What is Impulse response: Definition and 86 Discussions
In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system).
In all these cases, the dynamic system and its impulse response may be actual physical objects, or may be mathematical systems of equations describing such objects.
Since the impulse function contains all frequencies, the impulse response defines the response of a linear timeinvariant system for all frequencies.
Hello friends,
I have a problem with a exercise sheet. Given is the impulse response of a discret element. The task is to draw the block diagram. But I think that the solution in the sheet is wrong. Because based on the difference equation (Exercise.pdf) there should be 3 delay elements. I have...
As the title says, I am studying this topic for my control systems fundamentals course. I think I intuitively understand the meaning of the convolution integral that relates input, output and the impulse response, but I am failing to prove it graphically.
For example, the intuitive explanation...
Homework Statement
Hi there, I've been trying to gain some intuition on how the convolution sum works, but as I dig deeper I am realizing that there is an issue with my intuition of signals and systems, in particular the unit impulse response.
My issue is trying to understand how a unit...
Homework Statement
Homework Equations
Find laplace of x(t) and h(t)
Multiply the laplaced values to get Y(s)
Find inverse laplace to get y(t)
The Attempt at a Solution
In book the circled term isn't there. Why does that go away?
Book gets y(t) as
In laplace why does the e5t term go away?
Homework Statement
Homework Equations
Use Laplace then multiply in laplace domain then do laplace inverseThe Attempt at a Solution
Book answer is A
I don't get the first term of eat in option A.[/B]
Homework Statement
Hello everyone,
In the following problem I have to find the unknown impulse response g1(t) given the input and output signals, as shown below:
(the answer is already there, at the moment I am trying to understand how to get there).
Homework Equations
[/B]
I have...
Hey guys I was just studying for finals and I came across something in my textbook that either wasn't explained properly or something I just don't get.
So this page explains that the coefficient of y_n[k] is A_0, which is represented by b_0/a_0, I can see that a_0 is determined by multiplying...
I bolded the portions I need help with.
1. Homework Statement
A series circuit consists of a resistor with a resistance of 16 ohms, an inductor with inductance of 2 H, and a capacitor with a capacitance of 0.02 F.
At time t = 0 there is no charge on the capacitor and no current in the circuit...
Hello,
I am trying to estimate transfer function of unknown LTI system, given output and assumed input as point process.
I have measurement of output, while input, which is assumed to be point process, could be created synthetically using known times and amplitudes.
My questions:
1. What is...
Homework Statement
I have an impulse response h(n)=e^(0.1n)*[u(n)u(n8)] and an input x(n)={0,1,2,3,0}, how do I find the output y(k)?
[/B]Homework EquationsThe Attempt at a Solution
i don't even know how to solve. should i try convolution or should i substitute the values of x(n) in h(n)...
Hi!
I don't know if I'm in the right forum of this site but I'm trying anyway. I was just wondering if someone could explain how the step and impulse response is related to an angular position (of e.g. a spacecraft )? Just a little about the theory since I am trying to actually understand...
Homework Statement
Consider a LTI system defined by the following difference equation: ##\mathrm{y}[n]=2x[n]+4x[n1]2x[n2]##
a) Determine the impulse response of the system
b) Determine the frequency response of the system
Homework Equations
DTFT...
Homework Statement
Consider a LTI system for which the filter coefficients are ##{\mathrm{h}_k}=\{1,2,1\}##. Find the output when the input is ##\mathrm{x}[n]=3\mathrm{cos}(\frac{\pi}{3}n\frac{\pi}{2})3\mathrm{cos}(\frac{7\pi}{8}n)##. Identify two frequencies in this composite signal. Show...
Hello. I would need some clarifications about the impulse response of a RC circuit.
1. Homework Statement
Find the impulse response relative to the vc(t) voltage.
NOTE: delta(t) is the exact dirac's delta of infinite amplitude, not an approximated peak.
Homework Equations
δ(t) = d θ(t) /...
Homework Statement
I would like to know a way to design an impulse input in a Matlab Simulink model. I know there are step input and ramp input blocks but there is no impulse input block.
Homework Equations
The Attempt at a Solution
If any working is needed please let me know
Homework Statement
Find the impulse response for the systems governed by the following equations:
3y(t)'+5y(t)=x(t)+x(t)'[/B]Homework EquationsThe Attempt at a Solution
I tried to obtain the homogeneous solution for h(t)[/B]
and then I failed to obtain the coefficients of the solution
Homework Statement
An electrical network has the unitimpulse response :h(t)=3t⋅e4t .If a unit voltage step is applied to the network, use the convolution integral to work out the value of the output after 0.25 seconds.
Homework Equations
Convolution integral: y(t)=f(t)*h(t)
Unit step...
Homework Statement
Where $$v = y  bu$$
It's given that the transfer function is
$$h(t) = b u(t) + v(t) = b \delta(t) + e^{at}b \mu(t)$$
Homework EquationsThe Attempt at a Solution
I can't seem to figure out how the impulse response above was found. I understand that the impulse response is y...
It is theorem of any course on signals that a linear time invariant system, whether in discrete or continuous time, is BIBO stable if and only if its impulse response is summable. The fact that summability implies BIBO stability is easy to prove. In fact, it's on the wikipedia page of BIBO...
I saw in some books, that:
Y(s)/X(s) = H(s)
where,
Y(s) is the laplace of the output
X(s) is the laplace of the input
H(s) is the laplace of impulse response.
How to prove it? In the book Benjamin Kuo, he only mentions it without proof, and did not find it in the book of Oppennheim.
Hi, I have a discrete system with input x(t) and output y(t).
Using the formula frequency response H(f) = y(f)/x(f) in the Fourier domain.
Does this mean to find the frequency response I have to take the Fourier Transform of
y(t) to get y(f) and divide it by the Fourier transform of x(t) ...
Homework Statement
I am having some problems to derive Inverse Fourier transform of sinc function & exponential function. It's actually for getting the Impulse response from the given frequency response [which comprises of both sinc function & exponential function]. Also need to know the...
y(n) = a * y(n1) + K * b * x(n1) + K * x(n), where a < 1.
(a) Calculate its impulse response, h(n).
the homogenous equation is l^n1(la) = 0 => 1 = a
so h(n) = [ka^n ] u(n)
(b) Calculate its step response.
I can't seem to find any examples online and my book says nothing...
Homework Statement
Consider the frequency response H(e^jw) = e^j3w(5 + cos(w) + 2cos(w)).
Find the impulse response h[n].
Homework Equations
H(e^jw) = Ʃ(from k = 0 to M) bk * e^jwk = Ʃ(from k = 0 to M) h[k] * e^jwk
The Attempt at a Solution
So I'm not sure at all how to get...
The transfer function of a passive bandpass filter has one zero and two poles.
The filter is:
Signal > L > C > R > Gnd,
where the signal is the input and the voltage across R is the output.
H(s) = \frac{sRC}{s^2LC+sRC+1}
Initial value theorem states that it's impulse response has...
I attempted by inputting u(τt)u(tτ) into the second part of the integral. Since I want to change the second part of the integral to go from [+∞, ∞]. And as for first part of the integral I added a u(tτ) term after the x(τ) to change the integral from [t,∞] into [+∞, ∞]. I am not sure if I...
Hi all,
I am faced with this question, I am stumped as it is presented in a different way to what I am used to:
The output from a FIR filter for a unit step input u[n] is
y[n] = δ[n] + 3 δ[n  1] + 6 δ[n  2] + 10 δ[n  3] + 15 u[n]
What is the impulse response of the FIR filter?
A...
Hi all. A problem I was working on required that I find the impulse response where I am given the output function ( y(t) ) of a system in terms of the input ( x(t) ). I read somewhere that to find the impulse response, you need a function that relates the output and the input, then you...
I am reading "Linear System Theory and Design" by Chen and he says (in what follows g(t,tau) is the impulse response function):
If a system is causal, the output will not appear before an input is applied. Thus we have Causal <==> g(t,tau) = 0 for t < tau.
However, this seems incorrect...
Homework Statement
Find the impulse response of a system with transfer function H(S) = (s+3)/(s^2+2s+1)
or H(S)=(s+3)/[(s+1)^2]
Homework Equations
Poles are s1=s2=1
y = Ae^st + Be^st
The Attempt at a Solution
In my notes I do not have an answer for the case when there is...
Homework Statement
a) Find the unit impulse response h(t) of an audio system that causes two echoes, one occurring at 0.5 seconds and the other one at 1.5 seconds. Please sketch H(w). (Magnitude and phase)
b) Design a system that can eliminate noise coming from the 60Hz power signal (thus...
greetings, helpful people around the world,
we all have heard once in our lives that the signal that is measure from your instrument, be it a spectrometer, optical microscope or an NMR machine, is not the real signal distribution, but the convolution of the real signal with an instrument...
Homework Statement
I'm trying to Solve for an impulse response h(t) Given the excitation signal x(t) and the output signal y(t)
x(t) = 4rect(t/2)
y(t) = 10[(1e(t+1))u(t+1)  (1e(t1))u(t1)]
h(t) = ?
y(t) = h(t)*x(t) > '*' meaning convolution!
I am unsure how to take the Fourier...
Homework Statement
Find the Impulse response of this system
3y[n]+4y[n1]+y[n2] = x[n] + x[n1]
Homework Equations
Eigenvalues = 1/3 and 1
hc[n] = k1[1/3]n+k2[1]n
3h[n] +4h[n1] +h[n2] = δ[n] + δ[n+1]
The Attempt at a Solution
I know that normally we would plug in hc[n] for two...
Hi all,
I'm having a lot of trouble understanding this step response:
Problem statement:
Consider an LTIC system with impulse response given by: h(t) = u(t)  u(t2)
Sketch the step response s(t).
I've already sketched h(t)...but,
I know that the step response is found by...
Homework Statement
We're supposed to convolve the signal
x[k] = u[k]  u[k8]
with its impulse response
h[k] = sin(pi*k/4)*( u[k]  u[k8] )
with the help of MATLAB.
Homework Equations

The Attempt at a Solution
The thing is that we don't know how to do this in MATLAB...
Homework Statement
An LTI discretetime system has frequency response given by
(a) Use one of the above forms of the frequency response to obtain an equation for the
impulse response h[n] of the system.
(b) From the frequency response, determine the difference equation that is...
Hi to everybody,
I could really use some help in order to understand how to obtain an impulse response from a frequency response.
I am dealing with acoustics, but my knowledge on the particular are basic.
I am trying to compare a theory for the scattering of sound from an object with...
Suppose that y(t)=x(t)\ast h(t).
(\ast denotes convolution)
Here are the signals:
How to find h(t) in time domain? Does there exist such h(t)?
Thanks in advance.
Homework Statement
Two identical circuits are cascaded, without the second circuit having any loading effect on the first circuit. If the laplace transform of the impulse response of the cascade is 4/(s+1)^2. a)determine the impulse response of each circuit alone as a function of time.
b)if...
Homework Statement
An LTI digital system with impulse response h[n] = 2(1/4)^n u[n1] produces an output y[n] = (3)^n u[n1]. Determine the corresponding input x[n].
Homework Equations
I believe that Y[z] = X[z]H[z]
The Attempt at a Solution
So I started by finding the...
Consider the passive highpass filter that consists of a resistor (R) and a capacitor (C). The frequency response is
H(\omega)=\frac{j\omega C R}{j\omega C R + 1}.
What would be the impulse response of this high pass filter? This question translates to how to evaluate the following Fourier...
I've been told that to calculate the difference equation of an LTI system, you simply take the sample values of the impulse response as the coefficients of the x[nk] terms in the difference equation. i.e. if h[n] = {1, 0.5, 0.25, 0.125} for n>=0, then y[n] = x[n]...
Homework Statement
How do i find the impulse response, h(t), given the following?
f(t) = 8t u(t)
y(t) = (2e^2t + 8e^t + 4t  6) u(t)Homework Equations
f(t) convolved with y(t) = h(t)
The Attempt at a Solution
I thought that you divide out y(t) by 8t to make f(t) = u(t) then take the...
Hi all,
I'm taking a fourth year timeseries analysis course for Physics students.
Homework Statement
Let us consider a simple physical system consisting of a resistor (with resistance R) and an inductor (with inductance L) in series. We apply an input voltage a(t) across the pair in...
i have a coax cable that will be used in data transmission. i have measured the open and short impedance and then characteristic impedance(Zo) for the cable. Eventually I will have a transmitter with Z_source in one end of the cable and receiver with Z_load at the other end of the cable. Is it...
Im struggling to do the following question. Any help would be appreciated
A following system has the following difference equation
y(n)+ 1/8y(n1)  5/8y(n2)=1/2x(n1)
First part is to calculate the system transfer function using the z transform. Then get the frequency response and...