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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Stereo echo cancellation for stationary source locations: why does adaption stagnate?

In a stereo echo cancellation system, the echo path for the far-end-signal in the near-end room is estimated by an adaptive filter. Since the same signal is transmitted by two similar far-end paths, ...
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How can I correctly plot an impulse_response() of a discrete transfer function?

I posted this question on stack overflow and I think it was the wrong place so I moved it here. Hello, I'm new to python, I just want to use the control library and I'm slowly learning, I did my ...
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Impulse Response of a Moving Average System

According to Discrete Time Signal Processing by Al Oppenheim 3rd Edition, the impulse response of a moving average filter is as below My question is that shouldn't h[n] be having the dirac delta ...
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why is it so hard to simulate up and down position on headphones?

i'm wondering how come simulating front,back,left and right source position on headphones is easy but up and down is not ? (maybe even impossible ?) is it due to the shape of the ear ? but should we ...
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Impulse response of a transfer function

Lets say we have a transfer function from an LTI-system that goes as follows, and we want the impulse response for it: $$\frac{10\cdot e^{\left(-\mathrm{i}\right)\cdot \pi\cdot f\cdot 8}}{5+\mathrm{i}\...
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How is $\delta(at+b)=\frac{1}{|a|}\delta(t+b/a)$?

This result has been used in the second last line of the pic. I don't know why it's true. Both functions are zero for $t$ not equal to $-b/a$. But at $t=-b/a$, a scaling factor $1/|a|$ has been ...
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Phase response of an LTI-system

I've got an LTI-system such as follows: $$y'(t)+{2} y(t)={5} x(t-{3}), t>0, \\ \\ y(0)=0 \ \text{ ja } x(t)=0, \ t<0.$$ From this i've already figured out the transfer function: $$H(f)=\frac{5\...
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How do impulse response guitar amp simulators work?

I am wondering how impulse response guitar amp simulators/modelers work. I thought it was a matter of convolving a signal of recorded impulse response in time-space with a guitar sample. I tried to ...
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31 views

FFT frequency-magnitude not correct when a positive gain EQ point is applied

I have a measurement system, which applies a log sine sweep as stimulus to a DUT and records the return signal. I then extract the impulse response, and perform an FFT on this to examing phase and ...
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What exactly is stored in the buffer array in the code below? Is it the values of x[n-k] or something else?

What exactly is stored in the buffer array in the FIR Filter code below? Is it the values of x[n-k] or something else? ...
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Impulse response of an infinite-length system

I have a system which is expressed as following: y[n] + $\alpha$ y[n-N] = x[n] where y is the output and x is the input. When I take the z-transform of both sides, I've found the transfer function ...
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A signal $g(t)$ is passed through a squaring device and then through an LPF such that bandwidth of the LPF tends to 0

I am solving a question, where a signal g(t) is passed through a squaring device and then through an LPF such that bandwidth of the LPF tends to 0. I understand that since for this filter the ...
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66 views

impulse response VS zero-input response

I am new in the field of systems and signals, and I have a rather basic for the majority of the group, question: Can we find the impulse response function of homogeneous ODE, instead of its zero-...
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23 views

replace input signal with δ will have the impulse response of the function?

Is my impulse response right? By definition,the impulse response is the output when the input is a impulse signal,so $y[n]=\sum\limits ^{n}_{k=-\infty}\frac{1}{2^{n-k}}\ x[k]$,the impulse response ...
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51 views

Finding the impulse response of a system

I have the following transfer function. $$ H(j\omega) = \frac{1+0.5 e^{-j\omega}}{1-1.8 \cos(\frac{\pi}{16}) e^{-j\omega}+0.81 e^{-j2\omega}}$$ I'm trying to find the impulse response of the system. ...
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Find the length of the impulse response of a Linear Phase Type 4 FIR filter

The length should be found such that the group delay is minimum It is given that the impulse response is real. One zero of the Transfer function is at $0.6e^{j\frac{\pi}{4}}$, and another one is at -...
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Why does knowing the impulse response allow you to determine the output for any LTI system?

Going over some notes on LTI systems and I’m quite confused about how knowing the impulse response of a system allows us to recover the systems’ response to any signal. In the textbook screenshot ...
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60 views

How does minimum-latency partitioned convolution reverb work when you receive input samples in chunks, rather than one at a time?

I'm writing a reverb system where I receive an input block of samples 480 elements long, do some operation on them, and pass the block on to the next effect. I've been reading up on partitioned ...
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obtain the differential equation from the impulse response

Assuming the equation: $y_3 = h_e(t)\ast (C_2\cdot Sigm(C_1\cdot y_0)+p)-h_i(t)\ast (C_4\cdot Sigm(C_3\cdot y_0))$ by $\ast$ : convolution $Sigm()$ : sigmoid function Impulse functions: $h_e=A\...
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I need to insert an underwater acoustic channel model to an existing code that compared between OFDM and GFDM

The acoustic channel model that I have will output the channel impulse response. However, my signal is modulated in frequency domain (by doing fft). Hence, I want to obtain a frequency response of the ...
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How to get the inverse of Filter based on channel

Given a signal $X$, and a channel $h$, and the received signal $Y = Filter(h,1,X);$ What's the inverse of filter, it means if I know $h$, how can I get back $X$ ?
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59 views

Convolution between two vectors. Length and normalization

I have an RIR vector $h[n]$ with $N$ samples and an audio source $x[n]$ with $M$ samples. I wish to simulate a 5 seconds audio segment with $x[n]$ randomly located within (timewise). Using MATLABs <...
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Difference between the two forms of input-output relationships of an LTI system

$$y(t)=f(t)*h(t)\tag{1}$$ $$y(t)=H(s)e^{st}\tag{2}$$ $$H(s)=\int_{-\infty}^{\infty}h(t)e^{-st}dt\tag{3}$$ Let $f(t)$ in Eqn $(1)$ be $e^{st}$. In many worked out examples, I have found that the two ...
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Arbitrary shaped RIR generator

I wish to simulate some sound sources convolved with a Room Impulse Response (RIR) and impinging on a spherical microphone array. I could find a couple of generators online (such as this one), though ...
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56 views

Help regarding property of unit impulse function

We know that using properties of unit impulse function it can be shown that $$\int_{t_1}^{t_2} x(t) \delta^{(n)}(t-t_0) dt=(-1)^nx^{(n)}(t_0),\quad t_1<t_0<t_2$$ (source: Continuous and ...
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107 views

Finding impulse response of an RC circuit from its step response [duplicate]

I have to find the impulse response of an RC circuit (c up ). I have to find it from the step response $g(t)$. I found that $V_i - V_c - V_r = 0$ , with $V_r = V_u$ So $V_u = V_r = R I_r$ , with ...
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42 views

Impulse Response Function-Green's Function

Assuming a input-output system $$u(t) = c \cdot \big(h(t)\circledast m(t) \big)$$ where its impulse response function is: $$ h(t) = \begin{cases} \frac{A}{\tau}te^{-\frac{t}{\tau}}, &...
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58 views

Computing response of LTI system in terms of its step response

I have solved a problem, Kindly help me in determing if I solved it correctly. I will post the question and my own working below. Problem My working
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145 views

pole/zero plot & impulse response

in a mock exam of dsp was asked this question, and even in knowing how to compute DFT's of the plot, I wondered if there was a fast way of pairing these plots to their respective impulse response? ...
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52 views

Missing delay in heavyside step function

I found the following task that was inspired by an example in the book A. V. Oppenheim and R. W. Schafer, "Discrete-Time Signal Processing", 3rd Edition, 2014. Task: Consider the 2nd-order IIR ...
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Time gating of FFT for audio Measurements or Multi Time Windowing

I am learning more about DSP specifically for audio measurement purposes. I can an app, where I can create a log sine sweep from start frequency to end frequency over a certain length. I can perform ...
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Determining position and g-forces from accelerometer and gyroscope data

I'm analyzing gyroscope + accelerometer data acquired from an IMU for a run of a water skiing slalom course, sampled at 100Hz. The double spikes represent spurious ~15G jitter from crossing both ...
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92 views

My impulse response does not tend to zero

I am doing an IFFT of frequency response data achieved with Simulation tools. When I plot my impulse response it looks wrong as the response does not tend to zero as it should. Instead there seems ...
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What is difference between natural response and zero-input response of a system and how to find natural response? [duplicate]

In most books it is said that natural response is another name to zero-input response while in some resources is is mentioned that the classification is based on poles of transfer function and input....
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Methodology for log some sweep audio measurement impulse response

I am trying to implement a method for measuring the response of a loudspeaker in a room using a log sine sweep stimulus. To check my method: 1. I create the stimulus using: Make recording length ...
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Solving impulse response using summation of singularity functions

I'm stuck at Problem 2.56 of Alan Oppenheim's Signals and Systems book. Here is the solution given. I did learn basic differential equations before from Boyce's book but I have never encountered ...
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Simple Impulse Response DSP Hardware

I developed some complex chains of filters and crossovers. After that I have created IRs from the entire chains. Applying these IRs in software works perfectly. Now I wonder what is the easiest (and ...
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What is the difference between an impulse response and a kernel?

It seems to me they are two terms used to refer to the same concept, but, according to the Wikipedia page on Guassian filter a Gaussian filter is a filter whose impulse response is a Gaussian ...
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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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55 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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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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315 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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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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705 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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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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135 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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96 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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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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59 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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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 ...