PCM

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PCM

• Professor Dr. Miguel Alonso Jr.

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Outline

• Sample and Hold, and Sampling Frequency
• Quantization
• Dynamic Range and SNR Calculations
• Amplitude Companding
• D to A and A to D

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Introduction

• Concerned with the transfer of information in
  digital form
• Advantages
• Noise Performance
• Ability to process signal at the source and
  destination DSP
• PCM is the most common technique used today in
  Digital Communications for representing an analog
  signal by a digital word.
• PCM is a technique for converting analog signals
  into a digital representation

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Sample and Hold, and Sampling Frequency

• The first step is to sample and hold the analog
  input
• PAM
• Natural, not good for sampling
• Flat-top PAM
• Sampling frequency must meet the Nyquist Criteria
  because of Aliasing
• Fs 2Fmax

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Quantization

• Once the signal has been sampled, the binary
  conversion process can begin
• In PCM systems, the sampled signal is segmented
  into different voltage levels, with each level
  corresponding to a different binary number.
• This process is called quantization
• Converted to the closest binary value provided in
  the digitizing system
• At each sampling interval, the analog amplitude
  is quantized into the closest available
  quantization level

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• Resolution
• q Vmax / 2n
• Quantization error or Noise results when the
  analog signal being sampled lies in between two
  quantization levels
• Example
• 3 volt 40Hz Sine wave sampled in a 4-bit PCM
  system
• Fs ?
• Q?, Fclock ?

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Dynamic Range and SNR calculations

• Dynamic range for a PCM system is defined as the
  ration of the maximum input or output voltage
  level to the smallest voltage level that can be
  quantized and/or reproduced by the converters
• Vfs/q
• DR Vmax/Vmin 2n
• DRdB 20log10 Vmax/Vmin
• DRdB 20log10 2n

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• SNRdB for a PCM system
• SNRdB 1.76 6.02n
• Signal to quantization noise
• SNRq(dB) 10log 3(2n)2
• Example A digitizing system specifies 55dB of
  dynamic range. How many bits are required to
  satisfy the DR spec? What is the SNRdB ? What is
  SNRq(dB) ?