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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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
46 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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0answers
17 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
51 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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0answers
44 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
55 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
46 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
66 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
45 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 : $$ h (t)...
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2answers
59 views
How does an LTI system produce multiple values from a unit impulse
I understand that in a discreet system, an impulse is 1 at the origin point and 0 everywhere else. I've seen many examples showing the impulse response of an LTI system to be many points, have many ...
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1answer
29 views
channel estimation for cdma
I am looking for a method to make a multi-user channel estimation with CDMA.
Here is my question:
Is there a way to estimate multi-user channels with their spreading codes? If yes, what is the ...
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1answer
50 views
Calculating an output of a system (Z- transform question)
I have a following question to answer:
An LTI system is described by its impulse response h[n]. For input x[n] it gives output y[n].
$$h[n] = u(n) - u(n-N) $$
$$x[n] = u(n) - u(n-M)$$
I want to ...
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1answer
46 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
57 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
438 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
99 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
90 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
81 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
115 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
789 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).$$
If I assume $x(t) = u(t)$ I have that the ...
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1answer
131 views
Impulse response of a second order LTI
I have a set of measurement which I want to model with 2nd-order difference equations (first order eqs don't model well enough).
The equation is
$$y[n] = \alpha_1 y[n-1] + \alpha_2 y[n-2] + \beta_0 ...
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1answer
55 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
33 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
71 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
98 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
$$ h[n]= 3\delta[n] − 2 \delta[n−1] − \delta[n−2] + \delta[n−3]$...
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4answers
908 views
Why is the first value in digital first-order IIR filter impulse response not the largest?
When I create a digital first-order IIR low-pass filter with scipy (code below), I get the following coefficients:
B: [ 0.1367 0.1367]
A: [ 1. -0.7265]
The ...
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1answer
91 views
Impulse response from Frequency response: why using $e^{j\omega}$ as an input?
Every resource that I can find uses this identity when deriving impulse response:
$h[n] = IDTFT \Big\{H(e^{j\omega}) \Big\}$
Suggesting that the input signal was $e^{j\omega}$. But by definition ...
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1answer
78 views
Phase wrap when computing impulse response from frequency response [closed]
Short:
I have the frequency response of a system as a set of complex numbers.
I want the impulse response for that system.
Problem: The phase of my frequency response wraps around 2pi multiple times....
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2answers
55 views
How can I calculate what a recording would sound like if it was played through my speakers and mic?
I am trying to isolate the sound of someone speaking while music plays back in a noisy environment.
I have multiple speakers and a microphone in my system. I am able to
play back just music and ...
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1answer
55 views
Simple question about Sinc()
Suppose I use the ideal lowpass filter eq to attempt creating a IIR filter using it
:
$$
h[n] = \frac{\sin(\omega_c \, n)}{\pi \, n}, \qquad -\infty < n < \infty
$$
Obviously, I can't really (...
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6answers
252 views
Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter
I would like to approximate a moving average filter with an IIR filter of much lower order than the tap-length of the moving average filter. Optimality shall refer to the $L_2$ norm of the impulse ...
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2answers
103 views
How to compute the impulse response from incomplete frequency response data?
I need to compute the impulse response of a system, but I only have access to the frequency response data.
This data contains the output magnitude of the system (for a fixed input amplitude) at ...
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1answer
54 views
Poles of the transfer function in Z Transform
Given that:
$H(z)$ has 4 poles maximum.
$H(z)$ has a pole at $z_1=a+bi$
Given that the impulse response $h[n]$ is:
Symmetric: $h[n] = h[-n]$
Real: $\forall$$n$ , $h[n]$$\in$$\mathbb{R}$
How we can ...
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1answer
132 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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0answers
67 views
Estimation of the frequency response data using Matlab command invfreqz?
I would like to determine frequency response and then impulse response of the displacement equation (eq. 1 please see screen shot of the task below). In this example we study a response of the finite ...
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1answer
71 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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0answers
97 views
extracting a room response [duplicate]
So I have a wav file containing a record of a sine sweep played on my pc and recorded by a mic. And I want to extract the room impulse of it, I've looked online but I couldn't find any clear answers. ...
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2answers
114 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
50 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 ...
3
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0answers
94 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 ...
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1answer
218 views
Impulse response of a causal system from transfer function in z-domain
The transfer function is $$H(z)=(z+1)/(z^2+z+0.5)$$
I need to find the impulse response h[n] of a causal system with x[n] as unit impulse.
I have tried to find the impulse response by the following ...
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3answers
190 views
Why use transfer functions than differential equations?
I have some simple questions regarding DSP and Control Systems, but found no simple answers. I just need simple and easy to understand answers, not complex answers with huge maths.
Why we use ...
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1answer
67 views
Homework Help: What does $h[0] = 1$ represent? What is $\ln \big| H(e^{j \omega})\big|$?
I have been staring at this problem for a week now...
Suppose $H(e^{j \omega})$ is the frequency response of a stable and causal minimum-phase discrete-time system with $h[0]=1$ ($h[n]$ is the ...
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2answers
116 views
Calculating impulse response of system
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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2answers
2k views
How do I calculate the impulse response of an ideal band-pass filter?
I understand the FR of an ideal BPF is just 1 between the two cutoff frequencies and 0 everywhere else above and below them both. But with arbitrary cutoffs, how would one find the IR of this ideal ...
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1answer
51 views
Add multiple aborption coefficients into virtual impulse response
I've got some code which creates a virtual impulse response of a room with arbitrary dimensions. I want to know, how can I add more than one absorption coefficient into it?
...
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0answers
309 views
BIBO Stability of an impulse response
I am trying to prove if $h_1[n] = 2^{-n} u[n]$ and $h_2[n] = (0.1)^n$ are BIBO stable or not, but I'm not sure if these analysis are correct. I'm having some trouble to understand this specific ...
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2answers
96 views
What Is the Derivative of the Function $ s \left( t \right) = \left( 1 - {e}^{\frac{-t}{RC}} \right) u \left( t \right) $?
What is the derivative of the following function
$$ s \left( t \right) = \left( 1 - {e}^{\frac{-t}{RC}} \right) u \left( t \right) $$
with respect to $t$, where $u(t)$ is a unit step ...
2
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1answer
626 views
Designing high-pass filters using impulse invariance
One of the main disadvantages of realizing digital filters using impulse invariance is aliasing. According to the Nyquist sampling criterion, in order for the frequency response of the digital filter ...
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2answers
73 views
How do I show an impulse response leads to a zero-phase frequency response?
I'm trying to understand how to show that with real coefficients, the phase response of a filter is 0. Here is the impulse response
$h[n] = b_1d[n+1] + b_0d[n] + b_1d[n-1]$
How should I approach ...
