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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6answers
461 views

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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1answer
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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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1answer
30 views

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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2answers
228 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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4answers
107 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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2answers
83 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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0answers
38 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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2answers
45 views

Impulse response of an LTI system given the input and output signals

I have been given the input and output signals of an LTI system as: $x[n] = (\frac{1}{2})^nu[n] + 2^nu[-n-1]$ $y[n] = 6(\frac{1}{2})^nu[n] - 6(\frac{3}{4})^nu[n]$ I have found the system function $...
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0answers
54 views

MATLAB- Add Envelope to Sound Signal

I’m in the process of making a convolution reverb and I’m trying to add an envelope to my impulse response signal and plot it in order to change the RT60 of my sound signal (Just a song). I’ve looked ...
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4answers
189 views

why only impulse signal for convolution?

Why do we only use impulse response for convolution for getting output of LTI systems. why we don't use unit step or any other signal for this purpose?
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1answer
788 views

Determing inverse Z-transform using impulse response?

In Matlab there is a command iztrans for finding inverse Z-transform. But how can we find inverse Z-transform using impulse response? The Matlab command ...
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1answer
73 views

Relation between impulse response and Region of convergence?

Is there any relation between impulse response and Region of convergence?Means position/location of ROC depends upon impulse response or not?? Please kindly guide about cases for both continuous and ...
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1answer
85 views

Impulse response measurement : practical questions

To measure system impulse response I can do the following steps : system input : it is excited with an excitation signal having a duration t_exc with a bandwidth bw_exc (for example sine linear sweep)...
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0answers
71 views

Relation between PDP (Power Delay Profile) and channel impulse response

I am traying to perform a simulation in Matlab and I faced up with some practical/theorical problems. The channel I want to simulate is frequency selective fading. The packets are short compared with ...
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1answer
129 views

Proving linearity and time-invariance

This question was asked in one of our quiz. Question is Determine if the system with the input-output relationship given by $$y(t) = \int_{t-10}^{t} \cos(\tau)x(\tau)d\tau$$ is linear and time ...
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1answer
62 views

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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2answers
112 views

Cross-correlation of maximum length sequence with noise

Background I am using a maximum length sequence to find the impulse response of a linear system. I want to calculate the expected SNR. I know that my signal amplitude is scaled by the length of the ...
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1answer
218 views

How to normalize frequency response charts

I want write a simplistic program that can transform a high-quality voice recording in a way that it sounds like it was recorded using a specific low-quality microphone. I have obtained the mic's FR ...
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1answer
48 views

convolution expression h(n,k) = h(n-k)

As a new to DSP concepts want to understand the meaning of impulse response and why we do $h(n-k)$ in convolution and $h(n+k)$ in correlation.
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1answer
38 views

Impulse response of a system in z domain

The question 3-23 in the "Discrete-Time Signal Processing - Second Edition" is: and the solution is: I cannot understand the solution. In the second row of the answer when I multiply (-4) with ...
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1answer
158 views

Impulse and step response

While trying to determine the unit step and impulse response for a discrete LTI system I had several problems: $$ \begin{aligned} (Hx)[n]&=(Hx)[n-1]+\frac{1}{N}(x[n]-x[n-N]) \\x[n]&=(Hx)[n]=0\...
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1answer
905 views

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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1answer
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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1answer
52 views

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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1answer
157 views

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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3answers
102 views

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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0answers
55 views

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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3answers
2k views

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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0answers
39 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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1answer
36 views

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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2answers
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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1answer
46 views

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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3answers
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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1answer
28 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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1answer
79 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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1answer
82 views

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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2answers
291 views

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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1answer
294 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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1answer
63 views

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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2answers
193 views

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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1answer
489 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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1answer
108 views

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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1answer
25 views

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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2answers
263 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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1answer
315 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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1answer
80 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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1answer
72 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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1answer
630 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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1answer
58 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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2answers
204 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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