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 Invariant method for digital filter design
One of the known methods for discretizing analog filters is impulse response invariant. We get the impulse response in time domain, discretize it and then get the Z transform.
What I am trying to ...
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1answer
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Drawing conclusions from impulse response of a discrete LTI system
I have an impulse response of an LTI system which is
h(n)= n*u(n)-u(n-2) where n=[0,3] (1)
Now regarding the stability and causality of this system, i've drawn the ...
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1answer
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Kernel vs impulse response: what's the difference? [duplicate]
I am reading The Scientist and Engineer's Guide to
Digital Signal Processing by S.W. Smith. In Chapter 9: Applications of the DFT in the 3rd paragraph he writes "kernel (impulse response)"
...
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49 views
Can time-invariance be determined from a given a transfer function?
I've the following function.
$$ G(z) = 2 + \frac{-1+5z^{-1}}{(1-0.5z^{-1})(1-z^{-1})}$$
Calculating it's inverse using $\mathcal Z$-Transform, I get the following function:
$$g[n] = 2\delta[n] + 8u[n] ...
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1answer
37 views
Impulse response from frequency response in Matlab
I am trying to design equalization filter and therefore I want to define my own amplitude and phase response and then to obtain the impulse response of the filter. I thought that the output of the ...
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1answer
52 views
finding onset of an impulse signal, basics?
New to signal processing, but making good progress, I think.
I have a series of (many) impulses I generated, which will be used as impulse responses to model our church's acoustics, in this time of ...
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2answers
140 views
Behaviour of System by Impulse Response
In a book by Alan Oppenheim, it is given that for a LTI system, its characteristics are completely determined by its impulse response. But if impulse response of a system is basically an input output ...
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1answer
33 views
How to get Step Response from an Impulse Response in Simulink?
Im sorry if it seems like a trivial question but I am confused right now. Im currently watching my professors lecture. And he basically how given $\lambda(t)$ as ...
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0answers
81 views
Find a LTI system such that $\mathcal{T}\{\frac{\sin t}{t}\} = \frac{\sin 2t}{t}$
Let
$$x(t) = \frac{\sin t}{t} \qquad\text{and}\qquad y(t) = \frac{\sin 2t}{t}$$
Is it possible to find a LTI system such that $\mathcal{T}\{x(t)\} = y(t)$?
If not, what's the reason for ...
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2answers
76 views
Impulse response of a time scaling system
Assume a bandlimited signal $X(t)$. Given that the output for this signal is $X(t/2)$, what will be the impulse response $h(t)$ of such a system?
\begin{array}{l}
X( \omega ) \ =\ \int ^{\infty }_{-\...
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What is the DFT of a binomial filter?
I hope this question is not too simple, I just started learning digital image processing. The 1D binomial filter of size 2 is defined by $B_2 = \frac{1}{4}\begin{bmatrix}1 & 2 & 1\end{bmatrix}$...
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37 views
Transfer function coefficients and impulse response - FIR filter
I am currently working on a FIR filter (varying in time). I have the real coefficients of the filter, but I would like to know if they correspond to the coefficients from the impulse response (as $b[k]...
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2answers
54 views
impulse response cascaded with time reversed of itself
Consider a filter with real-valued impulse response $h[n]$. The filter is cascaded with another filter whose impulse response is $h'[n] = h[-n]$, i.e. whose impulse response is the time-reversed ...
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1answer
38 views
Why is there a negative in front of the phase response equation for this complex exponential?
first time on here!
I'm working through "Digital Signal Processing using MATLAB" by Vinay and Proakis. Good book.
I am stuck on this example tho.
Shouldn't the imaginary part in the denominator (...
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2answers
34 views
Argument of Dirac delta function is quadratic with complex roots
For example, we write $$\delta(at + b) = \frac{1}{|a|}\delta\left(t+\frac{b}{a}\right)$$
In a similar way, $$\delta(t^2 + t + 1)=\underline{\hspace{1cm}}$$
Thanks for the help.
Purna.
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1answer
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Composing two Impulse Responses
Pardon my layperson understanding. My application is audio design.
What is the correct operation / algorithm to compose two impulse responses (IRa, ...
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1answer
70 views
Calculate Impulse Response of a System From Its Input/Output Waveform via FFT
From the theory, I knew something like :
$y(n) = x(n)*h(n)$
$Y(n) = X(n)H(n)$
$H(n) = \frac{Y(n)}{X(n)}$
Now I have $y(n)$ and $x(n)$ from a system, and $y(n)$ is 2176 samples long, $x(n)$ is 2176 ...
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1answer
32 views
How to find the perfect regularization number?
I have an issue!
Assume that we are going to solve $Ax=b$ but $x$ contains noise.To minimize that noise we can use regularization:
$$x = (A^TA + \lambda I)^{-1}A^Tb$$
Where $\lambda$ is a small ...
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2answers
31 views
How can i derive step response in terms of impulse response from the convolution sum?
If it is discrete LTI system,
How can i derive step response in terms of impulse response from the convolution sum?
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1answer
28 views
Why is $\delta[an]=\frac 1 a \delta[n]$ in discrete time?
Why is $\delta[an]=\frac 1 a \delta[n]$ in discrete time? Prove.
Hi, I want to prove it but I don’t know on what facts to rely. In continuous time we have integral and dt in that integral that turns ...
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Extract Impulse Response of a System From its Input/Output Waveform
I am a new engineer for signal processing field.
I want to extract the system impulse response from input and output of the system, i.e. so-called system identification, more specfically, for ...
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6answers
403 views
Design a LTI system which returns DC value of the input signal
Suppose that $h(t)$ is the impulse response of LTI system. The input signal $x(t)$ is periodic with period $T$. Determine $h(t)$ so that the output signal $y(t)$ only be the DC component of $x(t)$. Is ...
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1answer
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How to extract two signals from one signal by selecting right index?
Assume that we want to solve
$$AX=B$$
Where both $A, X, B$ are matrices.
I solved this by using ordinary least squares:
$$X = (A^TA)^{-1}A^TB$$
And I got this result for one column in $X$.
Here ...
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1answer
27 views
LTI system impulse response [closed]
I am learning signal processing and need some help with this question
$h[n]=-x[n]+2x[n-1]-3x[n-3]$
Given the following input signal $x[n]$ calculate y[n] the output of the system $x[0]=2, x[1]=0, x[...
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2answers
55 views
Unit impulse vs Kronecker delta vs Dirac delta?
Apparently these 3 terms are similar, but what is exactly difference between them and what is exact value of each of them at time zero,1 or infinity?
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4answers
89 views
Help understanding impulse response
I am having trouble understanding the impulse response function.
I have a beam of 10 m long. I place 2 sensors, one at point A and one at point B. I then excite the beam at point E (shown in picture) ...
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2answers
61 views
Characterizing an unknown LTI system
What are the best approaches to characterize an unknown discrete time LTI system? I believe one of the approaches is to input a known input and measure the output to find a transfer function. What are ...
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22 views
Characterizing a non-LTI system
How should we characterize a non-LTI system? For example we have: $y[n]=x[3n]+x[2n]+x[n]$ which is clearly not LTI. Also, the impulse response will be $h[n]=3\delta[n]$ and if we take the DTFT of this ...
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2answers
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Impulse response of an LTI system given the input and output signals
I have been given the input and output signals of an LTI system as:
$x[n] = (\frac{1}{2})^nu[n] + 2^nu[-n-1]$
$y[n] = 6(\frac{1}{2})^nu[n] - 6(\frac{3}{4})^nu[n]$
I have found the system function $...
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MATLAB- Add Envelope to Sound Signal
I’m in the process of making a convolution reverb and I’m trying to add an envelope to my impulse response signal and plot it in order to change the RT60 of my sound signal (Just a song). I’ve looked ...
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4answers
162 views
why only impulse signal for convolution?
Why do we only use impulse response for convolution for getting output of LTI systems. why we don't use unit step or any other signal for this purpose?
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1answer
223 views
Determing inverse Z-transform using impulse response?
In Matlab there is a command iztrans for finding inverse Z-transform. But how can we find inverse Z-transform using impulse response? The Matlab command ...
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1answer
41 views
Relation between impulse response and Region of convergence?
Is there any relation between impulse response and Region of convergence?Means position/location of ROC depends upon impulse response or not??
Please kindly guide about cases for both continuous and ...
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1answer
54 views
Impulse response measurement : practical questions
To measure system impulse response I can do the following steps :
system input : it is excited with an excitation signal having a duration t_exc with a bandwidth bw_exc (for example sine linear sweep)...
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0answers
27 views
Relation between PDP (Power Delay Profile) and channel impulse response
I am traying to perform a simulation in Matlab and I faced up with some practical/theorical problems.
The channel I want to simulate is frequency selective fading. The packets are short compared with ...
3
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1answer
66 views
Proving linearity and time-invariance
This question was asked in one of our quiz. Question is
Determine if the system with the input-output relationship given by
$$y(t) = \int_{t-10}^{t} \cos(\tau)x(\tau)d\tau$$
is linear and time ...
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1answer
57 views
Identifying impulse based on experimental data
I have conducted an experiment in which the impulse was exerted on sound bowl (it was hit by a hammer). As a result I have obtained acceleration from accelerometer on 3 axis, calculated net ...
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2answers
83 views
Cross-correlation of maximum length sequence with noise
Background
I am using a maximum length sequence to find the impulse response of a linear system. I want to calculate the expected SNR. I know that my signal amplitude is scaled by the length of the ...
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1answer
83 views
How to normalize frequency response charts
I want write a simplistic program that can transform a high-quality voice recording in a way that it sounds like it was recorded using a specific low-quality microphone.
I have obtained the mic's FR ...
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1answer
39 views
convolution expression h(n,k) = h(n-k)
As a new to DSP concepts want to understand the meaning of impulse response and why we do $h(n-k)$ in convolution and $h(n+k)$ in correlation.
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1answer
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Impulse response of a system in z domain
The question 3-23 in the "Discrete-Time Signal Processing - Second Edition" is:
and the solution is:
I cannot understand the solution. In the second row of the answer when I multiply (-4) with ...
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1answer
83 views
Impulse and step response
While trying to determine the unit step and impulse response for a discrete LTI system I had several problems:
$$
\begin{aligned}
(Hx)[n]&=(Hx)[n-1]+\frac{1}{N}(x[n]-x[n-N]) \\x[n]&=(Hx)[n]=0\...
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0answers
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Stereo echo cancellation for stationary source locations: why does adaption stagnate?
In a stereo echo cancellation system, the echo path for the far-end-signal in the near-end room is estimated by an adaptive filter. Since the same signal is transmitted by two similar far-end paths, ...
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273 views
How can I correctly plot an impulse_response() of a discrete transfer function?
I posted this question on stack overflow and I think it was the wrong place so I moved it here.
Hello, I'm new to python, I just want to use the control library and I'm slowly learning, I did my ...
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2answers
218 views
Impulse Response of a Moving Average System
According to Discrete Time Signal Processing by Al Oppenheim 3rd Edition, the impulse response of a moving average filter is as below
My question is that shouldn't h[n] be having the dirac delta ...
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1answer
51 views
why is it so hard to simulate up and down position on headphones?
i'm wondering how come simulating front,back,left and right source position on headphones is easy but up and down is not ? (maybe even impossible ?)
is it due to the shape of the ear ? but should we ...
2
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1answer
130 views
Impulse response of a transfer function
Lets say we have a transfer function from an LTI-system that goes as follows, and we want the impulse response for it:
$$\frac{10\cdot e^{\left(-\mathrm{i}\right)\cdot \pi\cdot f\cdot 8}}{5+\mathrm{i}\...
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3answers
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How is $\delta(at+b)=\frac{1}{|a|}\delta(t+b/a)$?
This result has been used in the second last line of the pic. I don't know why it's true. Both functions are zero for $t$ not equal to $-b/a$. But at $t=-b/a$, a scaling factor $1/|a|$ has been ...
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0answers
53 views
Phase response of an LTI-system
I've got an LTI-system such as follows:
$$y'(t)+{2} y(t)={5} x(t-{3}), t>0,
\\ \\ y(0)=0 \ \text{ ja } x(t)=0, \ t<0.$$
From this i've already figured out the transfer function:
$$H(f)=\frac{5\...
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3answers
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How do impulse response guitar amp simulators work?
I am wondering how impulse response guitar amp simulators/modelers work. I thought it was a matter of convolving a signal of recorded impulse response in time-space with a guitar sample.
I tried to ...
