Digital%20Signal%20Processing,%20Cellular%20Automata,%20and%20Parallelism

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Digital Signal Processing, Cellular Automata, and
Parallelism

• Karl Schramm
• San José State University
• Computer Science Department
• CS 240
• Spring 2003

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Outline

• Introduction to digital signal processing
• Relationship of DSPs and CAs (Hint
  parallelism)
• An overview of parallel computing
• The future?

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Introduction to Digital Signal Processing

• Manipulation of a signal
• Signals are waveforms
• Typically carried out in realtime
• Calculations are handled by Digital Signal
  Processors (DSP)

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DSP Uses

• Telecom
• Multiplexing
• Signal encoding/decoding
• Compression
• Military
• Sonar Radar processing
• Visual tracking systems for laser-guided weapons
• Communication encryption/decryption
• Medical
• CAT MRI imaging
• Entertainment
• Audio visual analysis and effects

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DSP Overview

• Receives a signal, processes it, and outputs
  result
• Several DSPs can be linked together in a serial
  chain
• Can be implemented in software or hardware
• Hardware is best for realtime performance

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Analog to Digital Conversion

• Converts a continuous, analog signal into a
  discrete, digital signal
• Analog signal is sampled at a regular interval
• Sampled values are stored as a data stream
• 1D array

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Sampling

• Shannons sampling theorem
• A signal must be sampled at a rate at least 2x
  the of the maximum frequency component (Nyquist
  frequency) or else aliasing will occur Nyquist
  (1928), Shannon (1949)
• Aliasing is the inability to accurately
  reconstruct a signal from sampled data
• Low-pass analog filter (anti-aliasing filter)
  applied before sampling

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DSPs vs. CAs

• Both perform the same function
• Receive data process it
• DSP calculations are usually complex
• A DSP chain is similar to the successive
  generations of a CA
• Calculations of CAs dont usually change over
  time
• A DSP can be viewed as a 1D Continuous CA
• Signal is a continuous valued array

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CAs as DSPs

• CAs can be used in sound synthesis
• Quantized CA values can be used to play a tone or
  trigger a MIDI note (CAMUS)
• Continuous CA values can be used to generate a
  signal (CASound)

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CAs and Parallelism

• Parallelism is an important aspect of CAs
• Cells are independent entities
• Parallelism allows CAs to be used to model
• Fluid dynamics
• Cell crystal growth
• Etc.
• CAs are parallel machines
• SIMD
• Shared Memory
• DSPs must exhibit parallelism to be like a CA

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Flynns Taxonomy

• SISD
• Single Instruction stream Single Data stream
• von Neumann architecture
• SIMD
• Single Instruction stream Multiple Data stream
• MIMD
• Multiple Instruction stream Multiple Data stream
• MISD
• Multiple Instruction stream Single Data Stream
• Pipelined architecture

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Parallel Computing Memory Configurations

• Shared Memory
• Processors share a single address space
• Processors communicate via memory
• Multicomputer
• Name is derived from the term message passing
  multiprocessors
• Processors dont share a single address space
• Processors communicate by passing messages via an
  interconnection network
• Difficult to program
• cant share memory
• message passing is error prone
• Typically scales better than a shared memory
  system

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Requirements for Parallelism

• Data must be parallelizable
• Divide and conquer
• Must have a parallel hardware architecture

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DSP Data Parallelism

• Digital signal is an array of values
• Arrays can be accessed in parallel
• Used in smoothing and simple low-pass filters
• Otherwise limited value in DSP
• Decomposition
• Divide a signal into many smaller, simpler
  signals
• Smaller, simpler signals can processed in
  parallel
• Used in many crucial DSP applications
• Encoding/decoding information on a carrier signal
• Frequency analysis
• Advanced filtering
• Multi-band equalization
• Etc.

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Superpostion and Decomposition

• A signal can be decomposed into several smaller,
  simpler signals
• Decomposed signals can added together to form the
  original signal
• Processing decomposed signals has the same effect
  as processing the original signal if the system
  is linear

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Linear Systems

• Homogeneity
• Modification in the input signals amplitude
  results in a corresponding modification in the
  output.
• f(x)t ty
• Additivity
• For any two inputs, the sum of the outputs is the
  same as if the sum of the two inputs had been
  processed together.
• f(x1) ky1
• f(x2) ky2
• f(x1) f(x2) ky1 ky2
• f(x1 x2) ky1 ky2

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DSPs and Linearity

• Most DSP operations are linear
• Nonlinear DSP operations are parallelizable as
  well
• Subdivide the data array
• Emulate the nonlinear operation with a linear
  operation

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Fourier Decomposition

• Decomposes signal into sine cosine signals
• Sinusoidal waves are easy to process
• Uniformity
• Simple representation (amplitude phase)
• Sinusoidal fidelity
• If a sine wave is input to a linear system, the
  output will be a sine wave at the same frequency

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Fourier Equations

• Continuous Fourier Transformation
• X(f) ? x(t)e-i2?ft dt
• Discrete Fourier Transformation (DFT)
• X(m) ?x(n)e-i2?nm / N
• Fast Fourier Transformation (FFT)
• Optimized DFT algorithm
• Eulers relationship
• e-i? cos(?) isin(?)

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DSPs and Hardware Parallelism

• Minor hardware parallelism is achieved with
  Harvard architecture
• Adds a separate memory store and bus for
  instruction data
• Allows for concurrent retrieval of instructions
  and data

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DSPs and Hardware Parallelism

• Several of the same type of DSP can be linked
  together into a multiprocessing array
• SIMD MIMD
• Shared multicomputer memory architectures
• Linking processors requires glue logic
• Glue logic controls data flow and task
  distribution
• Some DSPs are designed with glue logic built in
• Analog Devices SHARC family
• Texas Instruments TMS320 family

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Summary

• CAs are parallel computational devices
• SIMD, Shared Memory device
• DSPs can be parallel computational devices
• SIMD, Shared Memory device
• MIMD, Multicomputer
• Parallelism is the tie that binds

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The Future?

• Sony, IBM, and Toshibas Cell Microprocessor
  technology
• A single processor has 4 - 16 general-purpose
  processor cores, known as cells
• Cell processors are linked together via high
  speed communication bus
• Devices with Cell chips can be connected over a
  high-speed network to perform distributed
  computing
• May be first used in the Sony Playstation 3 video
  game console
• Process streaming video data over a network
• Earliest expected rollout date is 2005

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References

• 1 Lyons, R. (2001). Understanding Digital
  Signal Processing.
• Upper Saddle River, NJ Prentice Hall.
• 2 Margolus, N. (1993). CAM-8 A Computer
  Architecture Based on Cellular Automata.
• Cambridge, MA MIT Laboratory of Computer
  Science.
• Available http//www.ai.mit.edu/people/nhm/cam8.
  pdf
• 3 Miranda, E. (2002). CAMUS A Cellular
  Automata Music Generator.
• Available http//website.lineone.net/edandalex/
  camus.htm
• 4 Rorabaugh, C. (1998). DSP Primer.
• New York McGraw-Hill.
• 5 Schramm, K. (2003). CASound Sound
  Synthesizing 1D CA.
• Available http//sjsu.rudyrucker.com/karl.schra
  mm/applet/
• 6 Smith, S. (1997). The Scientist and
  Engineer's Guide to Digital Signal Processing.
• San Diego, CA California Technical Publishing.
• 7 Spooner, J., (August 6, 2002). Chip trio
  allows glimpse into Cell.
• CNET News.com
• Available http//news.com.com/2100-1001-948493.h
  tml?tagfd_top
• 8 Wilkinson, B. Allen, M. (1998). Parallel
  Programming Techniques and Applications Using
  Networked Workstations and Parallel Computers.
• Upper Saddle River, NJ Prentice Hall.
• 9 Wolfram, S. (2001). A New Kind of Science.