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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impulse response of a system from its step response;confusion

If the step response of a system is given as $$c(t)=(10e^{-5t}-2e^{-10t}+1)u(t)$$ then its impulse response is _______? My Approach: we know: $$h(t)= \frac {d}{dt} c(t)$$ Process(1): $$h(t)= \{ ...
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Difference between $H(\omega)$ and $H(j\omega)$ [duplicate]

What is the difference between $H(\omega)$ and $H(j\omega)$, in terms of impulse response. And if so, when do I have to use one or another.
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118 views

Impulse Invariant mapping [closed]

Can someone help me to better understand the Impulse Invariant mapping? : $$h[n] = T \cdot h(nT)$$ I don't understand why the discrete-time impulse response, $h[n]$, is taken from the sampled ...
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Calculating output of a system given impulse response and input

I'm trying to calculate the output given an impulse response $h(t)=e^{-t}u(t)$ and input $x(t)=\cos(2\pi t)$. I know I need to use the convolution but given that cosine is periodic, I don't see how ...
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Proof of $E[y(n)]=E[x(n)] \, \sum h(k)$

If $h(n)$ is the impulse response of the discrete LTI system, $x(n)$ is the white noise process with variance $\sigma_x^2$ and $y(n)$ is the output, prove that $$\mu_y = \mu_x \, \sum_{k=0}^\...
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How to obtain impulse response from a plot of magnitude of frequency response?

I have a plot of a magnitude response of a frequency response, how can I get the impulse response using only this plot and nothing else?
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Impulse Response to LTI

I am new to DSP, and I am self-studying using mostly Proakis. I have a question. There are some examples in the text where you will be given the impulse response of an LTI system, and then asked to ...
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Applying the inverse FFT to even out a room's sound - What is the more efficient algorithm?

I have a way (the standard way) to correct for my room's acoustics, but I'm wondering if there's a more efficient algorithm, something that doesn't involve going to the frequency domain maybe? I ...
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Solving for impulse response h[n] given input-output pairs

This is a homework problem that I've worked on and I want to confirm some of my reasoning. I'm given two sets of input-output pairs of a particular system, $S$, that we know is linear time-invariant ...
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determine the impulse response of given second order difference equation

$y[n]-3y[n-1]-4y[n-2]=x[n]$ i solved it as follows : 1.first calculated natural-response(ZIR i.e,zero input response) by using characteristic equation it came out as $y_n[n]=[c_1(-1)^{n}+c_2(4)^...
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Is system $h(t) = u(t)-u(t-1)$ LTI or not?

$$y(t) = \int_{0}^{\infty} x(\tau)h(t-\tau) \ \mathrm{d}\tau$$ where $h(t) = u(t)-u(t-1)$. I have some problem with understanding whether system LTI or LTV just looking the impulse response of the ...
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759 views

Impulse response function from pole-zero graph

I know that that the poles of this system are: $s_1 = -1 + 2j$ and $s_2 = -1 - 2j$. I think to solve this problem I would need to find the laplace of this plot, with the formula: $$ W(s) = \frac{\rm ...
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What is the product of Dirac Delta function and $t$? [closed]

$t\cdot \delta (t)$ Does it equal to zero? If so, how can we prove it?
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657 views

When can the impulse response become zero?

The article Efficient Use Of Sparse Adaptive Filters (Proc. Asilomar Conference, Khong et al., 2006) introduces adaptive filters for the estimation of channels or systems having a sparse impulse ...
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Room Impulse Response Inverse Problem

This article here talks about a room impulse response generator which takes the source and destination coordinates, sound speed, sampling rate, room dimension and wall reflection coefficients as input ...
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Is the system $h(t)=\frac{u(t)}{t+1}$ time-variant or time-invariant?

Following this answer , I tried like this $$h(t)=\frac{u(t)}{t+1}$$ where $u(t)$ is unit step function. I can write the input-output relation like this: \begin{align} y(t)&=\int_{-\infty}^{+\...
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Interpretation of system response to unit impulse

I want to understand the meaning of unit impulse response when time flows. An example is given below: In the example the left signal depicts a $\delta[n]$ function value of which is $1$ only at $n=0$....
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808 views

FIR filter reverse engineering from step response

I am working on a reverse engineering problem - I am trying to reconstruct a filter. I have: The step response of the system. (I could calculate the impulse response by derivating) I know: The ...
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Is this system time invariant?

I've been working at this problem for a while now, and can't seem to come to a solid conclusion - is this system time invariant? $y(t) = \int_{-\infty}^{t} e^{-9(t-\tau)} x(\tau)d\tau $ My reasoning ...
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1answer
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How do I calculate the step response of a discrete-time system?

I am given the impulse response $$h[n]=2\left (\frac{1}{2} \right )^n\sigma [n]-\delta [n]$$ where $\sigma$ is the unit step function and $\delta$ is the unit impulse function. I know that $$a[n]=\...
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1answer
4k views

Impulse response from difference equation without partial fractions

I have a system with input $x[n]$ and output $y[n]$, described by the difference equation $$y[n] - 0.3y[n-1] + 0.1 y[n-2] = 3x[n] - x[n -1]$$ and I am trying to find the frequency and impulse ...
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605 views

Impulse response of a linear time-variant system

Is the impulse response of a LINEAR TIME-VARIANT system unique? I know that it's unique for the L.T.I case!!! Advance thanks for the HELP....
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308 views

Finding audio signal time delay: cross-correlation vs. impulse response?

I need to find a time delay between the two audio signals, one comming from one set of speakers, and the other being the source signal that is initialy sent to speakers. I send some noise through ...
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Find the impulse response of an LTI system?

why there is a 3/2 in the (b) problem? Does the impulse response even exist?
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3answers
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Multiplication of two impulse function $\delta(t)\cdot \delta(t)=?$

If a impulse function is mulplied with a function $f(x)$ then the formula will be apply $$f(x)\delta(x-a)=f(a)\delta(x-a)$$ so from this formula mulplication of two impulse function will be $$\...
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obtaning discrete-time system impulse response $h[n]$ from step response $s[n]$ [duplicate]

The discrete-time system of figure below a step response: $$s[n] = \left[ 5 - 4 \left( \frac{4}{5} \right)^n \right] u[n]$$ Find the impulse response of the system and verify it from the system ...
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176 views

Determine the Unit Impulse Response of ARMA Filter for 8 First Indices [closed]

I have this problem, I've checked for almost 3 hours in books and internet for the unit impulse response for n = 0 : 7 but nothing. I've benn working on how to get h[t] but I end up on a dead end at:...
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1answer
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Exponential decaying step response in LTI System

I'm attempting to better understand the relationship between step responses, impulse responses, and convolutions. Say that I have a system where if I apply a constant input, my output decays from a ...
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899 views

Does the impulse response of a system have any physical meaning?

In other words, what does the impulse response tell us about the characteristics of the system? For simplicity, let's assume we deconvolve a discrete output and a discrete input to obtain an impulse ...
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Given the input and the output, how to determine the impulse response?

I would like to find the impulse response, $h[n]$, of an LTI system given the input $$x[n] = [1,-3,2]$$ and the output $$y[n] = [1,-1,-4,4]$$ I know that $y[t]=x[t]*h[t]$, but I am having hard ...
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498 views

How to evaluate an impulse/response model in MATLAB

This is my first experience in signal processing, so don't treat me badly :) However, I have estimated an impulse-response model using the MATLAB System Identification toolbox. The output, validated ...
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2answers
616 views

Room impulse response 'noise'

I am working on getting room impulse response(RIR) and the first order reflections of a room. For now I am stuck at getting proper RIR. I followed Joseph's work and implemented on my own. My setup ...
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1answer
264 views

What is the spectrogram of an impulse response used for?

I saw that in acoustics an estimated impulse response of a room can be transformed using STFT/wavelets to a spectrogram as an analysis tool. However, I did not understand how the spectrogram is ...
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1answer
247 views

Proper method for generating Channel coefficients in MATLAB

I am trying to estimate the coefficients of a Moving average model using popular estimation method such as Least Squares (LS). For educational purposes, I am trying to see if LS can work well when the ...
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1answer
586 views

What is the time unit of the converted Channel Impulse Response?

I don't have a lot of background on wireless communication but as far as I understand, applying IFFT on Channel Frequency Response (CFR) would transform the data into time domain Channel Impulse ...
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1answer
131 views

How to convert multi-band Energy Time Curve (ETC) to Impulse Response (IR)?

I am running my own sound simulator. Now I have obtained the Energy Time Curve (ETC, expressed by energy) by physical simulation, and they are stored in 8 discrete frequency bands (because decay of ...
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1answer
630 views

Why does raised cosine pulse through Butterworth filter introduce (significant) ISI?

Here is a simple MATLAB experiment: ...
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1answer
340 views

Can I assume system is LTI when given by DTFT of impulse response

I'm having hard time to grasp it probably because i don't fully understand it. I understand that when a system is given by $h(t)$ (in general $h(t-\tau)$) i can assume that it is a LTI system. So i ...
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2answers
782 views

LTI system with Laplace transform

Given the input $$x(t)=u(t)$$ and the corresponding output signal measured as $$y(t)= 2 e^{-3t} u(t)$$ determine the impulse response $h(t)$. This what have done so far: $$ h(t)= \mathscr{L}^{-1} \...
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Find transfer function given impulse

I am given the following discrete time transfer function : $$G_d(z^{-1})=z^{-d}\frac{b_0+b_1z^{-1}}{1+a_1z^{-1}}$$ which has the following impulse response $$g_d[n]=\{0,1,-0.1,-0.05,...\}$$ How can I ...
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Time-varying “impulse response”

According to many references [1,2], the time-varying "impulse response" can compute wireless channel output $y(t)$ at time $t$ using the following expression: $$ y(t) = \int h(\tau, t) x(t - \tau) d\...
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1answer
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Determine impulse response given input and output: which ROC?

Let's suppose I have to find the impulse response of a discrete time LTI system given a specified input and its output through the system. I think I'm going to get the $\mathcal Z$-transform of input-...
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2answers
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Calculating the inverse filter for the (exponential) sine sweep Method

I am currently working on my Bachelor-Thesis about Real-Time convolution and Impulse Response Measurements. After reading different papers about the (exponential)sine sweep method I didn't find an ...
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1answer
362 views

Two-sided impulse response and its inverse in real life

Dear StackExchange gurus, I would like to pose this question from a practical standpoint rather than a theoretical one, although perhaps some context in the latter might come useful. Real-life ...
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1answer
290 views

Impulse response of a continuous system sampled with zero-order hold

I've a continuous system $$F(s) = \frac{K}{Ts+1}.$$ I sample it with zero-order hold with sampling period $T_s$. The discrete system transfer function is $$ \begin{aligned} G(z) &= % \frac{z-1}{z}...
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2answers
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Why does python's scipy.signal.dimpulse introduce delay in impulse response?

Consider a simple linear, time invariant system of the form: $y_k = cy_{k-1} + (1-c)x_k$ The impulse response of this system can be computed by either dimpulse or by applying lfilter to a vector ...
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How do I show that the total system has the impulse response $h[n] = aδ[n] + bδ [n - 1] + cδ [n - 2]$ and determine the constants a,b and c?

Given is the illustrated circuit diagram of a linear, time-invariant, time-discrete system: How do I show that the total system has the impulse response $h[n] = aδ[n] + bδ [n - 1] + cδ [n - 2]$ and ...
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What is impulse response (or equivalently the frequency response) of the channel ?

Please allow me to ask this silly question. I googled, but I still not clear about this. What is impulse response of a channel (wireless communication channel). Someone can explain me with a lot of ...
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1answer
322 views

Experimental determination of impulse response function

I am doing an experiment (I major in physics, not familiar with signal processing so there may be some naive mistakes, please be kind) which requires acting arbitrary pulses on a system. I use an AWG ...
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144 views

Impulse response of LTI Systems

I am trying to solve the attached question. Please I would appreciate if some one can check my approach and tell me if I am correct and how can I proceed to find h0(t) [![enter image description here]...

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