Discrete-Time Signals

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Discrete-Time Signals

• Week 2

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Continuous-Time Versus Discrete-Time Signals

• Continuous-time signal a signal defined by a
  function of a continuous-time variable.
• Discrete-time Signal a signal defined by
  specifying the value of the signal only at
  discrete times, called sampling instants.

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Continuous-Time Versus Discrete-Time Signals
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Distinction between Discrete-Time and Quantized
Signals

• Quantized Signal A quantized signal is one whose
  values may assume only a countable number of
  values, or levels, but the changes from level to
  level may occur at any time.

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Periodic and Aperiodic Signals

• Periodic a signal x(t) is periodic if and only
  if
• x(tT0)x(t), -?lttlt? (1)
• where the constant T0 is the period.
• Aperiodic Any deterministic signal not
  satisfying (1) is called aperiodic.

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Periodic Signals
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Aperiodic Signals
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Some Elementary Discrete- Time Signals

• Unit sample
• Unit step

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Some Elementary Discrete- Time Signals

• Exponential sequence
• Sinusoidal sequence

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Some Elementary Discrete-Time Signals
(2) Unit step
(1) Unit sample
(3) Exponential sequence
(4) Sinusoidal sequence
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Energy and Power Signals

• Total energy
• Average power
• X(t) is an energy signal if and only if 0ltElt?, so
  that P0.
• X(t) is an power signal if and only if 0ltPlt?,
  thus implying that E?.
• Signals that satisfy neither property are
  therefore neither energy nor power signals.

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Addition, Multiplication, and Scaling

• Addition
• Multiplication
• Scaling

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Convolution of Two Discrete- Time Signals

• Convolution
• Properties
• 1. Commutative property
• 2. Associative property
• 3. Distributive property

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Correlation of Two Discrete- Time Signals

• Cross-correlation function
• Autocorrelation function
• p0 maximum