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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 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