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This module gives an introduction to the continuous time impulse response of LTI systems.

Introduction

  • The output of an LTI system is completely determined by the input and the system's response to a unit impulse.

    System output

    A continuous time system H takes the input f(t) and produces the output y(t).
    We can determine the system's output, y(t), if we know the system's impulse response, h(t), and the input, f(t).
  • The output for a unit impulse input is called the impulse response.
    An impulse input delta(t) going through a continuous time system H, producing the system's impulse response, h(t). delta(t) 'shocks' the system suddenly and h(t) is the response to the shock.

Example approximate impulses

  1. Hammer blow to a structure
  2. Hand clap or gun blast in a room
  3. Air gun blast underwater

Lti systems and impulse responses

Finding system outputs

By the sifting property of impulses, any signal can be decomposed in terms of an integral of shifted, scaled impulses.

f t τ f τ δ t τ

δ t τ peaks up where t τ .

The functions δ(t-τ) and f(τ) as functions of τ. δ(t-τ) is a peak of infinite height and zero width at point t. f(τ) is some function with a strange shape. Point t is marked on the graphs of both of them.

Since we know the response of the system to an impulse and any signal can be decomposed into impulses, all we need to do to find the response of the system to any signal is to decompose the signal into impulses, calculate the system's output for every impulse and add the outputs back together. This is the process known as Convolution . Since we are in Continuous Time , this is the Continuous Time Convolution Integral .

Finding impulse responses

  • Theory:
    1. Solve the system's differential equation for y(t) with f t δ t
    2. Use the Laplace transform
  • Practice:
    1. Apply an impulse-like input signal to the system and measure the output
    2. Use Fourier methods
  • We will assume that h(t) is given for now.
    • The goal now is to compute the output y(t) given the impulse response h(t) and the input f(t).
      A system with impulse response h takes the input f and produces the output y.

Impulse response summary

When a system is "shocked" by a delta function, it produces an output known as its impulse response. For an LTI system, the impulse response completely determines the output of the system given any arbitrary input. The output can be found using continuous time convolution.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
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Brian Reply
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Damian
How we are making nano material?
LITNING Reply
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LITNING Reply
What is meant by 'nano scale'?
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What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
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Adin Reply
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
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Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Damian Reply
research.net
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Introduction about quantum dots in nanotechnology
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Damian Reply
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Source:  OpenStax, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15
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