Real time signal processing SYSC5603 (ELG6163) Digital Signal Processing Microprocessors, Software and Applications Miodrag Bolic

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. 2 2

DSP System

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.

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

Non-real time signal processing

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

Stream processing

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

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

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.

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

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.

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.

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.

Address pattern

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

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