Questions tagged [infinite-impulse-response]

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

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Impulse Response for an Anti Causal Linear Shift Invariant System

I have a system given by $$y[n] - \frac{1}{4} y[n-1] - \frac{1}{8} y[n-2] =3x[n] $$ I'm asked to determine the impulse response of both an anti-causal and a causal Linear Shift Invariant System ...
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How to design IIR digital filters

Practical Infinite-Impulse-Response (IIR) filters are usually based upon analogue equivalents (Butterworth, Chebyshev, etc.), using a transformation known as the bilinear transformation which maps the ...
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Stopband's edges in bandpass IIR filter in MATLAB

I've tried to get an IIR bandpass filter having the passband [0.1,0.5] Hz and working at the sampling frequency 8 Hz using the following command: ...
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What are the equations for magnitude plots of the common IIR filters? (Are the ones I have so far correct?)

I need equations that describe the magnitude plots of basic IIR filter types. I had looked into this a few years ago and saved some equations but it only covers part of what I need, and I can't recall ...
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Is there an equation that will graph the shape or predict the maximum amplitude of a single sample impulse fed through a One-Pole LPF?

If you feed a single sample impulse of a given amplitude through a One-Pole LPF you get an envelope that looks like this: The output of the LPF from its peak will settle into an exponential decay ...
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what is purpose of IIR filter? [duplicate]

I am working on Digital Signal Processing. I know theory very well but I don't understand why IIR filter is used in place of FIR. What is advantage?
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Summation of two IIR filters

Actually my question is how to get the weighted average of two or three IIR filters given their transfer functions, which is nearly equal to this question. How to calculate the total transfer function ...
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simple iir filter implementation in C++

I am programming the simplest way of implementing and IIR filter. However, I am struggling with the use of buffers. Do any of you have any simple implementation of an IIR filter implementing manually ...
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When is the sum of two (parallel) minimum-phase filters also minimum-phase?

Say I have two minimum-phase filters: $$\frac{A(z)}{B(z)} \: \text{ and } \: \frac{C(z)}{D(z)}$$ That is, the roots of $A(z)$, $B(z)$, $C(z)$ and $D(z)$ are all in the stable region. If add them ...
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How to take multiple IIR filters efficiently

I have a collection of IIR filters (exponential decay at various decay rates). I'd like to compute all of them on a discrete time series efficiently. Is there a way to do this that is faster than $$O(\...
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How can initial conditions be taken into account to calculate a system's terminal value using the final value theorem or some other technique

I wish to calculate the Final Value of the following system given initial conditions not at rest, and assuming the X will not change from its initial condition value. The transfer function is $$H(z) = ...
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What does poles in unit circles center mean?

Suppose i have all my poles in unit circle center. What kind of information this gives me? Can i determine if this filter is IIR or FIR?
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Approximation and IIR Filters

Consider the discrete-time time-invariant system with input $x[n]$ and output $y[n]$ satisfying $$y[n] = \sum_{k=1}^5{x[n-k]}$$ Consider approximating the desired system with a second-order IIR system ...
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How to practically correct for group delay imposed by a digital filter (Python)

I'm using Python to filter a signal using a Butterworth filter (scipy.signal.butter) and subsequently passing this through a forward-backward filter with cascaded second order sections (scipy.signal....
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267 views

Frequency response of a digital state variable (Chamberlin) filter

I recently implemented a digital state filter based on the recommendation here. I've tested this filter's performance as a very low cutoff low-pass filter with limited coefficient quantization ...
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Mitigate floating-point numerical errors for very-low corner frequency low-pass filter with DSP

I'm designing a low-pass filter for a digital signal processing application that ideally just passes a very small bandwidth above DC. I'm using an IIR biquad filter for this, where the coefficients ...
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What is the purpose of the recurrence relation in low and high pass (audio) filters?

Newbie here. I'm familiar with time and frequency domains from math. I think I understand what low and high pass filters do, sonically. But digging into an implementation of ...
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Why does Pre-warping work with a notch filter but not a low pass filter?

Hey guys a little bit of a continuation from a previous post I made here, I found the solution as why the pre-warping was not working at the time, However I was just playing around and found out pre ...
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IIR filter relationship between number of poles, order and second order sections

I have ported Iowa Hills Code Kit to a mcu to calculate IIR filter coefficients. They are used to initialize the CMSIS Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure. Trying to ...
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855 views

Are IIR filters (and specifically Butterworth filter) causal?

I am new to signal processing. I am learning now about filtering and I am trying to implement high pass filter (HPF),and later band-pass filter (BPF). I implement the filters in ...
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What is the best way(In terms of speed) to implement a direct form type 2 IIR Filter in VHDL?

I am trying to implement a 4th order direct form type II IIR filter in VHDL(Specifically, in xilinx FPGA) and when i implement it i get correct output yet very low maximum clock rate(Around 80 Mhz). ...
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IIR bandpass filter with very low corner frequencies

I'm trying to get in the MATLAB Signal Processing Toolbox a bandpass IIR filter having the following specifications: pass-band [0.1-0.5] Hz and stop-band attenuation 30 dB. I'm using the following ...
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Question about ideal filters

Following shows the discrete time Fourier transform of an ideal low pass filter with cutoff frequency $\omega_c$: $$H\left(e^{j\omega}\right) = \begin{cases} 1, & \text{if $|\omega| \le \omega_c$...
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856 views

Notch filter: differences between IIR and FIR filters

I'm trying to understand this great answer from Matt L. . It's said that "One advantage of IIR filters is that steep filters with high stopband attenuation can be realized with much fewer ...
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How do software equalizers work?

Recently, I have been studying IIR and FIR filters, and trying to create a parametric equalizer using a microcontroller. More specifically, I use the ADC on it to sample the audio at about 44 kHz, and ...
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Frequency conversion in IIR lowpass-to-lowpass transformation

We use $\ z^{-1} \xrightarrow{} \frac{z^{-1}-\alpha}{1-{\alpha}z^{-1}}$ and $ \alpha = \frac{\sin(\omega_c^{'}-\omega_c)/2}{\sin(\omega_c^{'}+\omega_c)/2}$ for a lowpass-to-lowpass frequency ...
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76 views

Calculation of gain at certain frequency in case of nth order IIR filter

There is this method for to set 0dB gain to be at wanted frequency (fc) (Octave/Matlab example for biquad LPF): ...
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Highpass filter square wave

Generated a 1kHz square wave in Audacity and normalized it to 0dB (fs = 44100Hz): Added a 24dB/oct high pass filter (std Audacity plug-in), cutoff frequency set to 100Hz. Result: Zoomed version: ...
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3 dB bandwidth of a filter

I am solving one of the question from signal processing about calculating the 3dB bandwidth of the filter. But I am stuck once I got the magnitude response of the filter. Can someone help me with this?...
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Stop band ripple vs stop band attenuation

What is difference between stop band ripple and stop band attenuation in context of filters?
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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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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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393 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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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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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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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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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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855 views

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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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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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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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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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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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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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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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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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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