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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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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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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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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86 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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1answer
29 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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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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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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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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89 views

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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158 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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539 views

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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471 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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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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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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1answer
157 views

Is there a way to determine the quality of an impulse-response relationship?

I'm new to system ID so be gentle. I have a modeled signal of streamflow that I would like to map to an observed signal of stream height. This lends itself nicely to a simple impulse-response kind of ...
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1answer
131 views

How to convert multi-band Energy Time Curve (ETC) to Impulse Response (IR)?

I am running my own sound simulator. Now I have obtained the Energy Time Curve (ETC, expressed by energy) by physical simulation, and they are stored in 8 discrete frequency bands (because decay of ...
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Multiplication of two impulse function $\delta(t)\cdot \delta(t)=?$

If a impulse function is mulplied with a function $f(x)$ then the formula will be apply $$f(x)\delta(x-a)=f(a)\delta(x-a)$$ so from this formula mulplication of two impulse function will be $$\...
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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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Impulse response from frequency response in Matlab

I am trying to design equalization filter and therefore I want to define my own amplitude and phase response and then to obtain the impulse response of the filter. I thought that the output of the ...
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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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113 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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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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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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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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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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114 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
55 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
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Identifying impulse based on experimental data

I have conducted an experiment in which the impulse was exerted on sound bowl (it was hit by a hammer). As a result I have obtained acceleration from accelerometer on 3 axis, calculated net ...
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104 views

impulse response cascaded with time reversed of itself

Consider a filter with real-valued impulse response $h[n]$. The filter is cascaded with another filter whose impulse response is $h'[n] = h[-n]$, i.e. whose impulse response is the time-reversed ...
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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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Calculate Impulse Response of a System From Its Input/Output Waveform via FFT

From the theory, I knew something like : $y(n) = x(n)*h(n)$ $Y(n) = X(n)H(n)$ $H(n) = \frac{Y(n)}{X(n)}$ Now I have $y(n)$ and $x(n)$ from a system, and $y(n)$ is 2176 samples long, $x(n)$ is 2176 ...
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How can i derive step response in terms of impulse response from the convolution sum?

If it is discrete LTI system, How can i derive step response in terms of impulse response from the convolution sum?
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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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54 views

What do the function blocks mean?

What I don't understand is what exp(.) and ln(.) mean. For example y(t) and ...
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325 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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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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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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1answer
167 views

How to get Step Response from an Impulse Response in Simulink?

Im sorry if it seems like a trivial question but I am confused right now. Im currently watching my professors lecture. And he basically has $\lambda(t)$ as ...
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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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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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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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Question about ideal filters

Following shows the discrete time Fourier transform of an ideal low pass filter with cutoff frequency $\omega_c$: $$H\left(e^{j\omega}\right) = \begin{cases} 1, & \text{if $|\omega| \le \omega_c$...
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1answer
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Determining a system's causality using its impulse response

I have the following input-output relation for a system: $$y(t) = Odd Part Of [x(t)]$$ My question is: Is the system causal? What my approach has been: I expressed $y(t)$ alternatively as: $$y(t) = \...
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186 views

Impulse response if initial conditions are given

In most books, impulse response of LTI systems are calculated by assuming initial rest condition, but how to calculate response of an impulse input if there are some initial conditions present ? My ...
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Convolution : Anechoic Speech signal and Impulse response

I am trying to perform convolution in MATLAB of an anechoic speech signal (2.1 s) and a impulse response (20 s) using the following code: ...
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54 views

Impulse Invariant method for digital filter design

One of the known methods for discretizing analog filters is impulse response invariant. We get the impulse response in time domain, discretize it and then get the Z transform. What I am trying to ...
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1answer
77 views

Drawing conclusions from impulse response of a discrete LTI system

I have an impulse response of an LTI system which is h(n)= n*u(n)-u(n-2) where n=[0,3] (1) Now regarding the stability and causality of this system, i've drawn the ...
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Kernel vs impulse response: what's the difference? [duplicate]

I am reading The Scientist and Engineer's Guide to Digital Signal Processing by S.W. Smith. In Chapter 9: Applications of the DFT in the 3rd paragraph he writes "kernel (impulse response)" ...

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