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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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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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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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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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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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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How to determine a number of taps in channel

I need to determine the number of taps of a channel. I have the channel simulated via channel simulator. My task is to try to estimate the channel by using pilots position. How the channel was ...
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75 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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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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LTI system response to finite length pseudorandom noise [closed]

I am trying to understand how an LTI system responds to pseudorandom noise. Periodic pseudorandom noise has a spectrum that is an impulse train. If it is an input to an LTI system the frequency ...
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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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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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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 ...
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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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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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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
37 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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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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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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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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1answer
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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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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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1answer
162 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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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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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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166 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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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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209 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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2answers
147 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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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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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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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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255 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
56 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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54 views

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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