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 modify an LTI differential equation to be acausal or anti-causal?

I'm trying to wrap my head around causality in LTI-systems. Considering continuous time only, I'm happy with the fact that the system is causal iff the impulse response function $h(t)=0$ for $t<0$. ...
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0answers
25 views

Calculating frequency specific decay time of an echo/reverberation

How is it possible to calculate the decay times of specific frequencies utilizing the impulse response's frequency response? Such analysis is especially useful when analyzing reverberation and ...
3
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2answers
69 views

what is nyquist rate of $h(t)\cdot h(t)$ and $h(t)\circledast h(t)$

Let's say we have $h_c(t)$ as a continuous-time signal with bandwidth $B$ and we would like to sample it. To be able to reconstruct it correctly, the sampling rate must be greater than $2B$. Now ...
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5answers
413 views

Can two different impulse responses give the same frequency response?

I have two different impulse response each with different length, is it possible that they have the same frequency response?
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2answers
70 views

What does “how to identify impulse response of a system?” mean?

I don't know where to start from, I'm not familiar with math. I'm trying to understand this question "how to identify impulse response of a system?". As you can see as below figure, as I know, the ...
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0answers
29 views

Multi-Channel LTI Inverse system problem

A sequence $x[n]$ is the output of a linear time-invariant system whose input is $s[n]$. This system is described by the difference equation $(1.1)$ $$x[n]=s[n]-e^{-8\alpha}s[n-8]$$ $$\alpha>0$$ a)...
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0answers
32 views

Autocorrelation of evolving channel impulse response

I have a transmission system simulated with Matlab. I send the successive symbols $S$ (vector of symbols), convolve them to the propagation channel $H$ (vector of the channel impluse response ...
3
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1answer
58 views

What is the relationship between passivity of impulse response and passivity of the system?

What I mean by passivity of impulse response is that the energy of impulse response for this system is less than the input impulse signal energy. For example, in a discrete-time system, considering ...
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2answers
46 views

Interpolated impulse response for fraction delay?

I need to find a way to create some fractional delay in a signal processing application that I am working on. Separately to this, I have been messing around with basic filter design (despite reading ...
1
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1answer
220 views

Identifying the magnitude and impulse response from pole zero plot quickly

I have an exam next week and it's verty certain that a task of this kind will be there. Are there some good tips how to match the right pole zero plot to the right responses? No proof is needed in ...
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0answers
33 views

Smoothing the discrete acceleration

In order to know if my signal is increasing or decreasing, I'm using the discrete derivative $y[n] = x[n] - x[n-1]$ or a smoothed version of it (for example Exponential Weight Moving Average of $y[n]$ ...
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2answers
97 views

How to obtain impulse response from the differential equation of a system?

This year I'm having trouble with my Signals and Systems class. My major subject is Software Engineering and Electric and Electrical Engineering is my Minor. This question was my previous exam ...
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0answers
55 views

Output of an LTI System With Given Frequency Response?

I will have my final exam this week. While I was studing for it I coudn't solve this problem. I think that I should work more about Fourier Transforms. I m thinking that the solution can be obtain by ...
0
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2answers
48 views

Question regarding transfer functions and prerequsities for finding the real impulse response

The transfer function of a system is given by: $$\large H(s) = \huge \frac{V_{out}(s)}{V_{in}(s)}$$ In digital domain the principle is of course the same, just replace laplace transform with z-...
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1answer
51 views

Simulating musical instruments using their impulse response

I studying DSP and trying to find the limitation of 'teaching' a software to emulate a musical instrument by sampling its notes at different velocities and building an LTI system for simulating it. ...
3
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1answer
69 views

Compute step response from impulse response of continuous-time LTI system

The impulse response of the LTI system is $$h(t)=e^{-4t} u(t)$$ The expression for the step response is $$\frac14 \left(1-e^{-4t}\right)u(t)$$ My question is how $u(t)$ appears in the answer.
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1answer
35 views

How to calculate step response for $y''(t) - y(t) = x'(t) - x(t)$ in time domain?

How to calculate step response for $y''(t) - y(t) = x'(t) - x(t)$ in time domain? So, without Laplace or Fourier Transforms. This is what I tried: The Homogeneous solution of the differential ...
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1answer
258 views

Difference between step,ramp and Impulse response

As, we can determine the response of the system by its 'impulse response' then why we use 'step response' and 'ramp response'. Is there any difference between all these response?
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1answer
58 views

Impulse response of non-causal system

Suppose I have the following equation, where $x[n]$ is the input and $y[n]$ is the output: $$x[n]-x[n-1]=-10y[n-1]+2y[n]+2y[n+1].$$ The question asks me to compute the impulse response from this ...
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26 views

Assist on finding the impulse response fom a simple LTI graph

Could you please advise on the impulse response from this LTI graph? I need to plot it and find if it is stable and causal... Thank you!
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0answers
26 views

What is a “Unit Shock” in an Impulse Response Function?

Is a "one unit shock" in an impulse function of variable "temperature" a 1% increase or 1 more "unit" (1 degree)?
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1answer
54 views

find impulse response from step response

if we have LTI system and we know unit step response of this system(we haven't original signal) how we can calculate impulse response?
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0answers
104 views

Inverse z transform - Pair of complex conjugate poles

How can I perform the inverse z-transform on the following $H(z)$ to be able to calculate a real-valued impulse response $h[n]$? $$ H(z)=\frac{z^2}{z^2+0.8\sqrt{2}z+0.64} $$ My idea was to find an ...
2
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1answer
54 views

Impulse and unit step response

I'm trying to understand impulse and unit step responses, but I'm not sure if my understanding is correct. In general, are the following statements true: a) The impulse response for a system $x(t) \...
2
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1answer
224 views

How do real-time convolution plugins process audio so quickly

Okay, so in Logic Pro I can load up a Space Designer plugin (convolution reverb) with an impulse that's 9.1 seconds long, turn my mic on, and get real-time convolution reverb as the mic records ...
2
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1answer
64 views

is any filter whose impulse response has a discontinuity in the first derivative fundamentally high-pass?

a triangular (bartlett) window has a kink (discontinuity in first derivative). thinking in the continuous (not discrete) case, my intuition is that the fourier transform of any window with a kink ...
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2answers
116 views

Discrete Fourier Transform on Impulses?

So I'm used to DFT being on an equation like this: x(n) = cos(n), ∀n , with window n = 0,1,2 I can clearly plot discrete values and take a DFT to find Xk But I found this equation on a past exam ...
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1answer
65 views

Convolution reverb using a frequently updated frequency dependant impulse response

I am implementing a software to auralize a virtual scene but am kind of a newbie to DSP. The focus should be the calculation of the IR which is frequency dependant. But this means that the renderer of ...
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1answer
80 views

What is the impulse response of the system with this difference equation:

The difference equation is written: $$y(k)-\frac{5}{12}y(k-1)+\frac{1}{24}y(k-2)=x(k)-\frac{1}{2}x(k-1) $$ The system is linear, invariant and causal. For $x(k)=δ(k)$, the equation will be: $$g(k)-\...
2
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0answers
69 views

Measuring noise floor in an impulse response

Say I have an impulse response... (an envelope of the actual IR obtained using the Hilbert transform) ... question: how do I calculate the surrounding noise level? Visually this looks to be ~ -54 ...
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0answers
23 views

Room Impulse Response for CHiME speech database

Where can I find the .wav file or a MATLAB plot for the Bin-aural Room Impulse Response(BRIR) that is used to create the CHiME speech database? http://spandh.dcs.shef.ac.uk/chime_challenge/data.html
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1answer
57 views

Matching headphone responses

First post, and this isn't my field of study, but I'm giving this a go anyway: My latest endeavor is to use a bit of DSP magic to match up various pairs of headphones, at least in terms of their ...
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2answers
185 views

Check if a filter is IIR or FIR

I have the following equation: $$H(z) = \frac{z^3+5z^2+3z+1}{10z^3}$$ I want to find out whether if its IIR or FIR. Here is the steps I have gone so far: $$H(z) = \frac{1}{10}\frac{z^3+5z^2+3z+1}{z^...
0
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2answers
218 views

How to generate realistic echo to sounds?

I guess the most straightforward way of adding an artificial echo to a sound signal is to add its time-delayed version to the original signal. However, I am not sure how realistic that would sound ...
0
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1answer
82 views

Deconvolution using response to an Heaviside

I'm measuring a "charge" signal in function of time from an amplifier. Here is a measured signal (x-axis is the time in some arbitrary units, y-axis is the charge in ADU): I would like to get the "...
0
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1answer
212 views

Initialize a Room Impulse Response using reverberation time(T60)

I am doing Speech dereverberation using Non-negative matrix factorization. I need to initialize an impulse response($H$) such that its reverberation time ($t_{60}$) is $300$ ms. Let the length of $H$ ...
0
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2answers
112 views

Simulating the impulse response of a multirate digital filter

I have designed a CIC filter in Verilog and I would like to test its impulse response, but I am not sure where to start from. My input sampling frequency is 51200Hz, the filter is a third order ...
2
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1answer
170 views

BPSK modulation under bandlimited channel

I modulated signal using BPSK modulation and I have series of -1 and 1. Now I have to pass these signal from band limited channel that has frequency response of the form $$\frac{s^2}{as^5+bs^4+cs^3+ds^...
0
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1answer
64 views

LTI system impulse response output [duplicate]

If I have a LTI system which has impulse response $h(n) = \left(\frac{1}{2}\right)^nu(n)$ and the entry is $x[n]=u[n]-u[n-1]$ where $u[n]$ is the unit step function. In order to find the output I ...
5
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4answers
369 views

Sine sweep vs impulse response

What kind of pros and cons does these method for identifying a system have? I seem to have a hard time finding literature discussion in this issue. I am operating on a linear system, or the linear ...
1
vote
3answers
117 views

Inputs for system identification

What effects does have a different input such as impulse, step, sine sweep etc. on performing a system identification? I mean what is up/down side, and which one is best, and why chose one rather ...
1
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1answer
1k views

What does it mean to deconvolve the impulse response

I am learning DPS and I came across the problem of deconvolution and removing the impulse response from a signal? This still does little sense to me. My understanding of the impulse response is to ...
0
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0answers
41 views

Find impulse response and frequency response through given filter [duplicate]

I cannot find anything truly helpful in my book, and I find mostly theoretical answers and not practical. So I am posting the exact exercise I want to solve, and through it I hope I'll work some ...
-2
votes
1answer
106 views

LTI system output

I compute the output of a LTI system, can someone tell me if my answer is right..? and help me with my others questions? The impulse response is: $h(n) = \left(\frac{1}{2}\right)^nu(n)$ , entry is $x(...
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1answer
88 views

Magnitude value of filter frequency response

Can someone help me with this problem: Suppose we filter signals with the below pre-emphasis filter: $$y[n]=x[n]-0.8x[n-1]$$ I have to calculate the impulse response of the filter (ok easy) and ...
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1answer
68 views

pre-emphasis filter - parameter a

Can someone give my a link to study to solve this problem. I can not find any formula for this problem... Suppose we filter singals with the below pre-emphasis filter: $y(n)=x(n) - ax(n-1)$ How can ...
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0answers
45 views

Filter sharpening; a stub

Filter sharpening is a technique to sharpen the magnitude response of a digital filter. Finding information online about it is problematic since almost all google hits will be about image sharpening (...
0
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2answers
225 views

Eigenfunction of LTI causal system Z-transform

I am studying for my DSP final and I came across this question from the Oppenhiem and Schafer book 3rd edition. The question says 3.18 A casual LTI system has the system function $$H(z)=\...
0
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1answer
321 views

Prove that time-reverse yields inverse filter for deconvolution?

In reading literature on the construction of impulse responses from sine sweeps (e.g. papers by Farina), I see it stated over & over that the way the impulse response is constructed from a (...
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0answers
156 views

Problem implementing deconvolution to recover an Impulse Response

I’m new to DSP programming and I’m trying to learn a bit about convolution and deconvolution and FFTs. I have a project where I am taking a signal (a sine sweep) and convolving it with a shorter ...