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 Tc≤LTx 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 ~ 100’s 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
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