What is Fractional Scaling Digital Signal Processing?

FSDSP allows specific fractional scaling equations to be written for the spectrum of any signal or sound. The equations can then be used in algorithms as filters to shape or recognize the spectrum or as models to simulate or reproduce the spectrum.

FSDSP allows exact decimal/fractional decibel levels of attenuation or amplification at each frequency to selectively filter complex data sets and can achieve nearly any desired filtering characteristic with a high degree of accuracy, from sharp transitions within a narrow bandwidth to complicated structures within the passband. This prevents introduction of mathematical artifacts or loss of information from the filtered signal, as commonly happens with current stateof-the-art filters.

FSDSP is scalable and can be encoded into a field-programmable gate array (FPGA) device or within a DSP chipset. Compared to conventional DSP, FSDSP requires fewer equations, parameters, and steps to achieve fractional rates of attenuation or amplification of specific frequency regions translating into a reduction in the amount of time necessary for calculations, less error propagation, a reduction in the memory necessary for the calculations, and a reduction in the energy per operation.

FSDSP may be applied to Machine/Deep Learning for Feature/Pattern Detection, Extraction, and Synthesis. FSDSP captures the scaling behavior of complex time series, systems, and structured data within equations and can yield statistically identical simulations of these data sets.

FSDSP improves the response, stability, and machine learning capability of robotic platforms such as UAVs. Fractional Order Control Systems invoking FSDSP, such as a fractional order proportional-integral-derivative (PID) controller, provide greater stability and performance under strong perturbations, are more flexible and better able to adapt to dynamic properties of an environment, have more effective damping characteristics, and may recover faster and with greater accuracy from disturbances.

FSDSP can produce more accurate and realistic computer models and simulations of natural environments through computer-generated 2D imagery and 3D textures

FSDSP provides a method to easily filter out or amplify distinct frequencies or ranges of frequencies utilizing a fractional equalizer and may be applied in near-real time to live data streams from IoT.

FSDSP provides methods to clean up signals and increase signal-to-noise ratio from ubiquitous and noisy sensor/actuators that live at the edge of the network in IoT.