noise spaced equally at 832Hz. i tried to use the iircomb filter taken from mathworks website and i managed ...
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Coefficient Scaling of IIR filter to obtain unity gain response

I am designing a 2nd order IIR digital filter : My tf equation with coefficients is ...
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How to apply band-pass filter and get the filtered back from frequency to time domain in python?

I know this is basic for signal processing, but, I am not sure what is wrong about my approach. I have a signal that behaves as damped sine signal with a sampling frequency of 5076Hz and 15,000 number ...
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250 views

Analog Filter Prototype to Direct Form Second Order Cascade

I've been using the Faust programming language a lot lately for experimenting with DSP, and I've been digging into their implementation of an Elliptic (Cauer) Lowpass filter. Here's an example of such ...
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48 views

calculate fft convolution for an LTI system given its input (in time domain) and its poles and zeros

I have considered taking the fft (MatLab) of the input (x) and create frequency bins for the first half (problems with an odd number of samples, tried solution zero paddings) and evaluate the transfer ...
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How to improve accuracy while converting floating point coefficients to fixed point in the case of an all pole IIR filter

I am having an all pole IIR filter of order 5 with floating point filter coefficients ...
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Is there a simpler way to calculate the amplitude response of the following filter

I would like to calculate the amplitude response $|H(z)|$, $z=e^{j\omega}$, of the following filter: $$H(z)=\frac{\frac{b}{2}+z^{-2}}{2+bz^{-2}}$$ and I would like to avoid using Euler's formula and ...
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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 ...
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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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Why is the first value in digital first-order IIR filter impulse response not the largest?

When I create a digital first-order IIR low-pass filter with scipy (code below), I get the following coefficients: B: [ 0.1367 0.1367] A: [ 1. -0.7265] The ...
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1answer
272 views

Why can't realisable IIR filters have linear phase?

I am studying IIR Filter Design and came across this arbitrary statement in my textbook which says that 'physically realisable and stable IIR filters can not have linear phase'. Would really ...
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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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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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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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Calculating the true values of biquad filter coefficients from normalized form

I have a C code in which the IIR filter(BiQuad) uses only 4 (normalized) coefficients per stage (a2/a0,a1/a0,b2/b0,b1/b0) instead of 6 coefficients (a0,a1,a2,b0,b1,b2). I know that the value of a0 is ...
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A question about the Commutativity Property in discrete signals block diagrams

According to the Commutativity Property of block diagrams, we can place b0 at the entrance or at the exit of the block diagram, it wouldn't matter. My question is, if we placed it at the entrance, we ...
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32 views

Comparison of results with Direct form1 and Direct form2 implementation of IIR filters

The results obtained from Direct form1 and Direct form2 implementations (in C language) of IIR (BiQuad) filters are a little different. In the implementation, i have made the b0 coefficient as 1. So, ...
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Droop compensation - How to do it?

Lets say i have a LPF response that has some kind of droop (some attenaution in the passband, usually could be due to cic filter how to make CIC compensation filter,,,, or can also be due to large ...
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Calculating Transfer function numerator and denominator from the rationalfit model

I have a frequency response data called 'AC_data' which is a vector of complex numbers (real and imaginary part) at different frequency points. I have calculated a rationalfit model for the AC_data ...
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IIR filter relaxation time computation

Let's define the relaxation time of a filter as the delay needed for the impulse response of a filter to reach and remain under an amplitude threshold. Is there a closed-form solution to the ...
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422 views

Convolution with an impulse response does not give the same result as the frequency response

Context I am trying to design a linear-phase FIR filter with the following frequency and phase responses: Designing the filter Given its characteristics (peak filter at 1kHz with 9dB gain and Q=7), ...
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How would one design a (quasi) linear phase adaptive notch filter for a single complex tone?

While IIR notch filters are attractive, I need to retain phase linearity at the filter output. I imagine that it's possible to use a standard IIR notch filter: https://www.researchgate.net/...
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IIR Direct FormII Filter second order in VHDL, false output

I am trying to implement an IIR second order in Direct FormII in VHDL. To make it easier to understand for me and to avoid former timing issues, I implemented the operations sequentially. In my ...
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Can I set a constraint on the first tap of an FIR filter such that its inverse is stable?

Let's say I have the following FIR filter $h[n]$, so the output $y[n]$ for an input $x[n]$ is $$ y[n] = \sum_{k=0}^{m-1}x[n-k]h[k] $$ The inverse of this filter is given by the IIR difference ...
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116 views

Can I get some help plotting an IIR filter frequency response in Python?

The problem I'm trying to solve is described here. In my script, I used Euler's identity to calculate z^-n, such that z^-n = cos(omegan) - jsin(omegan). I find the magnitude of these values from a ...
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1answer
52 views

Polynomial division to separate FIR and IIR in cascade

I have a FIR filter $L(z)$ and an IIR filter $H(z) = \frac{B(z)}{A(z)}$ which are cascaded together as $L(z)H(z) = L(z)\frac{B(z)}{A(z)}$. For specific reasons I want to calculate a parallel topology ...
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Is this the correct solution for finding the samples of phase delay at a given frequency of an IIR BiQuad filter?

I want to calculate the number of samples of phase delay at a given frequency of an IIR BiQuad Filter. I believe I have solved this, but I would like to confirm I have done it correctly. My work is as ...
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Invertibility of an ideal differentiator

Is the system $y(t)= dx(t)/dt$ invertible or not? If yes, please determine the inverse system for it.
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What's wrong with this implementation of my IIR filter?

I posted this originally in the electronics stack exchange, as it's for an electronic purpose (digitally controlled boost) but it was pointed out to me that this would be the more appropriate place - ...
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what is matlab function is taking as sign of second order IIR filter?

I am getting confused from the implementation regarding matlab function filter([b0,b1,b2],[a1,a2],x) and other function similar as ...
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How would you put this “IIR Approximation of FIR Filters Via Discrete-Time Vector Fitting” into Matlab? [closed]

https://www.eee.hku.hk/~culei/publication/ISCAS-0590.pdf This paper talks about a way to approximate FIR filters using IIR via a method known as Discrete-Time Vector Fitting. I am confused on how I ...
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FIR butterworth also possible or just IIR?

can we use butterworth and other such filters like chebyshev,elliptic etc with FIR or they can be only used with IIR?
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IIR coefficients that simply boost the signal

Is there a way to get IIR coefficients that only amplify a signal, nothing more? I suppose some phase shifting would be ok as well as long as it's not too noticeable. Background: I am using a MiniDSP ...
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360 views

Examples where non-linear phase filters are used

I stumbled apon this old question: Why is a linear phase important? There the explanation of why linear-phase processing (filtering) is important is very clear. Also the effects on waveforms due to ...
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Impulse response of an infinite-length system

I have a system which is expressed as following: y[n] + $\alpha$ y[n-N] = x[n] where y is the output and x is the input. When I take the z-transform of both sides, I've found the transfer function ...
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117 views

Filter: IIR Filter

How IIR Filter coefficients formula derived? for LPF, HPF, BPF, BSF there are coefficients formula for a0, a1, a2, b0, b1. How it came? I would like to know the derivation for all those coeffs w.r.t ...
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Real-time audio processing FIR vs IIR

My project consists in filtering an audio signal from the microphone, in order to remove noise, and find the time distance between two peeks with the highest precision possible. I understood that an ...
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289 views

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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1answer
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Is there a way in MATLAB to approximate an FIR filter using an IIR Filter? [duplicate]

I am a student trying to understand how this is possible. I've done some research on the web with not many sources showing up with solutions to this problem that are usable. What techniques are used ...
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68 views

What is the need of IIR filter? When FIR have generally good/desirable characteristics?

FIR filters are generally stable and have linear phase response. These two characteristics are often desired in dsp So why do we need and use IIR filters,despite the fact that IIR filters often have ...

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