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

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IIR design with Yule-walker method (or equivalent) in Python

I would like to design an IIR from an impulse response (find optimal coefficients), and I want to do it with Python. With Matlab we can use the Yule-Walker method (yulewalk function in Matlab signal ...
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1answer
59 views

How to find the impulse response of this system with complex roots?

I've been working trying to analyze a causal stable system. Hopefully a numeric example such as the one I am working on, and the problems I face during it could be useful to others. I have this ...
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2answers
57 views

How to compare many bandpass filters (for their signal propogation delay)?

Let's say we have an audio signal sampled at 96 kHz, and we want to compare several bandpass filters to find the one with the lowest rectangular-envelope-propagation-delay (see graph below). The band ...
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1answer
37 views

How does an IIR system affect magnitude and phase of a sinusoidal signal

Consider an IIR system with impulse response $h[n]=\left( \frac{1}{\sqrt{3}} \right)^n u[n]$. If I apply $x[n]=\cos(n \frac{\pi}{2} + \varphi)$ at the input, how can I determine the change in ...
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0answers
43 views

What happens to a rectangular signal filtered with an Exponential Smoothing filter?

Filter given; $y[n] = \alpha x[n] + (1-\alpha) y[n-1]$. In principle all samples before the present one influence What happens to a rect-signal? How would it look like?
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2answers
58 views

How can I convert a step response that is described by the sum of two exponents to an IIR filter analytically?

If a system has the following step response: $$\begin{align} y(t) &= 1 - \Big(A e^{−t/T_1} + (1-A) e^{−t/T_2}\Big) \\ &= 1 - A e^{−t/T_1} - (1-A) e^{−t/T_2} \\ \end{align}$$ and I know the ...
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4answers
242 views

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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2answers
55 views

Calculating a NRR of an IIR

I'd like to calculate the Noise Reduction Ratio of a system. The system I have is $$ H(z)= \frac{z^{-5}}{1-0.1z^-1}.$$ For FIR Filters this can easily done by $$ \sum h[n].$$ For an IIR Filter this ...
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1answer
122 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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1answer
45 views

Simple question about Sinc()

Suppose I use the ideal lowpass filter eq to attempt creating a IIR filter using it : $$ h[n] = \frac{\sin(\omega_c \, n)}{\pi \, n}, \qquad -\infty < n < \infty $$ Obviously, I can't really (...
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6answers
187 views

Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter

I would like to approximate a moving average filter with an IIR filter of much lower order than the tap-length of the moving average filter. Optimality shall refer to the $L_2$ norm of the impulse ...
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1answer
41 views

Design digital filter with model order reduction (MOR) and other methods

IIR filters can be designed using different methods,such as: Analog Prototyping Direct Design Generalized Butterworth Design Parametric Modeling https://www.mathworks.com/help/signal/ug/iir-filter-...
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1answer
34 views

How would I calculate the state-variables of digital biquad filter (direct form II transposed) at steady-state?

I'm attempting to calculate the steady-state state variables for a digital biquad filter direct form II (transposed). Illustration For example, let assume the filter is fed a constant input of ...
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2answers
37 views

How do you initialize the output of a second-order-section filter?

I've got a 4 stage second-order-section filter. When I turn this filter on, it assumes it is starting from zero and takes forever to converge on the actual signal. For example, let's say I have a ...
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1answer
50 views

Question of Digital filter; stability and order

Below 1~6 are my question. Shortcomings of IIR filter. Mean of unstable. (Things that will happen when system is unstable.) How to select the best order(n). What happens when I raise order too much. ...
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1answer
121 views

IIR filter design fitting step response

I have access to the step response of a system and I want to find its poles and zeros without knowing the order of the system. Consider an example of a step response of the system shown in the ...
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1answer
114 views

Do you recognize this filter?

I'm trying to decipher the uncommented source code of SoundBox which is a little music tracker written in javascript. There is an included synthesizer, which applies a filter on the output samples. I'...
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0answers
41 views

IIR (non linear phase) filters

As you know, a nonlinear phase filter (in passband), distorts the frequency contents of passband region of signal. In general, Why do we use such filters in the case they cause distortion in the ...
2
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1answer
50 views

Find a stable transfer function $G(z)$ such that $|G(z)| = |H(z)|$

Consider the following causal IIR transfer function: $$ H(z) = \frac{2z^3 - 4z^2 + 9}{(z-3)(z^2+z+0.5)} $$ Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...
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1answer
63 views

Applying multiple IIR and FIR filters at once

I would like to appy multiple filters to a signal at once. Let's assume I got two frequency bands I want to extract. I compute a Butterworth Filter for 300-500Hz and one for 700-800Hz. I would like to ...
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2answers
91 views

How do you program a completely transparent crossover?

Or, if that's too broad, what is/are the most popular algorithms? Background: I have no formal DSP training but much informal tinkering. I am trying to program a crossover for an audio effect. ...
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1answer
93 views

Z-domain transfer function to difference equation

So I have a transfer function $ H(Z) = \frac{Y(z)}{X(z)} = \frac{1 + z^{-1}}{2(1-z^{-1})}$. I need to write the difference equation of this transfer function so I can implement the filter in terms of ...
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0answers
71 views

Estimating frequency when there's little isolation between signal and noise frequencies

Say I have a signal which is guaranteed to have a frequency between 110-120 Hz but is corrupted by interference signals that're very close to this frequency range. For example, let the interference ...
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0answers
197 views

All pass filter design for group delay compensation

I've designed an IIR bandpass elliptic filter in Scilab with the following parameters. Sampling Frequency = 25000 Hz Lower cutoff frequency = 100 Hz Upper cutoff frequency = 150 Hz Pass band ripple = ...
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0answers
115 views

IIR filter group delay

I've designed an IIR bandpass elliptic filter in Scilab with the following parameters. Sampling Frequency = 25000 Hz Lower cutoff frequency = 100 Hz Upper cutoff frequency = 150 Hz Pass band ...
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1answer
139 views

Stability condition for an iir filter

I have been out of touch with DSP for a while. I was trying to refresh my basics and ended up with this doubt on IIR filter stability condition. I understood that for an iir filter to be stable, the ...
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1answer
26 views

What does “ripple limit cutoff” mean?

So I'm reading the datasheet for MAX98357A. It's an audio amplifier that receives digital signal using I²S bus and has integrated digital low-pass filters of the IIR and FIR types. In addition to ...
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3answers
110 views

Distinguishing FIR and IIR from difference equation

Find the transfer function of the difference equation $$y_n = x_n + 1.2y_{n-1}$$ I fail to understand how one can distinguish between an FIR filter and an IIR filter by looking at the equation given ...
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0answers
95 views

Confusion over impulse invariance, matched z-transform, and bilinear transformation methods

In the DSP course that I am taking in my university as an undergraduate student, three methods are presented for mapping analog filters to digital filters - namely, impulse invariance, matched z-...
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1answer
101 views

Real-time modulated IIR filter

I've been learning to implement an IIR filter for a synthesizer project. It is now more or less stable when the parameters are constant, but ultimately I want the parameters to be arbitrarily ...
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0answers
51 views

How do I convert a two-pole two-zero transfer function from the s-domain to the z-domain?

I'm trying to convert the following IIR transfer function from the s-domain to the z-domain: $$ H(s) = \displaystyle\frac{\frac{s^2}{\omega_z^2} + 2\zeta_z\frac s\omega_z + 1}{\frac{s^2}{\omega_p^2} + ...
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2answers
61 views

How many coefficient sections should I select when designing filters with MATLAB FDATOOL?

I attach a picture about the results of a filter design in Matlab. It says that it has 12 sections. One section contains the coefficients of the transfer function. If I'm implementing this filter in ...
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1answer
68 views

Can a Goertzel filter response be mapped to a Direct Form II Biquad IIR Filter

I am looking at the structure of the Goertzel Filter, and it seems like I can map its coefficients to the standard implementation of the CMSIS DSP Biquad Cascade IIR Filter. Is this possible or should ...
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1answer
67 views

Is this sampling frequency right?

I designed a Butterworth second order bandstop filter on Matlab with the following parameters: Notch frequency: 150 Hz (the frequency I want to remove) Bandwidth = 8 Hz, that is Fc1=146 Hz Fc2=154 ...
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21 views

should block diagrams in Direct Form 1/2 contain empty branches to fit structure?

When creating a block diagram in a well-recognized structure (Direct Forms 1&2 in particular), does one remove branches where the coefficient is 0? This picture includes a coefficient of $b_1=0....
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2answers
58 views

Can I combine an IIR (an EWMA) with a maximum?

I'd like to have a exponentially weighted moving average (EWMA) which is raised to the value of the input signal whenever this is higher than the filter output. This taking of the maximum shall take ...
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4answers
69 views

Can I use IIR or FIR to get a sliding mean?

My output signal shall be computed by (meta code): o = 0 # or some arbitrary initial value for i in input: o = (o * 99 + i) / 100 print o I call this a "...
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1answer
28 views

historical context of impulse response-convolution

Hi All: I have zero background on the history of LTI systems so I was wondering when the concept of LTI and the fact that an LTI signal can be be completely described by its impulse response came ...
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1answer
166 views

Design Lowpass Filter With -7.5 dB/Octave Rolloff

I am working on a project that needs a lowpass filter with a -7.5 dB/Octave rolloff. This is somewhere between the rolloff of a one-pole and two-pole filter, so I wanted to ask what some standard ...
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1answer
220 views

Get difference equation of a filter from MATLAB transfer function coefficients

I need to get the difference equation of a specific elliptic filter. I calculated the transfer function coefficients in MATLAB with: ...
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2answers
483 views

Matlab `filtfilt` provides excessive transient

I observed that filtfilt suffers from an undesired behavior when I provide IIR bandpass filters having steep transition bands. Specifically, the output signal exhibits excessive transient response; ...
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0answers
68 views

How to transform a Fractional Order Laplace Transfer Function into a digital filter?

I'm working with loudspeaker impedance analysis. Electrical behavior of loudspeakers can be modeled with RLC networks. But real loudspeakers have components, that exhibit some non-linear and frequency ...
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0answers
24 views

why is that filter FIR not IIR [duplicate]

how is this filter an fir filter should not it be an iir because of the y[n-1 ] term
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0answers
30 views

Which IIR form has lowest round-off noise?

We are making some audio effects using IIR, and seeking ways to optimize its round-off noise. After searched some materials, most of them tells transposed form II has lowest round-off noise, and many ...
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1answer
31 views

Incorrect Butterworth filter outcome using Rational Transfer Funcion

I've been playing with Second-Order Butterworth high-pass filter for a while. I've calculated the coefficients using Matlab function and I wanted to use them to filter simple sine wave generated by ...
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2answers
98 views

Filtering without using any transforms

A composite signal is defined as $$x(t) = \sin(2\pi 10t) + \sin(2\pi 40t) + \sin(2\pi 60t) + \sin(2\pi 50t)$$ Separate the four frequencies without using any of the transform techniques.
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2answers
94 views

Stable digital filter with leading zeroes

I'm looking construct a stable pole-only filter where the feedback coefficients start with a block of zeroes, i.e. \begin{align} a_0 &= 1\\ a_i &= 0, \textrm{ for}\ 1 \le i \lt k\\ a_i &\...
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41 views

How to find maximum gain for second order recursive filter

Suppose I have the following filter: \begin{equation} \ y[n] + a_1 y[n-1] + a_2 y[n-2] = x[n] \end{equation} with complex poles $p$ and $p^*$ so $ a_1^2-4a_2<0 $. This gives: \begin{equation} \ p,p^...
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1answer
73 views

Is initializing a digital filter's output with no “momentum” a non-trivial task?

I'm working on implementing a filter with a very slow step response. This filter is implemented as a cascaded second-order-section filter (transposed direct form 2). I'm using the output of this ...
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3answers
530 views

Is there a common name for the first order IIR averaging filter?

Is there a term to describe this IIR averaging/smoothing filter? $ y[n] = \alpha x[n] + (1 - \alpha) y[n - 1] $