The impulse response of a dynamic system is its output when presented with a brief input signal, called an impulse.
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59 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
50 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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0answers
55 views
How to calculate impulse response
I only have this system as information :
$ y(t) = \int_{t-T}^{t} x(\tau) d\tau $ And I have to calculate the impulse response. I already have the solution but I don’t know which formula my book used....
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1answer
51 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
$$y[n] = \alpha_1 y[n-1] + \alpha_2 y[n-2] + \beta_0 ...
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1answer
40 views
Steady state value of a complex convolution
I am trying few problems on the introductory part of DSP. One of the problem asks to calculate the steady state response of a system with impulse response $h[n] = (\frac{j}{2})^{n} u[n] $ to an input ...
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1answer
26 views
Why is the impulse response function of this system 0?
Suppose I have an system $ y(t) = t^{2}x(t)$.
The impulse response of this system would be: $h(t) = t^{2} \delta(t)$.
Since $\delta(t) = 0$ for $t \neq 0 , h(t) = 0$ for $t \neq 0$.
And at $t=0, h(...
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2answers
38 views
Impulse response when input to a system is differentiated, and its applicability to find response to general inputs
I will first give a short explanation of what I am asking, and then give a more comprehensive context.
If we have a LTI dynamic system acted upon by inputs $y(t)$ and producing outputs $x(t)$,
,
we ...
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1answer
50 views
Convolution of Input signal and Impulse response
I can solve the output if the input is
$$ 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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votes
4answers
243 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
65 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
48 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
54 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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votes
1answer
45 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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votes
6answers
187 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
56 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
34 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$$\mathbb{R}$
How we can ...
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1answer
68 views
FIR Impulse response & transfer function
I am working though a dsp past paper and I have come across the questions "find the impulse response in the time domain" & "find the transfer function in the time domain" I know its really simple ...
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0answers
29 views
Estimation of the frequency response data using Matlab command invfreqz?
I would like to determine frequency response and then impulse response of the displacement equation (eq. 1 please see screen shot of the task below). In this example we study a response of the finite ...
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0answers
68 views
ACF and impulse response
These are questions according to the system identification.
I can understand some questions:
Is there a relation between autocorrelation function and impulse response?
Is it possible to identify the ...
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1answer
41 views
I want to get impulse response of causal system
I want to get impulse response of this causal system on first photo.
So I got frequency response on second photo from this system.
and now I am trying to transform this frequency response to impulse ...
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0answers
37 views
extracting a room response [duplicate]
So I have a wav file containing a record of a sine sweep played on my pc and recorded by a mic. And I want to extract the room impulse of it, I've looked online but I couldn't find any clear answers. ...
2
votes
2answers
76 views
Frequency response of marginally stable LTI systems
The frequency response of a system is defined as:
$$\int_0^\infty{h(t)e^{-j\omega t}dt}$$
where $h(t)$ is the impulse response. But in marginally stable systems, $h(t)$ does not decay so the integral ...
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votes
2answers
42 views
Equalize Speaker using impulse response
So I have this school project where my aim is to improve a loudspeaker in general, my idea is to mesure the impulse response of the room using a mic, then use this mesure to conceive a loudspeaker ...
3
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0answers
65 views
Multilateration of Sound in 3D Space
TL:DR - How can you find the 3D coordinates of a emitter than transmits an impulse signal?
STORY:
I'm working on something to improve my bird-watching. I've got a camera that can take pictures of ...
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1answer
103 views
Impulse response of a causal system from transfer function in z-domain
The transfer function is $$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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vote
3answers
98 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
63 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 ...
1
vote
2answers
87 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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votes
2answers
578 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
37 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
121 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
83 views
What is the derivative of the function $s(t)=(1-e^{\frac{-t}{RC}})u(t)$?
What is the derivative of the following function
$$s(t)=(1-e^{\frac{-t}{RC}})u(t)$$
with respect to $t$, where $u(t)$ is a unit step function?
I am getting $\delta(t)+\frac{1}{RC}e^{-t/RC}u(...
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1answer
241 views
Designing high-pass filters using impulse invariance
One of the main disadvantages of realizing digital filters using impulse invariance is aliasing. According to the Nyquist sampling criterion, in order for the frequency response of the digital filter ...
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2answers
59 views
How do I show an impulse response leads to a zero-phase frequency response?
I'm trying to understand how to show that with real coefficients, the phase response of a filter is 0. Here is the impulse response
$h[n] = b_1d[n+1] + b_0d[n] + b_1d[n-1]$
How should I approach ...
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2answers
337 views
How can I calculate Reverberation Time (RT60) from the Room Impulse Response using Python?
I have the following Room Impulse Response(RIR) in wave format here. I wanted to calculate Reverberation Time (RT60) of it by plotting its Energy Decay Curve using this Python code.
The RIR is ...
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2answers
39 views
unit step signal as sum of impulses from MIT OCW video
From MIT's OCW on Signals and Systems by A. Oppenheim, at 4:30 mark https://www.youtube.com/watch?v=jGk3w1b7UXQ&index=3&list=PLLNp7XoiSLQYygYw8Mzt763zZCQdzCZcd
He said that by forming the sum ...
2
votes
2answers
75 views
How to calculate time of arrival using room impulse response
I need to find the timestamp of arrival of a particular signal at a receiver location within a room. The known parameters are the room impulse response h for a ...
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votes
1answer
42 views
impulse response of a system from its step response;confusion
If the step response of a system is given as $$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)= \{ ...
2
votes
0answers
53 views
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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votes
1answer
47 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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0answers
33 views
BER Graph for a PSK Modulation through a linear channel model
This is the graph that occurs when M-PSK symbols pass through a linear channel with impulse response given in a vector h. The simulation is done in Matlab and I am unsure about the result because of ...
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1answer
631 views
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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1answer
35 views
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
$$\mu_y = \mu_x*\sum_{k=0}^\infty h(...
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votes
2answers
306 views
How to obtain impulse response from a plot of magnitude of frequency response?
I have a plot of a magnitude response of a frequency response, how can I get the impulse response using only this plot and nothing else?
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3answers
506 views
Impulse Response to LTI
I am new to DSP, and I am self-studying using mostly Proakis. I have a question. There are some examples in the text where you will be given the impulse response of an LTI system, and then asked to ...
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0answers
29 views
Applying the inverse FFT to even out a room's sound - What is the more efficient algorithm?
I have a way (the standard way) to correct for my room's acoustics, but I'm wondering if there's a more efficient algorithm, something that doesn't involve going to the frequency domain maybe?
I ...
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votes
3answers
432 views
Solving for impulse response h[n] given input-output pairs
This is a homework problem that I've worked on and I want to confirm some of my reasoning.
I'm given two sets of input-output pairs of a particular system, $S$, that we know is linear time-invariant ...
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1answer
189 views
determine the impulse response of given second order difference equation
$y[n]-3y[n-1]-4y[n-2]=x[n]$
i solved it as follows :
1.first calculated natural-response(ZIR i.e,zero input response)
by using characteristic equation it came out as
$y_n[n]=[c_1(-1)^{n}+c_2(4)^...
2
votes
2answers
91 views
Is system $h(t) = u(t)-u(t-1)$ LTI or not?
$$y(t) = \int_{0}^{\infty} x(\tau)h(t-\tau) \ \mathrm{d}\tau$$
where $h(t) = u(t)-u(t-1)$.
I have some problem with understanding whether system LTI or LTV just looking the impulse response of the ...
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1answer
242 views
Impulse response function from pole-zero graph
I know that that the poles of this system are: $s_1 = -1 + 2j$ and $s_2 = -1 - 2j$. I think to solve this problem I would need to find the laplace of this plot, with the formula:
$$
W(s) = \frac{\rm ...
