Questions tagged [impulse-response]
The impulse response of a dynamic system is its output when presented with a brief input signal, called an impulse.
339
questions
75
votes
4answers
201k views
What is meant by a system's “impulse response” and “frequency response?”
Can anyone state the difference between frequency response and impulse response in simple English?
27
votes
6answers
17k views
Flipping the impulse response in convolution
During convolution on a signal, why do we need to flip the impulse response during the process?
15
votes
1answer
9k views
How do I find a system's impulse response from its state-space repersentation using the state transition matrix?
Suppose we have a linear represented in the standard state space notation:
$$ \dot{x}(t)=Ax(t)+Bu(t)$$
$$y(t) = Cx(t) + Du(t)$$
In order to get its impulse response, it is possible to take its ...
14
votes
2answers
1k views
What bandpass filter design will yield the shortest impulse response?
Designing a simple 2nd order IIR bandpass Buterworth filter with a centre frequency of 500 Hz and a 1 octave bandwidth gives me the following frequency response ...
Now, if I take the impulse ...
10
votes
5answers
6k views
Why do linear systems show sinusoidal fidelity?
I am looking for a proof for sinusoidal fidelity. In DSP we study a lot about linear systems. Linear systems are homogenous and additive. One more condition it satisifies is that if a signal is a sine ...
8
votes
2answers
3k views
Does this lowpass filter have a noncausal impulse response?
I'm doing some measurements with my sound card, I have one output channel connected to one input channel.
I then send the sound card a unit impulse, i.e. a signal 1 value followed by zeros.
The ...
8
votes
2answers
3k views
Why do linear phase filters have symmetric impulse responses?
It was given as a fact that linear phase filters have symmetric impulse responses, but I don't see why that has to be true. Can somebody please explain or prove this?
8
votes
2answers
299 views
Evaluating loudspeakers
If you don't have a lot of money to spend but you want to estimate the frequency response of different loudspeaker setups what is the best way to do it?
I bought a very nice microphone and built a ...
8
votes
2answers
3k views
How to estimate the number of taps needed for subsequent channel estimation algorithms?
I recently implemented an MMSE channel equalizer, and I have read about many other types of channel estimation/compensation algorithms out there. However, one thing that is never talked about it how ...
8
votes
1answer
3k views
7
votes
3answers
13k views
For an LTI system, why does the Fourier transform of the impulse response give the frequency response?
I know that for a given system, the Fourier transform of its impulse response gives its frequency response.
I want to find where this property comes from, but haven't been able to find if it's a ...
7
votes
2answers
19k views
How to obtain impulse response from the differential equation of a system?
This year I'm having trouble with my Signals and Systems class. My major subject is Software Engineering and Electric and Electrical Engineering is my Minor. This question was my previous exam ...
7
votes
7answers
716 views
Intuition behind commutativity of convolution in LTI systems
Why is convolution commutative, as it seems to treat two signals in a different way in an LTI system?
If you imagine $y[n] = x[n] \star h[n]$ with $x[n]$ being an input signal and $h[n]$ being the ...
7
votes
1answer
227 views
How to send / receive a short impulse in an extremely noisy signal with high timing accuracy?
I am pretty new to DSP. I need a computer to transmit data to a receiver through audio signals in a loud outdoor environment. (I am writing the software for both sender and receiver so I can design ...
6
votes
2answers
12k views
Calculation of Reverberation Time (RT60) from the Impulse Response
I have some confusions regarding reverberation time (RT60). I need to calculate reverberation time from a given power envelope.
This is what I get. As you might see the line is curved close to zero (...
6
votes
3answers
5k views
Conceptually, how does real time convolution reverb work?
I've got an impulse response of a hall, it's 10 seconds long.
Now say I want to apply this reverb to a wav file of some singing. I would perform a convolution of the data in two wav files and that ...
6
votes
1answer
4k views
How do real-time convolution plugins process audio so quickly
Okay, so in Logic Pro I can load up a Space Designer plugin (convolution reverb) with an impulse that's 9.1 seconds long, turn my mic on, and get real-time convolution reverb as the mic records ...
6
votes
1answer
323 views
How to derive $r(t) = c(t) \circledast \frac{1}{2} h_b(t, \tau)$?
Consider a linear time-variant channel. The transmitted signal is $x(t)$, the channel impulse response is $h(t, \tau)$, and the received signal is $y(t)$. Then
$$ y(t) = \int_{-\infty}^\infty x(\tau) ...
6
votes
3answers
3k views
Sine sweep vs impulse response
What kind of pros and cons does these method for identifying a system have?
I seem to have a hard time finding literature discussion in this issue.
I am operating on a linear system, or the linear ...
5
votes
3answers
2k views
How do impulse response guitar amp simulators work?
I am wondering how impulse response guitar amp simulators/modelers work. I thought it was a matter of convolving a signal of recorded impulse response in time-space with a guitar sample.
I tried to ...
5
votes
6answers
546 views
Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter
I would like to approximate a moving average filter with an IIR filter of much lower order than the tap-length of the moving average filter. Optimality shall refer to the $L_2$ norm of the impulse ...
5
votes
4answers
3k views
Why is the first value in digital first-order IIR filter impulse response not the largest?
When I create a digital first-order IIR low-pass filter with scipy (code below), I get the following coefficients:
B: [ 0.1367 0.1367]
A: [ 1. -0.7265]
The ...
5
votes
3answers
355 views
Rough estimate of how close a human speaker is to a microphone?
Is there a known technique for estimating how close a human speaker is to a single microphone? I'm hoping that there is a known technique that can analyze an incoming audio signal that contains a ...
5
votes
2answers
624 views
Understanding $\mathcal Z$-transforms and pole locations
I am trying to gain a better understanding of pole locations in the $z$-plane of a given discrete transfer function, $H(z)$. I think I have a pretty good understanding of how to use the $\mathcal Z$-...
5
votes
2answers
6k views
Given the input and the output, how to determine the impulse response?
I would like to find the impulse response, $h[n]$, of an LTI system given the input
$$x[n] = [1,-3,2]$$
and the output
$$y[n] = [1,-1,-4,4]$$
I know that $y[t]=x[t]*h[t]$, but I am having hard ...
5
votes
5answers
3k views
Time-varying “impulse response”
According to many references [1,2], the time-varying "impulse response" can compute wireless channel output $y(t)$ at time $t$ using the following expression:
$$
y(t) = \int h(\tau, t) x(t - \tau) d\...
5
votes
2answers
4k views
Complex impulse response functions?
I think I must have misunderstood something regarding the relation between impulse and frequency responses.
I have calculated the Impulse Response Function, IRF, from the Frequency Response Function,...
5
votes
2answers
858 views
Does the impulse response of a system have any physical meaning?
In other words, what does the impulse response tell us about the characteristics of the system? For simplicity, let's assume we deconvolve a discrete output and a discrete input to obtain an impulse ...
5
votes
3answers
2k views
Estimating the Impulse Response of the Room Using Sweep Signal Microphone Recorded Signal (Input & Output of a Convolution)
I played this signal A (a 20Hz to 20000Hz sinusoidal sweep in 10 seconds) with a studio monitor speaker in a big church, and I recorded the result B with good microphones.
The result is very reverb-...
5
votes
1answer
2k views
Concept of finding forced response from difference equation?
I know how the process works, first from difference equation make a homogeneous equation and then find natural response , then find a particular response (in the form of input) substitute it back in ...
5
votes
0answers
385 views
Impulse Response / Frequency response Question [closed]
I have a major question. Please take a look.
I have this differential equation (DE):
$$
\frac{d^2y(t)}{dt} +\frac{dy(t)}{dt} +4y(t)= \frac{dx(t)}{dt} +2x(t)
$$
And I have to find impulse response (...
4
votes
5answers
683 views
Can two different impulse responses give the same frequency response?
I have two different impulse response each with different length, is it possible that they have the same frequency response?
4
votes
1answer
160 views
Guess the frequency response of a filter with little information
I have a processing unit that does a nice EQ filtering on soundfiles.
The only thing I can do is : I give the original .wav file, and the processing unit gives me back the filtered .wav. I have no ...
4
votes
3answers
633 views
Recover Filter Coefficients from Filtered Noise
I have a digital signal which may be represented as a pulse noise source filtered with an FIR (finite impulse response) filter. Suppose that the noise consists of discrete pulses (nonzero samples ...
4
votes
1answer
6k views
find impulse response from step response
if we have LTI system and we know unit step response of this system(we haven't original signal)
how we can calculate impulse response?
4
votes
1answer
4k views
Estimate the Filter Coefficients of 1D Filtration (Convolution)
I have an output signal $y$ which is an input signal $x$ convolved $\star$ with an impulse response function $h$ with some added noise $n$ :
$$y(t) = h(t) \star x(t) + n(t)$$
I know the input signal ...
4
votes
1answer
492 views
Impulse Response Question
For the differential equation
$$\frac{d^2y(t)}{dt^2}+\frac{3dy(t)}{dt} + 2y = x(t),$$
I was able to find the frequency response as $$H(j\omega)= \frac{1}{-\omega^2+3j\omega+2}.$$ However, I am not ...
4
votes
1answer
2k views
How to identify impulse response of noisy system?
My lecture slides mention that two-level ("2-tasoiset" in Finnish) signals are good in identification with linear systems. I am trying to understand this in noisy system. I cannot find any method ...
4
votes
1answer
319 views
Can I assume system is LTI when given by DTFT of impulse response
I'm having hard time to grasp it probably because i don't fully understand it.
I understand that when a system is given by $h(t)$ (in general $h(t-\tau)$) i can assume that it is a LTI system.
So i ...
4
votes
1answer
2k views
Group Delay of a system
Say I have an LTI system whose impulse response h[n] is:
$$
h[n] = \delta[n] + \delta[n-4]
$$
I want to find the group delay of this system. I know the group delay ($grd$) is defined as:
$$
...
4
votes
1answer
13k views
Get an input signal from LTI system output, find impulse response
I just study signal processing and I have some questions.
How to find impulse response $h[n]$ sequence of the system if I have
$x[n]$ and $y[n]$ (input and output) sequences? Hope there is a formula
...
4
votes
2answers
1k views
Example of an LTI system with complex impulse response
In general, I know that the impulse response $h(t)$ of an LTI system can be complex. However, all of physically realizable, useful systems I've come across have purely real impulse responses. I did a ...
4
votes
1answer
13k views
Identifying the magnitude and impulse response from pole zero plot quickly
I have an exam next week and it's verty certain that a task of this kind will be there.
Are there some good tips how to match the right pole zero plot to the right responses? No proof is needed in ...
4
votes
1answer
323 views
Measuring noise floor in an impulse response
Say I have an impulse response...
(an envelope of the actual IR obtained using the Hilbert transform)
... question: how do I calculate the surrounding noise level?
Visually this looks to be ~ -54 dB ...
4
votes
3answers
2k views
Impulse Response to LTI
I am new to DSP, and I am self-studying using mostly Proakis. I have a question. There are some examples in the text where you will be given the impulse response of an LTI system, and then asked to ...
4
votes
1answer
425 views
BPSK modulation under bandlimited channel
I modulated signal using BPSK modulation and I have series of -1 and 1. Now I have to pass these signal from band limited channel that has frequency response of the form $$\frac{s^2}{as^5+bs^4+cs^3+ds^...
4
votes
1answer
545 views
Analytical Calculation of the Impulse Response of an Arbitrary Filter
This is a rather general question. Suppose I have an arbitrary filter, $F$, defined in the Laplace domain;
$$
F=k\frac{\prod_i (s+z_i)}{\prod_j(s+p_j)}.
$$
How do I calculate the impulse response of ...
3
votes
6answers
430 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 ...
3
votes
3answers
100 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 ...
3
votes
1answer
456 views
What is the relationship between passivity of impulse response and passivity of the system?
What I mean by passivity of impulse response is that the energy of impulse response for this system is less than the input impulse signal energy.
For example, in a discrete-time system, considering ...
