ELEC5303 week 7 - PowerPoint PPT Presentation

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ELEC5303 week 7

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... compute the system response to any arbitrary input x(n) using the linear convolution: ... we can also represent any arbitrary discrete signal as a linear ... – PowerPoint PPT presentation

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Title: ELEC5303 week 7


1
ELEC5303 week 7
  • We have seen how a linear and time-invariant
    system can be represented using its response to
    the unit sample sequence.
  • This response, called the unit impulse response
    h(x), allows us to compute the system response to
    any arbitrary input x(n) using the linear
    convolution

2
Discrete-time Fourier Transform
  • This convolution representation is based on the
    fact that any signal can be represented by a
    linear combination of scaled and delayed unit
    samples.
  • Similarly, we can also represent any arbitrary
    discrete signal as a linear combination of basis
    signals.
  • Each basis signal set provides a new signal
    representation.
  • When the system is linear and time-invariant,
    only one representation stands out as the most
    useful.
  • It is based on the complex exponential signal set
    ej?n and is called the Discrete-time Fourier
    Transform

3
Discrete-time Fourier Transform
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Examples
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Properties of DTFT
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Properties of DTFT
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Example
8
Example
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Using Matlab
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Using Matlab
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Example
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Example
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Example
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Example
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Example
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Example
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