Questions tagged [impulse-response]

The impulse response of a dynamic system is its output when presented with a brief input signal, called an impulse.

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Does the impulse response of every stable system have finite energy?

I need to show that the impulse response of every stable system has finite energy. I have trouble solving this problem. Since impulse input signal is unbounded, I can't apply BIBO stability of system ...
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Deconvolution with unknown impulse response

This is not a duplicate of Filter secondary bounces of a pulse signal because in that question, a convolution model is finally not appropriate, whereas here, the question is about convolution. Given ...
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Filter secondary bounces of a pulse signal

I have a single "pulse" signal (looks like a gaussian but it is not exactly), followed by several bounces, with a constant period, that probably come from the electronics used (I don't have ...
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Non-uniformly partitioned convolution in real time

I am implementing a real-time convolution reverb. I currently have a working implementation, doing frequency-domain multiplication after FFT, using uniformly partitioned block sizes. This answer on ...
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How to find impulse response for the given system?

How can I find the impulse response for the following system in time domain? I actually would like to find my mistake in my attempt. Below is what I have tried according to the answer given for this ...
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How to design a system that stretches input by factor of 2?

In general, How do we design a system that takes input x(t) and outputs x(t/2)? I know that if system outputs x(t/2) then the frequency domain of output signal has the form X(2f). But what should be ...
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Impulse response synthesis in the frequency domain

Background - Create context I am trying to synthesise some impulse responses to simulate an active noise control system. I have already formulated the problem in the frequency domain so now I want to ...
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The discrete-time impulse response of an IIR filter

Suppose you begin with the following model of a discrete impulse response: $$h[n] = \begin{cases} \displaystyle\sum_{k=1}^K \alpha_k p_k^n & n \ge 0 \\ 0 & n < 0 \end{cases}$$ i.e. a linear ...
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What duration of a white noise burst is required for it to be "white" at a given frequency or frequency range?

I am running white noise bursts (with very short ramps on/off to prevent discontinuities) through underdamped resonant bandpasses which are tuned to any given $f_0$ and an underdamped $Q$. Continuous ...
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What is the expected amplitude of the flat frequency response of a Kronecker delta function? Does sample rate affect it?

I was instructed here: In the sampled-time domain a Kronecker delta, $\delta(n)$, has a perfectly flat spectrum. If you look at a table of discrete-time Fourier transform pairs, this is at the top ...
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What happens to the frequency response as a single sample Kronecker delta impulse widens into a square pulse, and then into two distinct steps?

1) Kronecker I was instructed here that a single sample Kronecker delta unit impulse function (goes from 0 to $A$ to 0 again in single sample) has a white noise type frequency response - all ...
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How to find time-varying impulse responses?

Given is a system that can be described as $y(t) = x(t)\cdot \sigma(t)$ with $\sigma(t) = \left\{\begin{array}{ll} 1, & t \geq 0 \\ 0, & t<0\end{array}\right. .$ The output of a ...
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How can I apply a filter to remove reverberation with python?

I am developing an algorithm that automates the processing of audio files for the assembly of datasets of machine learning models. Among the steps to be followed for the processing of the files is to ...
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Impulse response and amplitude-frequency characteristic of a communication channel

The task is to implement communication system for transmission of 32 multiplexed signals through communication channel represented by copper cable whose frequency characteristic is given by: $$H(f) = ...
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Characteristics of linear systems in the time and frequency domain

Why is the output signal obtained through frequency response different from the other two. ...
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Understand basic Impulse Response from Impulse, can you help me visualizing it?

I was looking at this graph from The Scientist and Engineer's Guide to Digital Signal Processing, copyright Β©1997-1998 by Steven W. Smith: where basically it shows how differnt representations can ...
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Analysis of impulse response in downsampling problem

Hey everyone, I'm stuck on this problem and I've got an exam in a few days. I think the filter H is used here so as to avoid aliasing artifacts, and afterwards went on to the second question. I've got ...
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Applying Lowpass filter on a signal in time domain gives ringing artifacts - how to get rid of them

EDITED AND UPDATED: My signal is an impulse response. In the following figure: The frequency spectrum of the impulse response (original signal) is shown by blue line. The original signal is ...
Tanmayee Pathre's user avatar
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Algorithm to "serialize" impulse responses

New user to dsp.stackexchange here. I'd like to know what's a quick and effective way to take 2 impulse responses and create one that's equivalent to both of these "in series" for audio ...
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On FFT, interpolating signal vs extending signal in time

When we interpolate, then FFT the output will have more bins. When we extend the signal in time, Then FFT output will have more bins too but: Interpolation increases max bin frequency but time ...
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Impulse response aquired by ifft seems to require circshift

On the system below: I have found W by inputing 20-1000 frequency and found amplitude and phase for each frequency. I've tested for minimum phase and none min S. But the answer is not logical for me. ...
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How do I obtain narrowband reverberation times in the bass range to detect room modes?

I calculate my impulse response according to this principle. Calculating the inverse filter for the (exponential) sine sweep Method. With the obtained impulse response I calculate my reverberation ...
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Equipment to test my theory on time varying systems

How can I make a linearly time varying system to test my theory? Can I ask for a PID microcontroller available from my university such that $K$ is gradually increased from 0 to $c$
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How to get an impulse response of a MIMO system?

So I have data vectors from a MIMO system and I wish to see the impulse response Any idea how I can proceed with this?
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Sine as input to an LTI system

Everywhere in theory (books , online) there is this statement "For sinusoidal inputs, any LTI has a sinusoidal output with the gain of $|H(s)|$, the same frequency, and a phase shift equal to $\...
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How to obtain an impulse response from an exponential sine sweep (23kHz/50kHz)

I am currently working on my master thesis and have so far generated a broadband ESS to obtain frequency response and impulse response. To generate the ESS as an excitation signal I use the following ...
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How can I find the impulse responce of this ODE?

$$ \frac{𝑑^2𝑦(𝑑)}{𝑑𝑑^2} + 2\frac{𝑑𝑦(𝑑)}{𝑑𝑑}+ 1 = 2π‘₯̈(𝑑)$$ a. Write Matlab source code evaluate the impulse response of the system. b. Write Matlab source code to evaluate and plot ...
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Why does convolution give the output of a passing a signal through a filter?

I have a rudimentary understanding of Convolution, the Convolution Theorem and why the output z(t) of an LTI system can be found using the convolution of input signal x(t) and the impulse response h(t)...
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Modeling an Acoustic Reflection from a Wall - a Paradox?

I am trying to simulate the reflection of a sound ray, that goes from a sound source, bounces off a wall, and is received by a microphone. The wall has a an absorption coefficient, and a specular ...
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upsample impulse response

I have a system and I know its impulse response $h$, this impulse response was recorded at $f_s = 48000 \texttt{Hz}$, now I can use Matlab to get the system output to an arbitrary signal ($x$) by ...
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Exponential/Logarithmic Sine Sweep - Inverse Filter Amplitude Correction

I am implementing the exponential/logarithmic sine sweep approach to impulse response measurement (as presented by Farina - http://pcfarina.eng.unipr.it/Public/Papers/134-AES00.PDF). My query is ...
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How can Haar basis be written as the impulse response of an LTI system?

Haar wavelets are defined as: $$\phi_{0,0}(t) = \begin{cases} 1, & \text{ for } 0<t< 1/2\\ -1, & \text{ for } 1/2<t<1 \\ 0, & \text{ ...
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Getting different results when fourier transforming in python vs mathematica?

I am interested in troubleshooting why I get a very different answer when doing fourier transforms of my data in Mathematica vs Python. The version in Mathematica is well behaved, yet all versions of ...
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Controllability matrix is full rank identity matrix

What does it mean, when my system has controllability matrix that is full rank and identity matrix? Having full rank means that the system is controllable, but does the Identity feature of my ...
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Proof for LTI Systems [duplicate]

Suppose we have a system $S$.If I know the impulse response $h(t)$ I can predict the output for any input $x(t)$ if a system is linear and time invariant.However how do we prove that statement?
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Impulse response of linear time-varying system

I am confused about linear time-varying system. For a time varying system, the output is given by \begin{align} y(t)=\int x(\tau) h_{\tau}(t) d\tau, \end{align} where $ h_{\tau}(t)$ is the output of ...
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Construction of Room Impulse Response - Short-Time-Fourier-Transform and Inverse-STFT - Matlab and NWaves (C#) Implementation

Background: I am working on a Unity Project (C#) and implementing a Room Impulse Response synthesis. I do ray tracing to create energy histogram for different bands. With these histograms it is ...
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LLTV Systems breakdown(2)

In this question I proved that for a linear linearly time varying system $S$ such that if $t_{2} = t_{1}+t_{0}$ then $h(t,t_{2}) = h(t,t_{1})+h(t,t_{0})\rightarrow$ $h(t,t_{0}) = g(t_{0})h(t) $ where $...
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Impulse response of a discrete time cascading system

My lecturer has decided that in order to pass our signal analysis class, we have to give a presentation on the blackboard in front of the entire class, so its kinda critical that i get this right. (...
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LLTV Systems linearity breakdown

Suppose we have a linear linearly time varying system $S$ such that the output depends on the input + the time at which the system becomes excited so $S(t,t_{0}) \rightarrow g(t_{0})S(t)$ and it is ...
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How to find the first and list point of an impulse in a RIR?

I'm looking for a simple algorithm where given a RIR sample file I can find the beginning of the impulse and the last point of the tail. If possible, would love to implement it in python.
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Linear phase with a non-integer delay?

Let's say you are given a frequency domain specification for a filter design. As a simple example, let's use an ideal (brickwall) LPF. Now the impulse response of an ideal LPF is a $\operatorname{sinc}...
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time-domain response to continous linear chirp

I am investigating the time-domain response of electromagnetic waves. The input signals are a chirp with linear frequency sweep 2.5 Hz->4.5 Hz -> 2.5 Hz and another signal which is abruptly ...
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Get the inverse transfer function from the measured response

What is a numerically stable way to obtain the inverse transfer function from a measured response? I have a system that shows a low-pass behavior. I would like to increase the bandwidth by some form ...
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Get the room impulse response by using inverse filter of sin sweep signal

I want to simulate the process of obtaining the impulse response of a room. What I did: Generate a room impulse response sequence by using the python module: ...
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Integral of product of two shifted Dirac impulses

In this question the multiplication of two impulse functions is discussed However, what if I have two shifted impulses say: $z(t) = \delta(t-\tau)\cdot \delta(t-\beta)$ Now if I want to integrate $z(t)...
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Impulse response of an LTI system

I want to find the impulse response of the linear time invariant system given by $y''(t)+4y'(t)+3y(t)=x'(t)+2x(t)$ using time domain analysis. As solved in the textbook "Continuous and Discrete ...
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A response of an unstable system

I'm dealing with the following question : The system realizes an accumulator, therefore its impulse response (h[n]) is just the unit step function multiplied by some factor . In the next subsections ...
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Causality of an estimated filter

Assume $\tilde{h}(f)$ is a filter estimated by an algorithm for (room) impulse response estimation working in the frequency domain. Is there a way to assert if such filter is causal? Specifically, ...
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LTI system: can I infer the system is causal based only on the transfer function without the ROC?

Suppose we have an linear time-invariant (LTI) system which acts on discrete signals. Suppose someone tells us the transfer function is: $$H(z) = \frac{1}{z-2},$$ but doesn't specify the ROC. Now the ...
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