Digital Signal Processing

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Digital Signal Processing

• Rejean Lau M.Eng
• Prepared for the Department of Engineering,
  Conestoga College

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What is Digital Signal Processing?

• Digital Signal Processing is distinguished from
  other areas in computer science by the unique
  type of data it uses signals
• These signals originate as sensory data from the
  real world e.g. seismic vibrations, visual
  images, sound waves, etc.
• DSP is the mathematics, algorithms, and
  techniques used to manipulate these signals after
  they have been converted into digital form
  E.g JPEG encoder/decoder
• The purpose of DSP is to manipulate the data, for
  the purpose of a specific application
• enhancement of visual images
• recognition and generation of speech
• compression of data for storage and transmission

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DSP Applications
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Components of a DSP System
Before going into the details, let us briefly
discuss the typical components of a DSP system
to see how everything fits in. Dont worry if
you dont understand all the terminology yet.

• An analog lowpass prefilter or antialiasing
  filter, which limits the highest signal frequency
  to ensure freedom from aliasing
• A sampler, which operates above the Nyquist
  sampling rate
• A quantizer, which quantizes the sampled signal
  values to a finite number of levels. 16-bit
  quantizers are commonplace.
• An encoder, which converts the quantized signal
  values to a string of binary bits whose length is
  determined by the number of quantization levels
  of the quantizer.
• The digital signal processing algorithm
  (implemented in hardware or software depending
  on the required speed), which processes the
  encoded digital signal in the desired fashion for
  the application
• A decoder, which converts the processed bit
  stream to a quantized, discrete-time signal
• A reconstruction filter, which reconstructs a
  staircase approximation of the discrete-time
  signal
• A lowpass analog anti-imaging filter, which
  extracts the central period from the periodic
  spectrum, removes the unwanted replicas, and
  results in a smoothed reconstructed signal.

5
ADC and DAC

• The signals encountered in the real word are
  continuous or analog light intensity that
  changes with distance, voltage that varies over
  time, a chemical reaction rate that depends on
  temperature
• Analog-to-Digital Conversion (ADC) and
  Digital-to-Analog Conversion (DAC) is what makes
  it possible for a computer to interact with these
  signals.
• Digital information is different from its
  continuous counterpart in two important respects
  it is sampled, and it is quantized.

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Sampling and Quantization

• Quantization is the process which converts the
  continuous (analog) to discrete (digital).
• Before quantization occurs, the continuous signal
  must first be sampled by a sample and hold
  circuit (see next slide)
• The number of levels of the quantizer is
  determined by the number of bits.
• A 16-bit quantizer has 216 65536 levels
• This means any sampled signal can be represented
  by one of the 65536 levels
• The quantization error is the difference between
  the sampled analog signal and the quantized
  digital signal

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Quantization Error

• Measured in a unit called the LSB, an
  abbreviation for least significant bit
• For an 8 bit ADC, an error of one LSB is 1/256 of
  the full signal range
• Quantization error is the difference between the
  sampled signal and analog signal due to the
  finite resolution of the ADC
• The magnitude of the quantization error at the
  sampling instant is between zero and half of one
  LSB
• Generally, the original signal gtgt 1 LSB and the
  quantization error is not correlated with the
  signal and has a uniform distribution
• RMS value is 1/v12 0.289 LSB
• At lower levels, the quantizing error becomes
  dependent of the input signal resulting in
  distortion
• The distortion is created after the anti-aliasing
  filter, so if the distortions are above ½ the
  sample date, they will alias
• In order to make the quantizing error independent
  of the input signal, noise with an amplitude of 1
  quantization step is added to the signal -
  technique is called dithering
• slightly reduced the signal to noise ratio, but
  completely eliminates distortion

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Sampling, Quantization and Quantization Error
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Sampling Theorem

• The sampling theorem indicates that a continuous
  signal can be properly sampled, only if it does
  not contain frequency components above one-half
  of the sampling rate known as the Nyquist
  Frequency
• What if we sample at less than twice the Nyquist
  frequency?
• Aliasing occurs and the original signal cannot be
  reconstructed from the samples

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Sampling Theorem

• Simple DSP system as dictated by the Sampling
  Theorem

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Sampling Theorem
12
Aliasing
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Sampling Theorem and Aliasing

• Sampling theorem in time and frequency domains
• Overlapping spectra in (f) caused aliasing

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Digital to Analog Conversion
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Multirate Data Conversion

• Uses more than one sampling rate in the same
  system
• Multirate data conversion is valuable for two
  reasons
• It replaces analog components with software, an
  economic advantage
• It can achieve higher levels levels of
  performance in critical applications
• Example
• Compact disc audio systems use
  multirate technique to achieve
• higher sound quality because analog components
  (1 precision)
• are replaced with digital algorithms (0.0001
  precision)
• Single bit ADC and DAC is a multirate technique
  where a higher sampling rate is traded for a
  lower number of bits
• - Popular in telecommunications and high
  fidelity music reproduction

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Multirate Data Conversion

• Consider the design of a digital voice recorder,
  a system that will digitize a voice signal, store
  the data in digital form, and later reconstruct
  the signal for playback
• First, pass the voice signal through a simple RC
  low-pass filter and sample the data at 64 kHz.
• Resulting digital data contains the desired voice
  band between 100 and 3000 hertz, but also has an
  unusable band between 3 kHz and 32 kHz
• Second, remove these unusable frequencies in
  software, by using a digital low-pass filter at 3
  kHz.
• Third, resample the digital signal from 64 kHz to
  8 kHz by simply discarding every seven out of
  eight samples, a procedure called decimation
• Resulting digital data is equivalent to that
  produced by aggressive analog filtering and
  direct 8 kHz sampling ? we have replaced a
  complex analog solution with a combination of a
  simple analog solution and software!

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Multirate Data Conversion

• Multirate techniques can also be used in the
  output portion
• The 8 kHz data is pulled from memory and
  converted to a 64 kHz sampling rate, a procedure
  called interpolation
• Involves placing seven samples, with a value of
  0, between each of the samples obtained from
  memory
• Resulting signal is a digital impulse train,
  containing the desired voice band between 100 and
  3000 hertz, plus spectral duplications between 3
  kHz and 32 kHz
• (refer back to Figs. 3-6 a,b to see why this
  is true)
• Cut everything above 3 kHz with a digital
  low-pass filter
• After conversion to an analog signal through a
  DAC, a simple RC network is all that is required
  to produce the final voice signal

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DSP Software

• Suppose you buy a DSP microprocessor device
  will have lots of built-in features for DSP
  analog inputs, analog outputs, digital I/O,
  antialias and reconstruction filters, etc.
• Question How do you program it?
• Worst case scenario manufacturer will you an
  assembler, and expect you to learn the internal
  architecture of the device.
• Best case scenario manufacturer provides a
  software package in a high level language such as
  C, to help in the programming libraries of
  algorithms, prewritten routines for I/O,
  debugging tools, etc.
• The DSP Software Engineers task is to manipulate
  signal pathways, algorithms for processing
  signals, analog I/O parameters possibly in a GUI
• E.g Visual DSP from Analog Devices, Matlab
  Simulink
• Once satisfied with the design, using a compiler,
  it is transformed into machine code for execution
  in the hardware
• Application packages are available for image
  processing, spectral analysis, instrumentation
  and control, digital filter design etc.

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DSP Software

• Performance Issues
• High level or Assembly?
• As a rule-of-thumb, expect that a routine written
  in assembly will be between 1.5 and 3 times
  faster than the comparable high-level program
• With application packages and optimized
  compilers, using a high-level language makes much
  more sense in terms of programmer efficiency and
  is what is the norm today (circa 2007)
• Reality the routines which need to be optimized
  for speed are written in assembly anyways and
  provided in a library, and the designer simply
  needs to use the correct package in a high-level
  language

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DSP Software

• The Conestoga College EET department has about 20
  ADSP-2181 kits available to be signed out by
  students in the SET program
• User manuals are also available for sign out
• The software tool Visual DSP is available for
  download from the Analog Devices web site (trial
  version free)