# Questions tagged [infinite-impulse-response]

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

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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 ...
1answer
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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 ...
2answers
1k views

### 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 ...
2answers
2k 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 ...
1answer
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### 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 ...
2answers
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### 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 ...
2answers
243 views

### 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 ...
2answers
34k views

### 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 ...
1answer
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### 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 ...
1answer
2k 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 ...
1answer
183 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?
0answers
395 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 ...
0answers
259 views

### 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 ...
1answer
671 views

### Difference equation and Impulse response of an IIR filter - deconvolution

Given the input to the IIR filter $$x[n]=\delta [n]+0.25\delta[n-2205], \quad \text{where}\quad \delta[n]= \begin{cases}1, &n=0\\0, & n\neq 0\end{cases}$$ What I want to do is to design an ...
3answers
725 views

### 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 ...
3answers
698 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 ...
0answers
99 views

### 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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### Matlab SOS Filter in C++

I'm struggling to validate that my C++ implementation of a filter I designed in Matlab is correct. My first issue is to make sure I'm implementing the sections in the right order. This is the output ...
1answer
92 views

### Is it possible to implement FIR band pass filter using two FIR band stop filters?

I am trying to filter a signal using a given FIR band stop filter. I have to implement a band pass filter. Assuming I want to get the signal between normalized cutoff frequencies [0.2,0.3] - can I ...
1answer
91 views

### Can I compute my IIR faster given limited possible input values?

I have an IIR routine in C++ I'm trying to speed up. Currently I'm using a DF2 implementation. Since my input signal will always be either 1.0 or -1.0 is it possible for me to optimize the algorithm, ...
1answer
1k views

### Calculate cut-off frequency of lowpass IIR-filter

Given a an IIR lowpass-filter in z-space: $H(z) = \frac{\sum_{i=0}^P b_{i} z^{-i}}{1+\sum_{j=1}^Q a_{j} z^{-j}}$ How to calculate it's 3dB cut-off frequency? I about evaluating it's fourier ...
1answer
397 views

### Noise Equivalent Bandwith of IIR and FIR Filters?

How do you calculate the noise equivalent bandwidth for an IIR or FIR filter?
1answer
3k views

### Gain of FIR/IIR filters

What are the formulas for signal and noise power gain of digital filters (FIR and IIR)? For a FIR, I've seen in Harris' windowing paper that the DC gain is the sum of the filter weights.  G = \...
1answer
547 views

### Very first values of y[n] in an IIR filter

I use a simple biquad IIR filter : ...
3answers
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### How can I prove stability of a biquad filter with non-zero initial conditions

Ok, so the situation is that I have a DFII biquad with some filter coefficients: \begin{align} w[n] &= x[n] - a_1*w[n-1] - a_2*w[n-2]\\ y[n] &= b_0*w[n] + b_1*w[n-1] + b_2*w[n-2] \end{align}...
2answers
1k views

### IIR issues when order is high

Thanks to all the people who helped me here, I finally achieved to implement a notch filter (*), with coefficients given by : http://www-users.cs.york.ac.uk/~fisher/mkfilter/trad.html When I do order=...
1answer
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### simplest Notch filter in the world

What do you think of this notch / band reject filter for a very very narrow band ? ...
1answer
254 views

### Scaling of a notch filter

Let's say I have an IIR filter that is a notch type with a peak at -20db. How do I modify the coefficients of the filter so that the peak is at -10 db for example? I know I can scale the denominator ...
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### Design of 10th order high pass filter using 2nd order biquads with Matlab and further substitution on to TI AIC3204

I am involved in designing a 10th order high pass filter with cutoff frequency 300Hz. My hardware AIC3204 has a 5 biquads of direct form I, 24bit coefficient so I have chosen the FDA (filter design ...
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### IIR: get magnitude and phase from coefficients

i'm trying to plot 1)the magnitude and 2)the phase response of an IIR eq with only its coefficients. i've found somewhere that one can find the magnitude response starting with the transfer function :...
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### interpolation of filter coefficients

i've read that it is possible to interpolate between two sets of filter coefficients (if they are close of course), but how to interpolate between two sets of coefficients which are of different ...
1answer
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### Choosing inverse Z-transform equation, given that $|a|<1$

Given that $|a|<1$, then which of those inverse-Z-transform equations are we to use? I am leaning towards the first because (as I understand it), $z$ is merely a complex number that is evaluated ...
1answer
232 views

### Group cascading IIR filters of different orders

Is it possible to make one IIR filter from various cascading IIR filters of different orders? I know it is possible to do it from filters of the same order, but what about filters with different ...
1answer
67 views

### Stability varying with order

I have been doing some research into modelling acoustic spaces, and (with help from this site) I've managed to take the frequency response of fibrous layer model, convert it to a reflection response ...
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### Designing an allpass IIR filter with arbitrary phase response

could you tell me step by step the algorithm to design an arbitrary phase response IIR allpass filter design ? I know Matlab uses a "brute force" algorithm to find an arbitrary group delay response ...
1answer
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### Complex Least Squares FIR filter design using Levinson' s algorithm

i'm trying to implement an arbitrary IIR filter design. I'm decomposing all the algorithm into smaller pieces that i can test. I currently am on the part where it designs a FIR filter from an ...
2answers
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### Least-squares digital IIR filter design (with arbitrary responses)

I'm studying the IIR filter design that is described in the book: Algorithms for the constrained design of digital filters with arbitrary phase and magnitude responses. You can get the code at page ...
3answers
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### Berchin's FDLS arbitrary filter design algorithm

I'm trying to use Berchin's FDLS methods (for those that don't know what it is, it's a way to design arbitrary magnitude and phase of an IIR Eq) I tried different things but neither gave me what i ...

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