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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Time delay of direct path in RIR measurement
I am trying to measure an RIR using my laptop and a JBL Flip 5 speaker. I have tried, both, the Matlab tool and a python code shared on gihub. My final goal is to compare with the image method and ...
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Question about impulse response of an ideal lowpass filter
Consider an ideal lowpass filter with a cutoff frequency of $\omega_c$. Following shows its impulse response:
$$h[n] = \frac{1}{\pi n}\sin(\omega_cn)$$
Also, some references shows $h[n]$ as:
$$h[n] = \...
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53 views
Definition of frequency response
I studied various signal processing materials for a long time, and I have a question.
Considering an LTI filter, one can define its frequency response by evaluating its transfer function $H(z)$ on the ...
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99 views
Audio signal arrival timing, impulse response, and reverberation
I'm building an application that requires determining the arrival time of an audio signal with a very high degree of accuracy (within 1ms would be ideal) using commodity smartphone hardware. I found ...
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1answer
26 views
DTFT of $(-1)^{n}\frac{\sin((7\pi / 8 )n )}{\pi n}$
The DTFT without $(-1)^{n}$ is relatively easy but with $(-1)^{n}$ I am not sure how it would be solved. I hope anyone can help
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A system having impulse response $ h(t)=u(t) $ stable or not?
I know that for a system to be BIBO stable its impulse response must be absolutely integrable and the impulse response $ h(t)= u(t)$ integrates to approach infinity (i guess)
I proceeded as$$ \int_{-\...
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1answer
26 views
Pulse shaping with root-raised cosine filter for a non-Gaussian channel
I am here to check whether my line of thinking is correct.
Root-raised cosine (RRC) filtering is one way to minimize intersymbol interference (ISI). Hence, we apply matched RRC filters on both sides ...
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91 views
Calculation of inverse impulse response in the frequency domain
I want to calculate the inverse impulse response of a LTI system in the frequency domain. I generate a simple impulse response $g$. For this I generate a vector of 100 zeros. I set the value of the ...
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72 views
Why is particular solution zero for an impulse excitation signal?
We were being taught the impulse response for a series RC Circuit- consisting of simply one resistance, one capacitor, and an impulse excitation all in series.
I get that the homogeneous part of the ...
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Numerically finding impulse response from a wave equation
I'm developing a song synthesizer (like Yamaha's Vocaloid). I decided to mimic the acoustics of human speech. I modeled the space between articulators as a solid of revolution, and came up with the ...
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1answer
32 views
RMS level from impulse response
I am trying to quantify the average differences between several impulse responses over the frequency range and over octave bands.
So, I am doing (in Matlab):
...
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108 views
Impulse response for an LTI system
I'm new to signal processing and working my way through a textbook. There is an exercise where a causal LTI system is given that responds to a rectangular pulse.
I have an exercise where a causal LTI ...
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64 views
Output of a stable LTI system (discrete)
Consider an LTI (linear and time invariant) system that is BIBO (bounded input
bounded output) stable and is such that $x[n] = 0$ for all $n < 0$ (note: this is sometimes referred to
as a relaxed ...
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1answer
51 views
The plot of instantaneous power of the Dirac function
I am very confused. I have tried researching this question for the last two weeks and I cannot get a conclusive answer.
I was wondering how would I go about plotting the instantaneous power in the ...
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Optimal control to maximize the ratio between two systems
I have two (or more) systems with analytic (but somewhat big and unwieldy) step responses $H_1(t)$ and $H_2(t)$ both of the same form (eq. A6a onwards in https://doi.org/10.1016/S0302-4598(97)00093-7),...
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47 views
Calculating cross-correlation using Walsh-Hadamard transform
I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse ...
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624 views
This is how my professor is finding the frequency response of an LTI system when given the impulse response. Is this wrong?
My DSP professor uses the freqz() function to find and plot the frequency response and I think it's wrong but I want to make sure before I point it out. Take this ...
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An Impulse in Complex Envelope (i.e. baseband) Notation?
In complex envelope notation, a modulated RF signal, say v(t), is represented in complex envelope notation as v(t) = Re{ g(t)e^(jwct)}, where wc is the carrier angular freq, g(t) = x(t) + jy(t), and g(...
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33 views
Calculate impulse response when output contributes in input
I have an exercise in which I need to find the impulse response for this given system:
$$y(n)=\frac{1}{2}y(n−1)+x(n−1)+x(n)$$
As per my knowledge, I need to find the homogenous solution. My homogenous ...
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1answer
49 views
Output of a linear time-invariant(LTI) system
I am very confused about one of the questions I received during an exam. How do I solve this question?
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1answer
60 views
Finding the impulse response given response to another signal
I was trying to solve this question :
I respresented $x(t) = u(t+1)-u(t-1)$
writing the convolution as $[u(t+1)-u(t-1)]*h(t) = y(t)$
I then used the property of differentiation to convert from the ...
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59 views
Impulse Response of real coefficient, LTI System
I'm trying to obtain the impulse response $h[n]$ of a system whose frequency response is $H(e^{j\omega})=R(\omega)e^{-25j\omega}$. I believed that $h[n]=h[n-25]$, would be the correct answer, however ...
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4answers
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What is the correct gain of an RRC Filter?
Breaking my brain all morning with this reading previous questions and googling ...
I have made an RRC filter from the equation on wikipedia. It works fine and I compared it to commpy library in ...
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1answer
62 views
Setting up RRC filter and useful equations
I have looked at previous answers but cant seem to get everything I need in one place to help me and my textbook doesnt explain this in practical terms.
Signal Parameters:
$F_s = 44100$
$R_s = 300$
$...
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39 views
Impulse Response for an Anti Causal Linear Shift Invariant System
I have a system given by
$$y[n] - \frac{1}{4} y[n-1] - \frac{1}{8} y[n-2] =3x[n] $$
I'm asked to determine the impulse response of both an anti-causal and a causal Linear Shift Invariant System ...
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62 views
What is impulse response in simple AWGN channel?
Assume a sender and receiver communicate through an AWGN channel. Let $x(t)$ be a transmitted signal and $y(t)$ be a received signal and $z(t)$ be the Gaussian noise. It is known that $y(t) = kx(t-\...
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70 views
Is Step the same as an Impulse + 1/s?
Isnt a Step (as a Transfer function -> $ \frac{1}{s} $) and Impulse (trans fcn -> 1) therefore Impulse + $ \frac{1}{s} $ should be equal to a Step in Simulink ...
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1answer
56 views
What is the decay rate (time constant) of two One-Pole LPF's cascaded in series?
If you have a One-Pole LPF, and set the cutoff frequency to $\frac{1}{2πt}$ where $t$ is the time to $\frac{1}{e}$ amplitude, it will provide an exponential decay in response to a step function (eg. ...
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40 views
Is there an equation that will graph the shape or predict the maximum amplitude of a single sample impulse fed through a One-Pole LPF?
If you feed a single sample impulse of a given amplitude through a One-Pole LPF you get an envelope that looks like this:
The output of the LPF from its peak will settle into an exponential decay ...
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2answers
173 views
DC gain from an impulse response
I am studying for my exam in signal processing. For one of the old exam sets, a discrete impulse response of a filter is given as $h[n]$
\begin{bmatrix}
-3&0&-3&0
\end{bmatrix}
With a ...
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1answer
92 views
Impulse response $h[n]$ from input and output signal using cross correlation on Matlab
I have two signals on Matlab, one being input and the other output. I want to know if taking the cross correlation of these signals would give me the impulse response?And if so, will taking the ...
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38 views
Deconvolution with noisy measurement of impulse response function
I observe a noisy 1D signal that has passed through some linear time-invariant filter:
$$z(t) = (h\star x)(t) + n(t)$$
where $h(t)$ is the filter, and I am hoping to recover $x(t)$. $n(t)$ is some ...
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1answer
94 views
Digital Signal Processing Filters Problem
Hello I need some help with this question.
$$𝑦[𝑛] = 𝑎_1𝑥[𝑛 − 𝑘_1] + 𝑎_2𝑥[𝑛− 𝑘_2] + 𝑏_1 𝑦[𝑛− 𝑘_3]$$
Set $a_1, a_2$, and $b_1$ to any positive or negative real numbers of your choice. Set $...
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Extrapolation of band-limited frequency data
I'm now studying "How to do accurate transform from band-limited frequency data specifically S-parameter data of high speed interconnect to the causal impulse response in time domain. There are ...
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1answer
130 views
Finding impulse response $h(t)$ by impulse matching; problem understanding Example 2.3 in “Linear systems and signals”, Lathi 3rd edition
Before the example it has been stated that in a system described by
$$
Q(D)y(t) = P(D)x(t), \quad (1.) \iff \\
(D^N + a_1D^{N-1} + ... + a_{N-1}D + a_N)y(t) = (b_{N-M}D^M + b_{N-M+1}D^{M-1} + ...+b_{N-...
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144 views
Stability of a system in time-domain
Consider a system for which the input $x(t)$ and output $y(t)$ are related by the differential equation $$\frac{d^2y(t)}{dt^2} + \frac{3}{2}\frac{dy(t)}{dt} - y(t) = x(t) \tag{1}$$Determine $h(t)$ for ...
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The impulse response of a LTI discrete system is $h[n]=\big(\frac{1}{3}\big)^n u[n]$. Find the response of this system to the input $x[n]= e^{jnπ/4}$
Hi I'm trying to solve the problem when studying for an upcoming test.
The given solution is
$1.2503 e^{jnπ/4 -0.2991}$, and is found by computing $H(Ω)$ and evaluating this at $Ω=π/4$.
when I try ...
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1answer
119 views
Single-sided Z transform with difference equations and the system function
I am working on this problem:
Given an impulse response,
find the system function,
find the difference equation representation,
find pole-zero plot,
find output $y[n]$ if the input is $x[n] = 0.25^n *...
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1answer
35 views
Impulse invariance vs. DT representation of a CT system: Where is the inconsistency?
Suppose you have a continuous-time (CT) system $h_c(t)$, bandlimited to $B$. Your goal is to represent the system as a discrete-time (DT) system $h[n]$, sampled at $f_s \leq 2 B$. Clearly $h[n]$ won't ...
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2answers
111 views
Output of a stable LTI system
Let $\mathcal{L}$ be a stable LTI system. Is it true that if input has finite energy then output also has finite energy? I'm not sure about that. We know that $$\int_{-\infty}^{+\infty}|h(t)|dt\lt\...
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Multiple short-range impulse responses aggregated to simulate a long-distance impulse response
I'm a biologist and I was thinking of ways that impulse responses could be used to simulate how an animal sounds over various distances in different types of forests.
Ultimately, if a tool was ...
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1answer
141 views
Find the length of the impulse response for the given output and input
Homework Question:
Consider a signal $x[n]=\alpha e^{j \omega_{0} n}+\beta e^{j \omega_{1} n}+\gamma e^{j \omega_{2} n} .$ What is the length of impulse
response $h[n]$ of a system (non-trivial) such ...
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Amplitude Matching for Exponential Swept Sine
I am working in the area of aerospace vibration testing and we use swept sine tests on structures and measure the response using the accelerometers. I tried implementing the technique "...
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1answer
129 views
impulse response of a causal LTI system
This is a difference equation to a causal LTI system:
$y[n] = ay[n - 1] + x[n] - a^Nx[n - N]$
Where N is a positive integer. I need to determine the impulse response of the system, so I have the ...
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15 views
Estimate IR's from single channel speech audio
I have a dataset of single-channel audios containing speech, recorded in a single room. I need to extract the room IR's. The goal is to simulate the room acoustics and adjust new speech audios ...
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4answers
116 views
Impulse response of system with $\max\left\{\lvert x[n] \rvert\right\}\ge\max\left\{\lvert y[n]\rvert \right\}$
Find a relation/condition for the impulse response, so for any $x[n]$ (input) with $y[n]$ (output) this relation is true:
$$ \max\left\{\lvert x[n] \rvert\right\} \ge \max\left\{\lvert y[n]\rvert \...
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1answer
426 views
Bode plot from from step response data
For quality control, I want to measure the frequency response of hardware I built. What I can easily generate on the hardware is a step response. Thus, I want to derive the magnitude and phase from ...
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1answer
67 views
Real impulse response
It will be great if someone can explain me what exactly means "real impulse response".
Further more , what is the effect of such a response on ROC (Laplace plane) and in particular if its ...
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1answer
43 views
If you would write the frequency-response in terms of projections through inproducts. How would you do it?
While studying for signals and systems I realised that the most intuitive way of understanding Fourier Series for me, was to see it as a projection (through inproducts) of a signal onto the orthogonal ...
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3answers
72 views
What do the function blocks mean?
What I don't understand is what exp(.) and ln(.) mean. For example y(t) and ...
