The impulse response of a dynamic system is its output when presented with a brief input signal, called an impulse.

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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 ...
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1answer
35 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
49 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 ...
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1answer
34 views

How to prove that this impulse response is stable?

This is the impulse response: Can anyone give a detailed method to prove that it is stable or not ?
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0answers
34 views

How to perform Wiener deconvolution in Matlab

I have an output signal y which is an input signal x convolved * with an impulse response ...
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1answer
33 views

What is a correct way to downsample an impulse train

So I have a signal which is caused by an impulse train. I can determine the impulse train with 500hz but sample my output signal with only 10hz. Then I want to calculate an impulse response function. ...
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2answers
34 views

linux commandline impulse response convolution reverb

I need to do an ir convreverb on a lot of wav files i got, always with impulse responses of different rooms. it does not have to be zero latency so even calculating the convolutional reverb would be ...
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0answers
15 views

Magnitude and Phasor Response of Direct Form 1

i want to draw the magnitude and phasor response of the given equation H(Z) = (0.0605 +0.121z^-1 + 0.0605z-2)/(1-1.194z-1 + 0.436z-2) i need Matlab code and also explain that how will i draw in my ...
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2answers
31 views

Re-recording audio vs. convoluting old audio data - differences?

I want to transform a studio audio dataset into a smartphone audio dataset (used for a speech recognition application). Would there be any difference in the resulting audio files using one of the ...
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0answers
9 views

Response to spatially varying impulse response

From this 2003 question paper: Is the following answer to part (a) correct: $$ g(x,y) = \{f*g\}(x,y) \\ = \int_m \int_n f(m,n) h(x-m,y-n) dm dn \\ = \int_n f(a,n) h(x-a,y-n) dn \\ = \int_n f(a,n) ...
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2answers
65 views

Convolving Room Impulse Response with a Wav File (python)

I have written the following code which is supposed to put echo over an available sound file. Unfortunately the output is a very noisy result which I don't exactly understand. Can anybody help me with ...
2
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2answers
73 views

Determining whether or not a system is BIBO stable

I'm trying to determine whether or not a system with impulse response $$ h(t) = \sum_{n=-\infty}^{\infty} \delta(t-2n) $$ is BIBO stable. I haven't touched this material for a very long time -- ...
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1answer
70 views

understanding discrete-time convolution in LTI systems

I'm trying to understand the discrete-time convolution for LTIs and its graphical representation. standard explanations (like: this one) start with the idea of decomposing an input signal $x[t]$ into ...
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4answers
222 views

What is meant by Impulse Response [duplicate]

I have read in all books that: Impulse(n) = 1 when n=0 , 0 otherwise So when we state impulse response of signal x(n) I do not understand what is its actual ...
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1answer
61 views

Find B given A and impulse response of B/A

Here is a small MATLAB function that computes B in B/A given A and the impulse response h of B/A ...
0
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1answer
48 views

Impulse response of the inverse system to the backward difference

I'm currently stuck on a problem. I have a DT LTI system $\mathcal{T}$ that depicts the first backward difference: $$y[n] = \mathcal{T} \{ {x[n] \} } = x[n] - x[n-1]$$ Its impulse response is ...
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2answers
83 views

Why impulse response

Why do people calculate impulse response? Generally systems are designed after modelling the possible input signals and calculating the appropriate filters for the desired outputs. Where does impulse ...
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2answers
360 views

Confusion regarding reverberation time (RT60) calculation

I have some confusions regarding reverberation time (RT60). I need to calculate reverberation time from a given power envelope. This is what I get. As you might see the line is curved close to zero ...
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2answers
338 views

How to calculate step and impulse response at multiple sampling rates

I'm struggling with a basic concept. Suppose I have a system $y(t)=e^{-at}u(t)\ast x(t)$ and I want to plot impulse response and step response using Matlab conv() function at various sampling rates. ...
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1answer
76 views

Inverse DTFT of $e^{-j\omega}$

I've been trying to solve the following problem, but I noticed that I get two different answers by means of two different techniques: Find the impulse response, $h(n)$, of the following system, ...
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1answer
97 views

Difference between real and complex impulse responses? [closed]

I want to know the characteristic differences between real and complex impulse responses. Thanks, JK
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1answer
54 views

Conceptual question from signal processing: impulse response and linear regression

In continuation to the previous question Conceptual questions from signal processing I have a doubt which is : Consider an Autoregressive model (AR(2)) : $y(t) = ay(t-1) + by(t-2)$ and a FIR (Moving ...
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2answers
75 views

What is the amplitude of the impulse resonse

I'm learning how to construct a discrete signal as a sum of impulse responses of the system. The final formula is then: $$ y[n]= \sum_{k= -\infty}^\infty x[n] h_{k}[n] $$ My question is, what is ...
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1answer
88 views

Property for time invariance of system in terms of its impulse response

From the textbook Signals and Systems by Oppenheimer ... If we define $h_k[n]$ to be the impulse response to $\delta[n-k]$, then for the system to be time-invariant, we must have $$h_k[n] = ...
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1answer
59 views

What is the impulse response for 2D functions

I study image processing and I am new to it. so my question is for example what is the impulse response for: $$ y(m,n) = 3\times x(m,n)+9 $$ $$ y(m,n) = m^2n^2 \times x(m,n) $$ where the $y(m,n)$ ...
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2answers
56 views

Computing impulse response for system with feedback terms

I'm trying to compute the impulse response for the following system: $$ y(n) = \frac{1}{2} \left( x(n) + x(n-1) \right) + \frac{1}{2} y(n-1) $$ and am told to assume that $y(-1)=0$. My solution: ...
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1answer
161 views

Differences between matlab's 'impulse' and 'lsim' command; create impulse response

I've got following problem: assume you've this continous system 1st order: $$ H(s) = \frac{1}{1+s} $$ s = tf('s'); sys = 1/(1+s); I'm going to discretize this ...
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0answers
42 views

Describing a time delay at a maximum for maxima and minima but tends to 0 elsewhere

I have two force-time signals obtained from a couple of force plates, corresponding to input/output signals for some system. Plotting the two together one of the first things I noticed was a time ...
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2answers
75 views

Impulse Response with non-delayed feedback

I've been trying to solve a Discrete LTI System problem where the overall impulse response of the following System, whose input and output sequences are, respectively, $x(n)$ and $y(n)$, has to be ...
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2answers
238 views

How to compute the impulse response from a transfer function

Say I have a transfer function, for example: $$H(z)=\frac{1}{1+0.1z^{-30}}$$ How can I compute the impulse response? (This is just an example, the important thing is that it is in closed symbolic ...
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1answer
129 views

How to calculate the zero state response?

In the following question and answer I kind of get it how it is calculated at surface but I don't get it fully. Can someone please explain the answer in depth?
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5answers
127 views

Frequency response creates non-causal impulse response

I have frequency response data. It is output from an acoustic simulator. I convert this into an impulse response, and get: In that picture the blue line is the impulse response. Mostly it is ...
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4answers
138 views

Impulse response of an LTI system

Why do we always characterize a LTI system by its impulse response and not another response like the step response, what does the impulse response have so special.
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2answers
550 views

Convert frequency response to impulse response

I am running an acoustic simulation. I put in a frequency and get out a complex number; the frequency response for that frequency. I wish to generate a 1024-sample impulse response (supposing my ...
3
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1answer
100 views

Analytical Calculation of the Impulse Response of an Arbitrary Filter

This is a rather general question. Suppose I have an arbitrary filter, $F$, defined in the Laplace domain; $$ F=k\frac{\prod_i (s+z_i)}{\prod_j(s+p_j)}. $$ How do I calculate the impulse response of ...
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2answers
82 views

What are the values on the x-axis when I plot the impulse response of a lowpass filter?

I am trying to develop a filtering routine, using Java, and I am using the windowing method. From my studies, I was told that if I make a plot of the impulse response of an ideal lowpass filter, I ...
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2answers
217 views

SRRC filter — filter span tradeoffs

I am simulating (in Matlab) the transmit portion of a comm system. I generate random data, then I want to modulate it to BPSK, pulse shape the data, and then potentially shift it up in frequency by a ...
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1answer
198 views

The impulse response, $h(t)$, of a system

I have this differential equation $$ y''(t) + y'(t) + y(t) = x(t) - 3x'(t) $$ I found the system response of the system: $$ H(f) = \frac{1 - 6\pi fj}{(2\pi fj)^2 +2\pi fj+1} ...
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2answers
216 views

Understanding Z-Transforms and Pole Locations

I am trying to gain a better understanding of pole locations in the Z-plane of a given discrete transfer function, $H(z)$. I think I have a pretty good understanding of how to use the Z-transforms ...
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0answers
164 views

Solving linear system and find impulse response

I have this linear system that is defined by the differential equation $$ y''(t) + 4y'(t) + 5y(t) = 2x(t) + 3x'(t) $$ with x(t) the input and y(t) the output. I'm asked to find two ...
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0answers
2k views

Difference between natural response and forced response?

Reference Second post on EdaBoard.com Time response of a system is the time evolution of the variables. In circuits, this would be the waveforms of voltage and current versus time. ...
3
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2answers
1k views

For a LTI system, why does the Fourier transform of the impulse response give the frequency response?

I know that for a given system, the Fourier transform of its impulse response gives its frequency response. I want to find where this property comes from, but haven't been able to find if it's a ...
2
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1answer
94 views

Guess the frequency response of a filter with little information

I have a processing unit that does a nice EQ filtering on soundfiles. The only thing I can do is : I give the original .wav file, and the processing unit gives me back the filtered .wav. I have no ...
0
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1answer
61 views

Implementing headphone transfer function (HPTF)

This document on HRTFs, A Spherical Far Field HRIR/HRTF Compilation, of the Neumann KU 100, talks about headphone compensation filters. Searching Google returns ...
0
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2answers
45 views

Combining HRTF with echo

I am experimenting with HRTFs. Specifically I'm trying to create 12 impulse responses that the brain can easily differentiate. The more distinct they are from one another the better. So I'm trying ...
0
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1answer
38 views

What is diffuse field equalisation?

I am using impulse responses from http://sound.media.mit.edu/resources/KEMAR.html These are available as either raw or diffuse-field equalized HRTFs. My question is: Which do I want? Raw, or ...
2
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2answers
551 views

Conceptually, how does real time convolution reverb work?

I've got an impulse response of a hall, it's 10 seconds long. Now say I want to apply this reverb to a wav file of some singing. I would perform a convolution of the data in two wav files and that ...
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3answers
164 views

inverse FFT when only a few time points are needed

I am developing C++ code to do some modeling that will take as input a parametric model of the complex frequency response (amplitude, phase) and produce as output an impulse response, e.g. using the ...
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1answer
91 views

Shift-Invariance of Dirac Comb?

Is a dirac comb a Linear and a shift Invariant System? I could prove the linearity, but I do not think it is shift invariant. How do do I prove it is shift variant?
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2answers
741 views

White noise vs. delta pulse and Ultraviolet catastrofe

Everybody explains that white noise has all frequencies equally strong. But, this immediately means that Ultraviolet catastrofe inevitably happens if power > 0 stays constant at any frequency and, ...