Real time signal processing

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Real time signal processing

• SYSC5603 (ELG6163) Digital Signal Processing
  Microprocessors, Software and Applications
• Miodrag Bolic

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Outline

• Real time signal processing
• Structural levels of processing
• Properties and parameters of signal processing
  algorithms
• Definitions of throughput, latency, concurrency,
  
• In order to prepare this material, Chapters 1 and
  3 from Ackenhusen99 are used.

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DSP System
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Real time signal processing

• x(n) input discrete time signal representation
  sampled every Tx.
• y(n) input discrete time signal representation
  sampled every Ty.
• Signal processing is a transformation F of input
  samples x(n) to obtain the output signal
  y(m)F(x(n))
• Tc is a computation time needed to process L
  input samples.
• System that has TcLTx is said to operate in
  real-time.

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Real time signal processing - Conditions

• Conditions for real-time processing
• the input sample period Tx
• the complexity of the transformation F
• the speed of the computer(s) which compute
  F(x(n)) as measured by Tc

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Non-real time signal processing
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Structural levels of processing

• Stream processing
• all computations with one input sample are
  completed before the next input sample arrives
• Block processing
• each input sample x(n) is stored in memory before
  any processing occurs upon it. After L input
  samples have arrived, the entire collection of
  samples is processed at once.
• Vector processing
• systems with several input and/or output signals
  being computed at once can work with streams or
  blocks

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Stream processing
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Block processing

• Short-time stationarity of signals
• Advantages
• Efficiency
• Fast algorithms such as FFT can be applied
• Some algorithms (median) require access to all
  the samples in the block and are difficult to
  execute in a stream manner.
• Disadvantages
• Latency

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Parameters of algorithms related to complexity

• Throughput
• Range and precision of numbers
• Data-dependent execution, whereby the instruction
  sequence is influenced by the incoming data
• Precedence relations within the algorithm, as
  well as the lifetime of data values within the
  computation
• Global versus local communication of data
• Random versus regular sequencing of data
  addresses
• Diversity of operations and the amount of
  "difficult" instructions

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Timing parameters

• The critical path determines the time it takes to
  complete an iteration of the computation.
• The latency of an algorithm is the time it takes
  to generate an output value from the
  corresponding input value.

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Throughput

• Throughput is defined as the reciprocal of the
  time deference between successive outputs.
• It depends on
• number of operations,
• Examples
• Speech coding 100s of operation per sample
• Video applications 5 to 10 operations per
  sample
• amount of data to process, and
• time available to process

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Range and precision of numbers

• A number is represented with a fixed number of
  bits - tradeoff between dynamic range and
  precision.
• Dynamic range is the range between the most
  negative and the most positive number
  encountered.
• The number of bits determines the number of
  numeric levels available
• Complexity increases with the number of bits.
• In a purpose-built (custom) architecture,
  increasing the number of bits increases the area,
  approximately as the square of the number of
  bits.

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Data-dependent execution

• High-speed computing is most easily achieved for
  algorithms that are regular, i.e., that perform
  the same operations on each piece of data.
• Data-dependent computations and data precedence
  requirements for sequential execution pose
  obstacles to achieving task parallelism
  (executing multiple tasks in parallel).
• The requirement of global communication increases
  the difficulty of achieving data parallelism
  (performing parallel computations on subsets of
  the data).
• Data dependencies are studied through temporal
  and spatial locality
• Temporal locality is described as the tendency
  for a program to reuse the data or instructions
  which have recently been used.
• Spatial locality is the tendency for a program to
  use the data or instructions neighboring those
  which were recently used.

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Data lifetime

• Computations that use a piece of data once and
  then discard it are more amenable to stream
  processing algorithms
• Stream processing algorithms require less
  storage, avoid the need to again find a piece of
  data from within a random memory array, and
  reduce the latency of results.
• Block processing algorithms, which collect all
  samples at once before acting upon them, require
  time to accumulate numbers, which introduces
  latency.

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Address pattern
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Diversity of operations

• Typically repetitive kernels of computation
• Examples
• FIR filter a multiply-add operation.
• FFT is the butterfly calculation.
• Challenges
• Linear or non-linear computation
• Nonstandard operations

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Concurrency

• Concurrency of operations quantifies the expected
  number of operations that will be simultaneously
  executed.
• Temporal concurrency pipelining
• Spatial concurrency represents a set of tasks
  that can be executed concurrently.
• Spatial concurrency parallelism
• Retimed FIR filter Multiplication and addition
  in O(1) time