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

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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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0answers
31 views

Reduced order models of original filter [closed]

For converts any causal LTI digital filter into state-space form,there is the following procedure : 1-The general causal IIR filter $$ y[n] = b_0 u[n] + b_1 u[n-1]+... + b_N u[n-N]- a_1 y[n-1] - ...
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6answers
121 views

Optimal n-th order IIR approximation to 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
31 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
31 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
33 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
43 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
93 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
107 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
34 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
47 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
47 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
73 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
49 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
67 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
95 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
79 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
60 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
25 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
86 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
69 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
88 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
40 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
56 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
59 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
66 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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0answers
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
53 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
66 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
140 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
186 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
380 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
58 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
27 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
85 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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0answers
38 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
62 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
501 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] $
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1answer
233 views

Complex IIR to Real IIR

I have created an IIR design algorithm that generates complex coefficients (there is no symmetry in the poles and zeros). However, the IIRs will be used to filter a real signal. Is there a closed form ...
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1answer
62 views

Does this equation have a closed form

I am on chapter 6 of "Understanding digital signal processing", 3rd Edition by Richard G. Lyons. But I am stuck on question 6.15. Here is the network in question. I wrote down the difference ...
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1answer
36 views

Audio signal series' beginning points(about 50) distort after a bandpass filter

I am using some bandpass filters to detect a certain freq of the sampled audio series in noisy environment. Everything is OK except this: I found that for many bandpass filters I tried(butterworth, ...
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1answer
120 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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2answers
319 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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1answer
382 views

Whats is the difference between FIR/IIR filters and Chebyshev/Butterworth filters

I am new to Signal Processing. From my understanding -- FIR/IIR just refer to the placement of poles and zeros in the z-domain helping us achieve convolution, if FIR and ??? in IIR. Chebyshev and ...
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1answer
51 views

Generic response of an IIR filter from its transfer function

How can I derive the general response of an IIR filter from its transfer function? I know that: $$H(z)=\frac{1}{1+\sum\limits_{m=1}^N{a_m z^{-m}}}$$ Thus: $$Y(z)=X(z)H(z)=\frac{X(z)}{1+\sum\limits_{...
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2answers
77 views

Typical filter orders

I am on my first DSP project where I want to implement lowpass/highpass filters for ECG application. I have started from MATLAB to give me orders and coefficients for my desired specs. I prefer to go ...