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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Help to identify this impulse/autocovariance
I have attached a picture of an autocovariance over a single lag. To my (inexperienced) eye this looks like some kind of impulse response but I am unable to identify the function. The picture is taken ...
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1answer
53 views
Computing response of LTI system in terms of its step response
I have solved a problem, Kindly help me in determing if I solved it correctly.
I will post the question and my own working below.
Problem
My working
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1answer
42 views
pole/zero plot & impulse response
in a mock exam of dsp was asked this question, and even in knowing how to compute DFT's of the plot, I wondered if there was a fast way of pairing these plots to their respective impulse response?
...
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1answer
47 views
Missing delay in heavyside step function
I found the following task that was inspired by an example in the book A. V. Oppenheim and R. W. Schafer, "Discrete-Time Signal Processing", 3rd Edition, 2014.
Task:
Consider the 2nd-order IIR ...
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23 views
Time gating of FFT for audio Measurements or Multi Time Windowing
I am learning more about DSP specifically for audio measurement purposes.
I can an app, where I can create a log sine sweep from start frequency to end frequency over a certain length. I can perform ...
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22 views
Determining position and g-forces from accelerometer and gyroscope data
I'm analyzing gyroscope + accelerometer data acquired from an IMU for a run of a water skiing slalom course, sampled at 100Hz.
The double spikes represent spurious ~15G jitter from crossing both ...
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2answers
71 views
My impulse response does not tend to zero
I am doing an IFFT of frequency response data achieved with Simulation tools.
When I plot my impulse response it looks wrong as the response does not tend to zero as it should. Instead there seems ...
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What is difference between natural response and zero-input response of a system and how to find natural response? [duplicate]
In most books it is said that natural response is another name to zero-input response while in some resources is is mentioned that the classification is based on poles of transfer function and input....
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15 views
Methodology for log some sweep audio measurement impulse response
I am trying to implement a method for measuring the response of a loudspeaker in a room using a log sine sweep stimulus.
To check my method:
1. I create the stimulus using:
Make recording length ...
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25 views
Solving impulse response using summation of singularity functions
I'm stuck at Problem 2.56 of Alan Oppenheim's Signals and Systems book. Here is the solution given.
I did learn basic differential equations before from Boyce's book but I have never encountered ...
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Simple Impulse Response DSP Hardware
I developed some complex chains of filters and crossovers. After that I have created IRs from the entire chains.
Applying these IRs in software works perfectly.
Now I wonder what is the easiest (and ...
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41 views
What is the difference between an impulse response and a kernel?
It seems to me they are two terms used to refer to the same concept, but, according to the Wikipedia page on Guassian filter
a Gaussian filter is a filter whose impulse response is a Gaussian ...
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40 views
Find output from a system with x(n) = u(n)
I've started learning signal processing and I'm trying to understand this exercise:
Assume an LTI system, described by the difference equation:
$$y(n) - y(n-1) - 6y(n-2) = x(n-1)$$
Q: Find ...
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1answer
52 views
Discrete Time Fourier Analysis
Suppose we're given the following:
$ x[n] = 2 + (-1)^n $, and are given the impulse response $ h[n] = u[n] a^n $, of an LTI system where $ |a| < 1$. We're asked to find the output $y[n]$, if $x[n]$...
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24 views
Impulse response of discrete time system
I am learning about discrete systems and in this derivation something struck me as quite odd. Solving for $A_0$ in this equation seems dubious as it ignored all other values of $n$. For example, at $n=...
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1answer
98 views
How to determine the filter type based on the impulse response?
When given a discrete impulse response, let us say it is from an FIR filter so it is finite, how can I assume the filter type?
The task is to recognize or to preclude one or more of the following ...
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138 views
How do I play and record audio at the same time?
So this question is more related to Matlab itself.
Some background info: I'm trying out the Exponential Sine Sweep method to obtain the Room Impulse Response with my laptop speakers and microphone ...
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1answer
236 views
What will the impulse response of a matched filter look like if the input is complex?
If $h(t)$ is the impulse response of a filter matched to a signal $s(t)$, I read that $h(t) = ks(t_o - t)$.
But what if the signal is complex? I went through the derivation of the matched filter and ...
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1answer
49 views
Self study question about Padé Approximation and transfer functions
Given a signal $x[n] = [1, 2, 3, 4, 5]$. How many transfer functions can be found with Padé approximation which have a causal impulse response and start with those five samples. How many of them are ...
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1answer
100 views
Numerical Calculation of impulse response out of frequency response
Currently I work on my Masterthesis which deals with structural dynamic simulation. As a part of it I have to filter a Signal with a FIR-Filter. From that Filter I know the Frequency Response (picture)...
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1answer
74 views
How to find the impulse response of filter that outputs the autocorrelation of the input?
I am trying to solve question 9.61 in the attached image.
I guess, by evaluating the autocorrelation for a specific instance, say $ t = 0 $ , that the impulse response, $h(t)$, should be : $$ h (t)...
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How does an LTI system produce multiple values from a unit impulse
I understand that in a discreet system, an impulse is 1 at the origin point and 0 everywhere else. I've seen many examples showing the impulse response of an LTI system to be many points, have many ...
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1answer
40 views
channel estimation for cdma
I am looking for a method to make a multi-user channel estimation with CDMA.
Here is my question:
Is there a way to estimate multi-user channels with their spreading codes? If yes, what is the ...
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1answer
55 views
Calculating an output of a system (Z- transform question)
I have a following question to answer:
An LTI system is described by its impulse response h[n]. For input x[n] it gives output y[n].
$$h[n] = u(n) - u(n-N) $$
$$x[n] = u(n) - u(n-M)$$
I want to ...
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1answer
71 views
Impulse response resampling : IIR aproximation vs windowing
I have a long measured impulse response and I wand to shorten it.
I imagined two options. The first is a simple windowing. The second is to model it as an IIR (prony, yulewalker, stmcb method) before ...
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1answer
87 views
Are there DC removal techniques that do not introduce a filtering transient?
I have an application in which I need to remove DC components from a sampled signal in real time (basically the same constraints of ECG, but it has nothing to do with the brain). My measured signal in ...
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7answers
488 views
Intuition behind commutativity of convolution in LTI systems
Why is convolution commutative, as it seems to treat two signals in a different way in an LTI system?
If you imagine $y[n] = x[n] \star h[n]$ with $x[n]$ being an input signal and $h[n]$ being the ...
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1answer
151 views
How to represent impulse function in 2D?
To be more specific I want to show that impulse function in 2D can be represented as $β(r)=δ(r)/πr$.
Also I want to show that each projection of a two dimensional impulse function at the origin is a ...
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1answer
112 views
Simple Impulse Response
I am trying to find the impulse response to this system:
At first it looks easy enough, $y(n)=x(n)(-1)^n$, set $x(n)=\delta(n)$, which makes $h(n)=(-1)^n$. But something seems wrong.
What am I ...
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2answers
124 views
Block diagram for a complex impulse response
I have this question regarding digital systems which might not handle sinusoidal signals in general. So let us say that I have a system with impulse response $h(n) = \{1+j, -1, 2j \}$ with first ...
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1answer
183 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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1answer
2k views
How to calculate impulse response of a RC circuit
I have an $RC$ circuit and I calculate the differential equation as
$$RC \frac{dV_c}{ dt} + V_c = V_g$$ that is the same of
$$RCy'(t) + y(t) = x'(t).$$
If I assume $x(t) = u(t)$ I have that the ...
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1answer
177 views
Impulse response of a second order LTI
I have a set of measurement which I want to model with 2nd-order difference equations (first order eqs don't model well enough).
The equation is
$$y[n] = \alpha_1 y[n-1] + \alpha_2 y[n-2] + \beta_0 ...
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1answer
62 views
Steady state value of a complex convolution
I am trying few problems on the introductory part of DSP. One of the problem asks to calculate the steady state response of a system with impulse response $h[n] = (\frac{j}{2})^{n} u[n] $ to an input ...
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1answer
39 views
Why is the impulse response function of this system 0?
Suppose I have an system $ y(t) = t^{2}x(t)$.
The impulse response of this system would be: $h(t) = t^{2} \delta(t)$.
Since $\delta(t) = 0$ for $t \neq 0 , h(t) = 0$ for $t \neq 0$.
And at $t=0, h(...
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2answers
127 views
Impulse response when input to a system is differentiated, and its applicability to find response to general inputs
I will first give a short explanation of what I am asking, and then give a more comprehensive context.
If we have a LTI dynamic system acted upon by inputs $y(t)$ and producing outputs $x(t)$,
,
we ...
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1answer
142 views
Convolution of Input signal and Impulse response
I can solve the output if the input is
$$ x[n] = \delta[n+1] + \delta[n] + 2\delta[n-1] + \delta[n-2]$$
and the impulse response is
$$ h[n]= 3\delta[n] − 2 \delta[n−1] − \delta[n−2] + \delta[n−3]$...
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4answers
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Why is the first value in digital first-order IIR filter impulse response not the largest?
When I create a digital first-order IIR low-pass filter with scipy (code below), I get the following coefficients:
B: [ 0.1367 0.1367]
A: [ 1. -0.7265]
The ...
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1answer
119 views
Impulse response from Frequency response: why using $e^{j\omega}$ as an input?
Every resource that I can find uses this identity when deriving impulse response:
$h[n] = IDTFT \Big\{H(e^{j\omega}) \Big\}$
Suggesting that the input signal was $e^{j\omega}$. But by definition ...
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1answer
98 views
Phase wrap when computing impulse response from frequency response [closed]
Short:
I have the frequency response of a system as a set of complex numbers.
I want the impulse response for that system.
Problem: The phase of my frequency response wraps around 2pi multiple times....
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2answers
57 views
How can I calculate what a recording would sound like if it was played through my speakers and mic?
I am trying to isolate the sound of someone speaking while music plays back in a noisy environment.
I have multiple speakers and a microphone in my system. I am able to
play back just music and ...
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1answer
62 views
Simple question about Sinc()
Suppose I use the ideal lowpass filter eq to attempt creating a IIR filter using it
:
$$
h[n] = \frac{\sin(\omega_c \, n)}{\pi \, n}, \qquad -\infty < n < \infty
$$
Obviously, I can't really (...
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6answers
298 views
Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter
I would like to approximate a moving average filter with an IIR filter of much lower order than the tap-length of the moving average filter. Optimality shall refer to the $L_2$ norm of the impulse ...
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2answers
132 views
How to compute the impulse response from incomplete frequency response data?
I need to compute the impulse response of a system, but I only have access to the frequency response data.
This data contains the output magnitude of the system (for a fixed input amplitude) at ...
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1answer
88 views
Poles of the transfer function in Z Transform
Given that:
$H(z)$ has 4 poles maximum.
$H(z)$ has a pole at $z_1=a+bi$
Given that the impulse response $h[n]$ is:
Symmetric: $h[n] = h[-n]$
Real: $\forall$$n$ , $h[n]$$\in$$\mathbb{R}$
How we can ...
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1answer
217 views
FIR Impulse response & transfer function
I am working though a dsp past paper and I have come across the questions "find the impulse response in the time domain" & "find the transfer function in the time domain" I know its really simple ...
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1answer
101 views
I want to get impulse response of causal system
I want to get impulse response of this causal system on first photo.
So I got frequency response on second photo from this system.
and now I am trying to transform this frequency response to impulse ...
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2answers
134 views
Frequency response of marginally stable LTI systems
The frequency response of a system is defined as:
$$\int_0^\infty{h(t)e^{-j\omega t}dt}$$
where $h(t)$ is the impulse response. But in marginally stable systems, $h(t)$ does not decay so the integral ...
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2answers
70 views
Equalize Speaker using impulse response
So I have this school project where my aim is to improve a loudspeaker in general, my idea is to mesure the impulse response of the room using a mic, then use this mesure to conceive a loudspeaker ...
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115 views
Multilateration of Sound in 3D Space
TL:DR - How can you find the 3D coordinates of a emitter than transmits an impulse signal?
STORY:
I'm working on something to improve my bird-watching. I've got a camera that can take pictures of ...
