Digital Signal Processing: System Analysis and Design

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Under the Radar. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Skip to main content. Create Account Sign in. September Society News. Upcoming Webinar! Conference News. Conceptually, data values are encapsulated in objects called tokens as they pass across dataflow graph edges.

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In dataflow, execution of actors is decomposed into discrete units, which are called firings [ 1 ]. For a given firing f and output FIFO K , the number of tokens produced onto K during f is referred to as the production rate associated with f and K. Similarly, we can define the consumption rate associated with a firing and an input FIFO.

Production and consumption rates are referred to collectively as dataflow rates. If for a given actor the dataflow rate on each FIFO connected to the actor is constant, then we refer to the actor as a synchronous dataflow SDF actor. An important task in the implementation of a dataflow graph is the task of constructing a schedule for the graph. A schedule specifies the assignment of actors to processing resources and the execution order of actors that are assigned to the same resource.

If all of these assignment and ordering decisions are made at compile time, the schedule is said to be static , whereas if some of the decisions are deferred to execution time, it is said to be a dynamic schedule [ 6 ]. If the decisions are made after compile time but prior to graph execution, the schedule is said to be a just-in-time schedule [ 7 ].

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Static and just-in-time scheduling techniques offer increased predictability and reduced run-time scheduling overhead at the expense of generality—they cannot be applied to all types of dataflow models. In this paper, we focus primarily on static scheduling techniques. In the dataflow graph execution model that we apply, a statically constructed schedule is executed iteratively, where each iteration is triggered by the availability of a new block of input samples from a DAQ device.

The dataflow graphs that we apply in this paper are sufficiently predictable to enable this form of static scheduling. The environment is based on a compact set of application programming interfaces APIs for implementing design components as dataflow actors. Each firing of A has a unique mode associated with it. Each actor mode has constant dataflow rates on all input and output FIFOs, while the dataflow rates can vary across different modes of the same actor.

Each CFDF actor has two associated methods, called the invoke method and the enable method. The invoke method is used to execute the actor in its current mode, while the enable method is used to determine whether or not there is enough data on the input edges and enough empty space on the output edges to support firing the actor in its current mode. The separation of concerns between enable testing and invoking is an important feature of the CFDF model [ 10 ].

What's Inside a DSP?

There are two main purposes for deep jitter measurement: 1 to increase the likelihood of capturing rare events that can cause communication errors [ 11 ] and 2 to enable estimation of tails in jitter probability distributions, as a replacement for or to improve the accuracy of distribution extrapolation [ 12 ]. Implementations of timing jitter measurement are available in instruments such as digital oscilloscopes. However, the computation time and memory requirements increase with waveform depth, and so, it is desirable to seek methods for faster yet still cost-effective jitter computation from deep waveforms.

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To address this problem and help accelerate jitter measurement, researchers have introduced parallel algorithms for constant clock period computation. For example, [ 13 ] exploits multi-core processors such as Intel central processing units CPUs together with their streaming single instruction multiple data extensions SSE [ 14 ] instruction sets to enable fast and accurate jitter measurement. This limits the amount of signal data that can be measured and results in high response time for engineers to start seeing measurement results.

Another jitter measurement algorithm was demonstrated in [ 15 ] that significantly improves measurement response time by partitioning the overall data set into windows and allowing jitter measurement results to be reported for earlier windows before later windows are received. This reformulation of jitter measurement eliminates the swallow and wallow characteristic and provides improved speed. However, a memory requirement limitation still remains: the memory required as in the approach of [ 13 ] is unbounded. In other words, the memory requirement grows without bound as the size of the data set is increased.

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  • This characteristic again limits the amount of signal data that can be measured, which is problematic, for example, in measuring relatively long signals or signals with high sample rates when memory resources are limited. A preliminary version of this paper was presented in [ 16 ]. In this prior work, we presented a novel deep jitter measurement system that loads and processes constant-frequency signal data from an input file. The contribution of the prior work was focused on streamlining memory requirements and efficiently trading off accuracy and performance.

    The contribution improved the algorithm of [ 15 ] to overcome its limitation of having unbounded memory requirements. This led to a novel deep jitter measurement system whose memory requirements are fixed for a given system design configuration—in particular, the memory requirements are independent of the amount of data that is processed when the system operates. This allows processing of unbounded signal streams: the measurement system can process as much data as it receives during a given execution of the system.

    In this paper, we go beyond the preliminary version in the following ways.

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    First, we incorporate methods to process input from a DAQ device under the constraint of gapless processing. Second, we present design optimization techniques that significantly improve memory management efficiency and system throughput. Additionally, we incorporate methods to dynamically monitor the frequency of the input signal and adapt relevant system parameters when changes in the input frequency are detected.

    In this section, we discuss our methods for dataflow graph design of gapless deep waveform analysis applications. As described in Section 1 , we present these methods in the context of a concrete application—deep jitter measurement. The deep jitter measurement system that we develop is a gapless DSP system where a DAQ subsystem supplies continuously arriving input samples, and these samples are processed to analyze the jitter of input waveform.

    The primary challenges when integrating jitter measurement algorithms with DAQ devices for real-time analysis include adhering to memory capacity constraints, ensuring that system throughput does not fall below the sampling rate of the DAQ device, and avoiding excessive latency in the jitter measurement computation. The methods developed in this section provide our system design foundations for addressing these challenges. The core dataflow-based system architecture presented in this section is built upon in Section 5 with various optimization techniques. These optimizations further improve the trade-offs among memory cost, throughput, and latency that are achieved by our deep jitter measurement system design.

    The dataflow graph for our deep jitter measurement system is designed to measure jitter continuously so that intermediate results of jitter analysis and the recovered clock period are accessible and so that computational latency is streamlined while meeting throughput constraints.

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    • A windowing method is applied to reduce the memory requirements of the jitter measurement system. The windowing method decomposes the input stream into a set of fixed-size subsequences. The fixed size is referred to as the window size W s.

      Digital Signal Processing System Design

      In our implementation, the dataflow graph memory requirements are dependent only on W s and not on the number of windows that is processed. Thus, the jitter measurement dataflow graph can be executed on an unbounded number of windows with predictable, bounded memory requirements. The window size is a system parameter that can be configured by the designer to control an associated trade-off between measurement accuracy and memory requirements for deep jitter measurement.

      Larger values of W s in general lead to improved accuracy at the expense of higher memory requirements. We discuss this trade-off further in Section 5. In design and implementation of gapless DSP systems, we are concerned with processing data that arrives continuously from one or more DAQ subsystems. The data processed by the system dataflow graph is accessed from one or more internal buffers on the DAQ devices rather than from files that are stored on disk. In our deep jitter measurement system, we employ a single DAQ device.

      To integrate use of the device into the system-level dataflow graph, we develop a source actor that encapsulates the functionality associated with acquiring data from the DAQ device. Here, by a source actor , we mean a dataflow actor that has no inputs; such actors are commonly used to model interfaces between dataflow graphs and sources of input data.

      Similarly, sink actors , which have no outputs, are used to model output interfaces of dataflow graphs. In the remainder of this section Section 4. The triggering process for the device also needs to be set up. The initialization mode handles these setup tasks, and then transitions the actor to the inject mode, which can be viewed as representing the steady state functionality of the actor.

      Upon each firing in the inject mode, a new frame of data is fetched from the internal buffer of the TDD and made accessible to the rest of the dataflow graph for processing. A new frame corresponds to a new window based on the window-based analysis described in Section 4. If we model the internal buffer as a self-loop edge connected to the DAS actor, then the enable method involves checking for sufficient data on this self-loop edge. In a dataflow graph, a self-loop edge is an edge whose source and sink vertices are identical.

      Digital Signal Processing: System Analysis and Design Digital Signal Processing: System Analysis and Design
      Digital Signal Processing: System Analysis and Design Digital Signal Processing: System Analysis and Design
      Digital Signal Processing: System Analysis and Design Digital Signal Processing: System Analysis and Design
      Digital Signal Processing: System Analysis and Design Digital Signal Processing: System Analysis and Design
      Digital Signal Processing: System Analysis and Design Digital Signal Processing: System Analysis and Design
      Digital Signal Processing: System Analysis and Design Digital Signal Processing: System Analysis and Design
      Digital Signal Processing: System Analysis and Design Digital Signal Processing: System Analysis and Design

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