Analog and Digital Signals

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Analog and Digital Signals
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Terminology

• Analog signal an analog signal is continuous in
  time and amplitude.
• Digital signal a digital signal exists only at
  discrete, equally spaced moments of time.
• Analog-to- digital converter hardware used to
  convert a continuous signal into a discrete
  digital signal.

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Analog-to- Digital Conversion
From Rosen and Howell,
Signals and Systems for Speech and Hearing.
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Analog Sine Wave
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Properties of A-D Converter

• Sampling rate the number of times the analog
  signal is sampled per second, e.g., if the signal
  is sampled 20,000 times per second the sampling
  rate is 20kHz. The amplitude value of the
  waveform is sampled 20,000 times in a second.

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Sampled sine wave
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Nyquist Theorem

• The sampling rate must be greater than twice the
  highest frequency of interest.
• If the sampling rate is not high enough, a higher
  frequency may appear as a different, lower
  frequencies when sampled. This is an alias.

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Example of aliasing
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Table of sampled waveform values
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Quantization
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Properties of A-D Converter

• Quantization
• Process of assigning a value to the sample.
• Which bin (quantizing step) does a sample belong
  in?
• The accuracy depends on the number of bits
  available.
• Quantizing error the amount by which the
  quantized value is smaller or larger than the
  sampled value.

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Quantization step size
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Quantization Error
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Sampled sine wave
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Digital to analog conversion
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Anti-imaging filter