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This module explains what is and how to use the Impulse Response of LTI systems.

Introduction

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

    System output

    A discrete time system H takes the input x[n] and produces the output y[n].
    We can determine the system's output, y[n], if we know the system's impulse response, h[n], and the input, x[n].
  • The output for a unit impulse input is called the impulse response.
    An impulse input delta[n] going through a discrete time system H, producing the system's impulse response, h[n].
    delta[n] 'shocks' the system suddenly. h[n] is the response to the shock.

Example impulses

Since we are considering discrete time signals and systems, an ideal impulse is easy to simulate on a computer or some other digital device. It is simply a signal that is 1 at the point n = 0, and 0 everywhere else.

Lti systems and impulse responses

Finding system outputs

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

x[n] k x[k] δ k [n] k x[k] δ [n-k]

The function δ k [n] δ [n-k] peaks up where n k .

The function δ[n-k]. It is simply 1 at point n and 0 everywhere else. Point n is marked on the graph. The function x[k]. It has a strange shape. Point n is marked on the graph.

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 Discrete Time , this is the Discrete Time Convolution Sum .

Finding impulse responses

  • Theory:
    1. Solve the system's Difference Equation for y[n] with f[n]= δ[n]
    2. Use the Z-Transform
  • Practice:
    1. Apply an impulse input signal to the system and record the output
    2. Use Fourier methods
  • We will assume that h[n] is given for now.
    • The goal is now to comput the output y[n] given the impulse response h[n]and the input x[n].
      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 discrete time convolution.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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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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