Effects of Continuous vs Discrete Frequency Scaling and Core Allocation on Energy Efficiency of Static Schedules for Moldable Tasks

Models for energy-efficient static scheduling of parallelizable tasks with deadlines on frequency-scalable parallel machines comprise moldable vs. malleable tasks and continuous vs. discrete frequency levels, plus preemptive vs. non-preemptive task execution with or without task migration. We investigate the tradeoff between scheduling time and energy efficiency when going from continuous to discrete core allocation and frequency levels on a multicore processor, and from preemptive to non-preemptive task execution. To this end, we present a tool to convert a schedule computed for malleable tasks on machines with continuous frequency scaling [Sanders and Speck, Euro-Par (2012)] into one for moldable tasks on a machine with discrete frequency levels. We compare the energy efficiency of the converted schedule to the energy consumed by a schedule produced by the integrated crown scheduler [Melot et al., ACM TACO (2015)] for moldable tasks and a machine with discrete frequency levels. Our experiments with synthetic and application-based task sets indicate that the converted Sanders Speck schedules, while computed faster, consume more energy on average than crown schedules. Surprisingly, it is not the step from malleable to moldable tasks that is responsible but the step from continuous to discrete frequency levels. One-time frequency scaling during a task’s execution can compensate for most of the energy overhead caused by frequency discretization.

Discrete Time, Discrete Frequency

This chapter is dedicated to exploring a form of the Fourier transform that can be applied to digital waveforms, the discrete Fourier transform (DFT). The theory is introduced and discussed as a modification to the continuous-time transform, alongside the concept of windowing in the time domain. The fast Fourier transform is explored as an efficient algorithm for the computation of the DFT. The operation of discrete-time convolution is presented as a straight application of the DFT in musical signal processing. The chapter closes with a detailed look at time-varying convolution, which extends the principles developed earlier. The conclusion expands the definition of spectrum once more.

EXPRESS: Design Considerations for Discrete Frequency Infrared Microscopy Systems

Discrete frequency infrared (DFIR) chemical imaging is transforming the practice of microspectroscopy by enabling a diversity of instrumentation and new measurement capabilities. While a variety of hardware implementations have been realized, considerations in the design of all-IR microscopes have not yet been compiled. Here we describe the evolution of IR microscopes, provide rationales for design choices, and the major considerations for each optical component that together comprise an imaging system. We analyze design choices in illustrative examples that use these components to optimize performance, under their particular constraints. We then summarize a framework to assess the factors that determine an instrument’s performance mathematically. Finally, we summarize the design and analysis approach by enumerating performance figures of merit for spectroscopic imaging data that can be used to evaluate the capabilities of imaging systems or suitability for specific intended applications. Together, the presented concepts and examples should aid in understanding available instrument configurations, while guiding innovations in design of the next generation of IR chemical imaging spectrometers.