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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Digital Signal Processing Filters Problem

Hello I need some help with this question. $$𝑦[𝑛] = π‘Ž_1π‘₯[𝑛 βˆ’ π‘˜_1] + π‘Ž_2π‘₯[π‘›βˆ’ π‘˜_2] + 𝑏_1 𝑦[π‘›βˆ’ π‘˜_3]$$ 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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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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108 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 $x[n]= e^{jnΟ€/4}$

Hi I'm trying to solve the problem when studying for an upcoming test. The given solution is $1.2503 e^{jnΟ€/4 -0.2991}$, and is found by computing $H(Ξ©)$ and evaluating this at $Ξ©=Ο€/4$. when I try ...
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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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23 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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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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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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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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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
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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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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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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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27 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
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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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
51 views

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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119 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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72 views

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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1answer
51 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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50 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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57 views

Can time-invariance be determined from a given a transfer function?

I've the following function. $$ G(z) = 2 + \frac{-1+5z^{-1}}{(1-0.5z^{-1})(1-z^{-1})}$$ Calculating it's inverse using $\mathcal Z$-Transform, I get the following function: $$g[n] = 2\delta[n] + 8u[n] ...
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69 views

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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1answer
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finding onset of an impulse signal, basics?

New to signal processing, but making good progress, I think. I have a series of (many) impulses I generated, which will be used as impulse responses to model our church's acoustics, in this time of ...
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159 views

Behaviour of System by Impulse Response

In a book by Alan Oppenheim, it is given that for a LTI system, its characteristics are completely determined by its impulse response. But if impulse response of a system is basically an input output ...
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1answer
113 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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Find a LTI system such that $\mathcal{T}\{\frac{\sin t}{t}\} = \frac{\sin 2t}{t}$

Let $$x(t) = \frac{\sin t}{t} \qquad\text{and}\qquad y(t) = \frac{\sin 2t}{t}$$ Is it possible to find a LTI system such that $\mathcal{T}\{x(t)\} = y(t)$? If not, what's the reason for ...
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86 views

Impulse response of a time scaling system

Assume a bandlimited signal $X(t)$. Given that the output for this signal is $X(t/2)$, what will be the impulse response $h(t)$ of such a system? \begin{array}{l} X( \omega ) \ =\ \int ^{\infty }_{-\...
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113 views

What is the DFT of a binomial filter?

I hope this question is not too simple, I just started learning digital image processing. The 1D binomial filter of size 2 is defined by $B_2 = \frac{1}{4}\begin{bmatrix}1 & 2 & 1\end{bmatrix}$...
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Transfer function coefficients and impulse response - FIR filter

I am currently working on a FIR filter (varying in time). I have the real coefficients of the filter, but I would like to know if they correspond to the coefficients from the impulse response (as $b[k]...
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97 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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Why is there a negative in front of the phase response equation for this complex exponential?

first time on here! I'm working through "Digital Signal Processing using MATLAB" by Vinay and Proakis. Good book. I am stuck on this example tho. Shouldn't the imaginary part in the denominator (...
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2answers
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Argument of Dirac delta function is quadratic with complex roots

For example, we write $$\delta(at + b) = \frac{1}{|a|}\delta\left(t+\frac{b}{a}\right)$$ In a similar way, $$\delta(t^2 + t + 1)=\underline{\hspace{1cm}}$$ Thanks for the help. Purna.
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Composing two Impulse Responses

Pardon my layperson understanding. My application is audio design. What is the correct operation / algorithm to compose two impulse responses (IRa, ...
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84 views

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 to find the perfect regularization number?

I have an issue! Assume that we are going to solve $Ax=b$ but $x$ contains noise.To minimize that noise we can use regularization: $$x = (A^TA + \lambda I)^{-1}A^Tb$$ Where $\lambda$ is a small ...
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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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Why is $\delta[an]=\frac 1 a \delta[n]$ in discrete time?

Why is $\delta[an]=\frac 1 a \delta[n]$ in discrete time? Prove. Hi, I want to prove it but I don’t know on what facts to rely. In continuous time we have integral and dt in that integral that turns ...
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Extract Impulse Response of a System From its Input/Output Waveform

I am a new engineer for signal processing field. I want to extract the system impulse response from input and output of the system, i.e. so-called system identification, more specfically, for ...
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Design a LTI system which returns DC value of the input signal

Suppose that $h(t)$ is the impulse response of LTI system. The input signal $x(t)$ is periodic with period $T$. Determine $h(t)$ so that the output signal $y(t)$ only be the DC component of $x(t)$. Is ...
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How to extract two signals from one signal by selecting right index?

Assume that we want to solve $$AX=B$$ Where both $A, X, B$ are matrices. I solved this by using ordinary least squares: $$X = (A^TA)^{-1}A^TB$$ And I got this result for one column in $X$. Here ...
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LTI system impulse response [closed]

I am learning signal processing and need some help with this question $h[n]=-x[n]+2x[n-1]-3x[n-3]$ Given the following input signal $x[n]$ calculate y[n] the output of the system $x[0]=2, x[1]=0, x[...
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134 views

Unit impulse vs Kronecker delta vs Dirac delta?

Apparently these 3 terms are similar, but what is exactly difference between them and what is exact value of each of them at time zero,1 or infinity?
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102 views

Help understanding impulse response

I am having trouble understanding the impulse response function. I have a beam of 10 m long. I place 2 sensors, one at point A and one at point B. I then excite the beam at point E (shown in picture) ...
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74 views

Characterizing an unknown LTI system

What are the best approaches to characterize an unknown discrete time LTI system? I believe one of the approaches is to input a known input and measure the output to find a transfer function. What are ...
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31 views

Characterizing a non-LTI system

How should we characterize a non-LTI system? For example we have: $y[n]=x[3n]+x[2n]+x[n]$ which is clearly not LTI. Also, the impulse response will be $h[n]=3\delta[n]$ and if we take the DTFT of this ...

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