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 time-invariant system for all frequencies.

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  1. N

    Engineering Finding Impulse Response of Difference Equation

    And really that's all I know how to do myself. If someone can explain/lead me through this, that will be very helpful. Thanks
  2. Elias_HH

    Engineering How to draw a block diagram of a discrete element with its impulse response

    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...
  3. cnh1995

    Output as the convolution of the Impulse response and input

    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...
  4. A

    Trying to intuit the unit impulse response

    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...
  5. J

    Output of transfer function given impulse response and input the

    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?
  6. J

    Step Response from the Impulse Response

    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]
  7. jsg94

    Determine impulse response given input and output signals

    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...
  8. Jayalk97

    Solving for the impulse response of a discrete time system?

    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...
  9. R

    Engineering Impulse Response of an RLC Circuit

    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...
  10. A

    A LTI Impulse Response Estimation with Point Process Input

    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...
  11. maearnie

    Solve Impulse Response Homework - h(n), x(n), y(k)

    Homework Statement I have an impulse response h(n)=e^(0.1n)*[u(n)-u(n-8)] 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)...
  12. I

    Impulse and step response related to the angular position of a spacecraft

    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...
  13. Captain1024

    Finding Impulse And Frequency Responses

    Homework Statement Consider a LTI system defined by the following difference equation: ##\mathrm{y}[n]=-2x[n]+4x[n-1]-2x[n-2]## a) Determine the impulse response of the system b) Determine the frequency response of the system Homework Equations DTFT...
  14. Captain1024

    Find the Output of an LTI System Given Input and Impulse Response

    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...
  15. F

    Solve RC Impulse Response: Voltage @ a RC Circuit

    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) /...
  16. A

    How to design an impulse input in Matlab Simulink

    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
  17. H

    Signals and Systems | Impulse Response Problem

    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
  18. T

    Use convolution integral to find step response of a system

    Homework Statement An electrical network has the unit-impulse response :h(t)=3t⋅e-4t .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...
  19. G

    Finding Impulse Response from Block Diagram

    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...
  20. B

    BIBO Stable if and only if impulse response is summable

    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...
  21. X

    Transfer function=Laplace of the impulse response?

    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.
  22. T

    Frequency and impulse response

    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) ...
  23. A

    Impulse response from frequency response

    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...
  24. C

    Calculate Step Impulse Response: y(n) = a*y(n-1) + K*b*x(n-1)+K*x(n)

    y(n) = a * y(n-1) + K * b * x(n-1) + K * x(n), where |a| < 1. (a) Calculate its impulse response, h(n). the homogenous equation is l^n-1(l-a) = 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...
  25. F

    Finding Impulse Response of Frequency Response

    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...
  26. L

    Effect of zeros on impulse response

    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...
  27. A

    Impulse Response Function Problem

    I attempted by inputting u(τ-t)u(t-τ) 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(t-τ) term after the x(τ) to change the integral from [t,-∞] into [+∞, -∞]. I am not sure if I...
  28. J

    Impulse response of FIR filter given the output is known

    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...
  29. perplexabot

    Understanding the Impulse Response: A Key Tool for Identifying Unknown Systems

    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...
  30. A

    Impulse Response of Causal Systems

    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...
  31. F

    Find Impulse Response of LTI system given transfer function

    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...
  32. jegues

    Signals unit impulse response h(t) ECHO

    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...
  33. O

    Theoretical impulse response and its normalization

    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...
  34. A

    Fourier Transform - Solving for Impulse Response

    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[(1-e-(t+1))u(t+1) - (1-e-(t-1))u(t-1)] h(t) = ? y(t) = h(t)*x(t) --> '*' meaning convolution! I am unsure how to take the Fourier...
  35. Faraz Murtaza

    Stability theory and impulse response

    a system is said to be stable if its impulse response approaches zero for sufficiently large time. why? please give me an satisfying answer..
  36. A

    Impulse Response of a discrete system

    Homework Statement Find the Impulse response of this system 3y[n]+4y[n-1]+y[n-2] = x[n] + x[n-1] Homework Equations Eigenvalues = -1/3 and -1 hc[n] = k1[-1/3]n+k2[-1]n 3h[n] +4h[n-1] +h[n-2] = δ[n] + δ[n+1] The Attempt at a Solution I know that normally we would plug in hc[n] for two...
  37. E

    Step response to an impulse response

    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(t-2) Sketch the step response s(t). I've already sketched h(t)...but, I know that the step response is found by...
  38. P

    Convolving a signal with its impulse response in MATLAB

    Homework Statement We're supposed to convolve the signal x[k] = u[k] - u[k-8] with its impulse response h[k] = sin(pi*k/4)*( u[k] - u[k-8] ) 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...
  39. C

    Obtaining Impulse Response & Frequency Response of LTI System

    Homework Statement An LTI discrete-time 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...
  40. B

    Impulse response from frequency response

    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...
  41. A

    How to Find h(t) in Time Domain for y(t)=x(t)*h(t)?

    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.
  42. G

    Engineering 2 identical circuits cascaded/laplace transform and impulse response

    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...
  43. Z

    Using an impulse response and an output to find an input using Z-transform

    Homework Statement An LTI digital system with impulse response h[n] = 2(1/4)^n u[n-1] produces an output y[n] = (-3)^n u[n-1]. 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...
  44. E

    The impulse response of a high-pass filter

    Consider the passive high-pass 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...
  45. P

    LTI Difference Equation from Impulse response

    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[n-k] 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]...
  46. M

    How do you find the Impulse Response, h(t)

    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...
  47. G

    Signals & Systems: Determine System Output

    Homework Statement Given: Impulse response: h(t) = u(t-1) - u(t + 1) (where u(t) is the unit step function) System input: x(t) = t*u(t) - t*u(t-2) Determine System output: y(10) = ? y(1) = ? max y(t) = ? |y(t)| is max at t = ? Homework Equations Convolution integral? y(t) = -∞∫∞...
  48. R

    Engineering Solving Impulse Response of RL Circuit

    Hi all, I'm taking a fourth year time-series 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...
  49. E

    How to derive impulse response from characteristic impedance

    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...
  50. C

    Frequency response and Impulse Response

    Im struggling to do the following question. Any help would be appreciated A following system has the following difference equation y(n)+ 1/8y(n-1) - 5/8y(n-2)=1/2x(n-1) First part is to calculate the system transfer function using the z transform. Then get the frequency response and...
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