ELG6163 Real Time

7/27/2019 ELG6163 Real Time

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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 samplesx(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 thenext input sample arrives

Block processing

each input sample x(n) is stored in memory before anyprocessing occurs upon it. AfterL 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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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 inthe 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 latencyof an algorithm is the time it takes togenerate an output value from the corresponding inputvalue.


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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 ofdata.

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 ofachieving data parallelism (performing parallel computations on

subsets of the data).

Data dependencies are studied through temporal and spatial

locality: Temporal localityis described as the tendency for a program to

reuse the data or instructions which have recently been used.

Spatial localityis 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 processingalgorithms

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 simultaneouslyexecuted.

Temporal concurrency pipelining

Spatial concurrency represents a set of tasks that can beexecuted concurrently.

Spatial concurrency parallelism

Retimed FIR filter: Multiplication and addition in O(1)time

ELG6163 Real Time

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