Information -

The Signal in the Noise:

Signals convey information.  In nature, this information may be in the form of an analog or continuous signal, such as a physical sound wave or radio wave.  With proper sampling and sensors, a microphone or radio in this example, we can numerically represent this physical analog wave as a digital signal which is a discrete sequence of numbers that represents all of the information contained within that waveform.

Often when sampling the environment, our sensors collect unwanted signals, disturbances, or extra information that is not relevant to the signal and obscures the information we want to collect.  This irrelevant information we term noise which interferes with our ability to extract meaningful information from the signal and can prevent technologies from working properly. 

Digital Signal Processing

is a Phantom Technology:

Digital Signal Processing (DSP) is often called the Phantom Technology as DSP is in nearly all modern electronics but takes place behind the scenes as algorithms in hardware or software.  More specifically, DSP is applying math encoded as algorithms in hardware or software to those numerical values of a digital signal in order to change the signal in some advantageous or useful way, such as in filtering a signal to extract the useful information as in tuning a digital radio.

As a research, development, and innovation laboratory, the sNoise Research Laboratory (sNRL) is leading the way to develop advanced Fractional Scaling Digital Signal Processing (FSDSP) tools, signal-shaping smart filters, and algorithmic mathematical solutions based on fractional calculus in order to better extract the signal from the noise to reveal the hidden reality of information shaping the technologies of our modern world.

In order to decode and clean up a signal that contains noise to make the signal useful, we filter or process the signal through electronic circuits or mathematical algorithms to separate and extract the signal from the noise.  Collectively, cleaning up and filtering a signal to reduce or eliminate noise is one example of Signal Processing.

Whether we realize it or not, everyday, our lives are influenced by signals and shaped by signal processing.  If you drive a car, used navigation maps with GPS, made a cell phone call, used a computer or the Internet, took a digital picture, played a video game, watched a movie on DVD, used a charge card, had a MRI or CAT scan, listened to the radio, or used RADAR or SONAR, you have used signal processing technologies.

Fractional Order Control Systems

for Dynamic and Emergent Robotics:

As the language of dynamic system models, FSDSP also extends to defining, modeling, and filtering of fractional order control systems (FOCS) and improves the response, stability, and machine learning capability of emergent robotic and AI platforms such as Unmanned Vehicle Systems (UAVs), self-driving vehicles, and satellites.   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.

By utilizing a fractional calculus approach to digital signal processing, Fractional Scaling Digital Signal Processing and Fractional Scaling Digital Filters provide sNRL the ability 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, all without introducing the mathematical artifacts of current state-of-the-art filters or resulting in a loss of information in the filtered signal.  FSDSP grants sNRL the ability to extract the signal from the noise more effectively with a higher resolution and level of performance than conventional digital signal processing filters and algorithms that are based on traditional integer-based calculus.

Fractional Scaling

Digital Signal Processing (FSDSP):

Fundamentally, Fractional Scaling Digital Signal Processing (FSDSP) allows fractional calculus, and thus fractional filtering (e.g., fractional scaling, fractional phase shifting, fractional integration, or fractional differentiation) to be performed on a signal.  In fact, FSDSP opens up access to a signal allowing each individual frequency the ability to be adjusted to any decimal level in magnitude and/or phase and also the ability to access or alter the time element of the signal or frequency.  FSDSP also encompasses a new class of digital filters (Fractional Scaling Digital Filters or FSDF) and further defines control systems (Fractional Order Control Systems or FOCS) in terms of Fractional Calculus.  Representing exact filtering solutions rather than approximations, FSDSP demonstrably exhibits extreme mathematical accuracy, precision, robustness, flexibility, and computational efficiency leading to cleaner signals and more effective control.

Next-Generation

Platform Technology:

As the next generation in digital signal processing technology, Fractional Scaling Digital Signal Processing (FSDSP) represents a game-changing platform technology for the digital age, offers the potential to revolutionize the way in which we currently see, model, filter, and control digital signals and systems, and represents a remarkable technological advancement over current digital filter designs.

Multiple Dimensional

Signal Processing:

FSDSP extends to signals across multiple dimensions and may be successfully applied whether that signal is single dimensional as in 1-dimensional arrays (1D time series signals), or a 2-dimensional space (2D static imagery), 3-dimensional space and time (dynamic video or spatio-temporal dynamic texture), or 4-dimensional (2D or 3D plus a time component or spacetime) digital signal.

In one sense, what the discovery of fractals did for shapes and computer-generated imagery, FSDSP does for signals and time. With the Potential to become the industry standard for digital signal processing filters, sNRL's patented FSDSP algorithms may rapidly accelerate technological developments in a variety of fields to generate robust solutions for the future and reveal the true hidden nature of reality.

Simulations - FSDSP is

the mathematics of Nature:

With FSDSP, sNRL can now shape any signal, accessing every frequency in both magnitude and/or phase allowing ultra-realistic simulations, revealing hidden information about recorded and measured quantities of real-world data, electromagnetic, or physical phenomena which may also lead to detailed predictive models or filters of these complex signals and phenomena.

Disruptive and Accessible

Advanced FSDSP Technology:

FSDSP provides a complete, organized mathematical framework and repository of Fractional Calculus encoded as a library of patented algorithms.  sNRL is actively working towards converting the FSDSP algorithms from MATLAB to a multi-language Software Development Kit (SDK) for edge computing and Application Programming Interface (API) for cloud computing with integrated AI and deep learning algorithms.  Custom interfaces and sample data for each field of use and data type are also planned for inclusion into the FSDSP SDK and API so that customers from a variety of scientific and engineering fields may more readily test, license, and implement the fractional calculus algorithms in both hardware and software products leading to widespread adoption potentially disrupting industry standards in many of these disciplines.

sNRL seeks Partnerships to bring

Fractional Calculus to the World:

The usefulness of fractional calculus and FSDSP including Fractional Scaling Digital Filters and their use in fractional order control systems extends across a multitude of disciplines and industries from control theory, cybernetics, economics, information theory, medicine, neuroscience, neuroengineering, cognitive science, and the human behavioral sciences to the environmental sciences, meteorology, geophysics, aerospace, control systems, robotics, mechanical engineering, mechatronics, sensors, electrical engineering, telecommunications, audio, video, and digital signal processing with numerous applications such as RADAR and SONAR Data Acquisition Systems.  Since Fractional Calculus encompasses all of Calculus, the current possibilities and the yet undiscovered potential uses are truly limitless.

Defining Fractional Calculus (FC)

Defining Fractional Calculus

Traditional Calculus, demonstrated to the left, is limited in what may be described, filtered, or modeled by the mathematics.

Gaussian White Noise (Differentiation of Brownian Motion):

• Here, a linear least-squares line fit to the power spectrum of a random white noise signal has a flat slope, also known as a scaling exponent (ß), of ß=0.

Brownian Motion (Integration of Gaussian White Noise):

• Integration of this same white noise yields a Brownian motion with a power spectrum with a increase in slope or scaling exponent of ß=2.

Scaling Exponent (ß) of Fractional Calculus:

• The scaling exponent may be used as both a measure of or to perform fractional integration and fractional differentiation through sNRL's patented FSDSP algorithms.  In this example, the act of integration of a single, first order integrator changes the slope or scaling exponent of the power spectrum of these signals from ß=0 to ß=2.  In contrast, differentiation of this white noise signal would have changed the slope or scaling exponent from ß=0 to ß=-2.

Defining Fractional Calculus

More Powerful Mathematics through Fractional Calculus:

• Fractional Calculus allows for the exploration of new mathematical territories that are not accessible with traditional methods. For instance, fractional derivatives or integrals can describe complex behaviors in systems where integer-order derivatives or integrals fail to provide adequate insights or even the ability for fine-scale modeling.

• As an analogy to a number line, Traditional Calculus is like using only Integers for calculations whereas Fractional Calculus is having access to integers, decimals, and fractions in calculations. The first is an approximation with mathematical artifacts and the second is an exact representation of the answer.​​

​

Real-World Signals Are Better Defined via Fractional Calculus:

• As an example, a half-derivative (ß=1) captures gradual changes in a system, providing a smoother transition between states or behaviors. In contrast, traditional operations tend to create sharp transitions as shown in the previous slide that may not accurately represent real-world phenomena.​

• As shown to the left, Fractional Calculus can capture all transitions between, above, and below 1st (ß=2) and 2nd (ß=4) order integrations or differentiations (ß=-2).

SYSTEM: A system is a set of interconnected components that work together to achieve a specific objective or function. It can include physical components (machines, sensors, actuators, and controllers), managed processes and interactions, and the relationships between them.

CONTROL SYSTEM: A control system is a collection of hardware and software components designed to manage and regulate the behavior of dynamic processes. It typically includes sensors, actuators, controllers (like microcontrollers or PLCs), and the necessary software algorithms. The system uses feedback loops and signals to adjust inputs to the system or the system itself based on desired outputs, ensuring that the overall system operates as intended in applications such as robotics, manufacturing, and automotive and aerospace engineering.

FRACTIONAL ORDER CONTROL SYSTEM (FOCS): A fractional order control system is an advanced control system that utilizes fractional calculus to manage and regulate dynamic and complex processes. It comprises specialized components, including sensors, actuators, and controllers, along with sophisticated algorithms that implement fractional order control strategies.

BENEFITS OF FOCS: Fractional order control systems provide a more accurate representation of real-world processes and are characterized by their ability to model and respond to a wide range of behaviors through fractional derivatives and integrals, capturing complex dynamics that traditional integer order control systems may overlook. FOCS, applicable across a broad spectrum of technological, medical, and industrial fields, enables more efficient control, providing greater flexibility, improved stability, and enhanced precision and adaptability in performance compared to traditional integer-order control systems.

Artificial Intelligence
meets Fractional Calculus:

sNRL aims to revolutionize the deep learning and AI industry by incorporating fractional calculus into code-libraries tailored for machine-learning and deep-learning applications.  While there are libraries and frameworks available for deep learning and AI, no existing solutions specifically focus on integrating fractional calculus algorithms into AI which would effectively change the way AI "thinks" by giving AI a larger "superset" of mathematical tools.

Foundational,

Foothold Technology:

​Fractional Calculus AI presents a unique opportunity for sNRL to establish a strong foothold in the market across the increasingly competitive landscape of deep learning and AI.  Our goal is to integrate sNRL's patented fractional calculus code-libraries and algorithms into deep learning and artificial intelligence systems, enhancing their performance and pushing the boundaries of what is possible in these rapidly evolving fields to drive innovation.

By leveraging the power of fractional calculus combined with AI, we aim to revolutionize anomaly detection, predictive modeling, time series analysis, and other critical areas of data analytics.  ​​sNRL is both developing code-libraries that integrate our patented fractional calculus DSP algorithms into existing deep learning AI frameworks and also coding our own Fractional Calculus AI frameworks (FC-AI) across multiple fields-of-use.

AI Access to

Fractional Calculus:

These FSDSP and fractional calculus AI code-libraries will allow practitioners to effortlessly incorporate fractional calculus principles into their models thus lowering the bar of entry to use this advanced technology, improving accuracy, solution convergence rates, and efficiency of calculations. Our libraries will support multiple programming languages and frameworks, ensuring compatibility and ease of use for a wide range of users.

Breaking Limitations
of an Exponential Market:

​​The deep learning and AI market is experiencing exponential growth, with organizations across industries adopting these technologies for improved decision-making, automation, and optimization. However, current algorithms have limitations in capturing long-range dependencies and accurately modeling complex systems. This is where fractional calculus provides a significant advantage, enabling more precise modeling and enhanced performance.

Simplifying

the Complex:

By building fractional calculus code toolboxes for AI, sNRL is providing AI an expanded mathematical library leading to more advanced solutions and the ability to tackle the toughest problems in signal processing. Additionally, the equations of FSDSP are computationally more efficient and can save energy, battery life, and memory used by AI. Our target market includes AI developers, data scientists, research institutions, government, and companies looking to harness the full potential of deep learning and FC-AI.

By investing in sNRL today, you will be supporting a startup at the forefront of innovation at the intersection of fractional calculus, deep learning, and AI. Together, we will redefine the boundaries of what is possible and pave the way for a new era of intelligent systems. Our patented algorithms and code-libraries have the potential to transform industries across the board, from finance and healthcare to robotics and autonomous systems.

A New Frontier

in Signal Processing:

Through key strategic partnerships and investments, sNRL will better be able to accelerate the development and deployment of our fractional calculus code-libraries enhanced with deep learning capabilities. By joining forces with sNRL, you will be part of an incredible journey to reshape the future of deep learning and AI, unlocking new frontiers in data analysis, modeling, and driving groundbreaking advancements.

Expert AI Example in Medicine:

• Medical Signal Analysis: An AI trained to analyze heart rhythms and detect anomalies, utilizing fractional calculus to improve signal clarity and reduce noise, enabling more accurate diagnostics.

• Neuroactivity Monitoring: A dedicated AI interpreting brainwave patterns, employing fractional calculus to model dynamic changes over time, aiding early detection of conditions like Alzheimer's.

• Audio Processing: An AI focused on speech patterns, using fractional calculus to filter and adjust audio signals in real-time, from enhancing clarity for hearing aids to identifying voice signatures related to medical conditions like Parkinson's.​

Real-World Impact:

• Expert AIs developed using sNRL's fractional calculus libraries are expected to significantly improve healthcare diagnostics, enhance decision-making processes, and contribute to better patient outcomes through advanced analytical capabilities.

SLMN: Expert AIs and Their Applications

Orchestration Neural Engine (ONE):

Role:

• ONE functions as the central coordinator, integrating outputs from expert AIs and managing system-wide operations, similar to the cerebrum's role in higher cognitive functions such as decision-making, information synthesis, problem-solving, and complex reasoning.  By this measure, ONE integrates data from various layers and diverse types of information to form a cohesive understanding.

• Utilizes fractional calculus to optimize planning and execution of multi-step processes by analyzing historical performance data and predicting ideal outcomes.

Capabilities:

• Responsible for adapting strategies based on real-time feedback, ONE mimics the brain’s ability to learn from experience and adjust actions accordingly, employing fractional calculus to model and anticipate changes in system dynamics.

• Integrates the functionalities of COMA, SIM, and MIST, ensuring seamless communication and collaboration among these components to enhance overall system performance.

• Facilitates dynamic resource allocation, allowing the system to prioritize tasks and allocate processing power where it is most needed, improving efficiency and responsiveness.

• Monitors system health and performance metrics, proactively identifying potential issues and making adjustments to maintain optimal operation.

Software Development Kit (SDK)

• Embedded Products
• Edge Computing
• Microcontrollers
• FSDSP Chipsets

Fractional Scaling Digital Signal Processing (FSDSP) Chip/Microcontroller

• Incorporates FSDSP/Fractional Calculus
• May be programmed through SDK
• May interface with API

Licensing Vehicle:

Revenue Generation

Product Portfolio:

FC Toolkits/AI Engine

Write Once...

Run Anywhere:

Expect nonlinear or exponential response out of proportion to our entry into market.  Once patented algorithms with AI are integrated into an API and SDK, codebase may be run on multiple types of datasets or deployed via multiple types of microcontrollers or chipsets. Design and maintenance of front-ends for specific fields of use ensure compatibility. Additional feature sets, analysis, and use cases continuously being developed and patented.

Standardized

Algorithm Search Engine:

Currently, one cannot just Google an algorithm for quick implementation. The sNRLTECH codebase provides a search engine for standardized algorithms and fractional order control system applications.  Essentially, the API and SDK provide plug and play capability for sensors to use advanced digital signal processing combined with AI for rapid incorporation into prototypes and licensing of any proprietary algorithms.

Although focused on Fractional Calculus and AI, the API and SDK may become a searchable database of proprietary algorithms that may be licensed with a percent of the licensing fee to sNRL for maintaining and licensing these algorithms.  This would also create a market for algorithms at Universities that otherwise go unlicensed making them more accessible. Scientists could add their own proprietary data or algorithms to the database and share in licensing fees.

Modularized Building

Block Architecture:

The sNRLTECH API and SDK creates an architectural framework of modularized building block algorithms that seamlessly link together so that any signal is processed correctly with minimal effort.  An import tool utilizing deep learning and AI would serve to orientate the input data correctly for the algorithms based on the type of data to be processed.  Rapid generation of FSDSP filters are obtained through a Data Equalizer GUI.

FCC Narrowbanding Mandate - Traditional Filters

FCC Narrowbanding Mandate - FSDSP Filters

With improved fractional scaling digital filters for tuning and isolating a signal from the interference of adjacent frequencies, FSDSP extends the usable reception range leading to fewer dropped calls and less noise in radio signals.

Encryption of Radio Signals within Noise (Military-Tactical Software Defined Radios) is also possible through FSDSP offering the ability to embed high resolution signals in what appears to be random noise or any other signal over open airwaves.

FSDSP EXCEEDS THE STATE-OF-THE-ART INDUSTRY STANDARD

FSDSP EXCEEDS THE STATE-OF-THE-ART INDUSTRY STANDARD

FSDSP EXCEEDS THE STATE-OF-THE-ART INDUSTRY STANDARD

FIELDS-OF-USE WHERE FRACTIONAL CALCULUS WILL HAVE AN IMPACT
Listed below are some identified disciplines and industries where FC will make a difference:

• control theory

• cybernetics

• information theory

• medicine

• neuroscience

• neuroengineering

• cognitive science

• human behavioral sciences

• environmental sciences

• meteorology

• geophysics

• digital optics

• broadcasting

• Finance

• Marketing

• control systems

• robotics

• mechanical engineering

• mechatronics

• sensors/sensing

• electrical engineering

• telecommunications

• Audio

• Video

• digital signal processing

• RADAR

• SONAR

• Data Acquisition Systems

• GPS

• Quantum Computing

• Telemedicine (Sensors)

• Spectroscopy

• Hyperspectral Imaging

• Imaging Medical Devices

• First Responder (XRAY)

• Heart Rate ID Security

• RF Communications

• Bluetooth

• WiFi

• Fiber Optics

• Telescopes (Theoretical Limit)

• Internet of Things (IoT)

• Robotics (UAVs, Autopilot)

• 3D Audio

• Speech Synthesis / Modification

• Adaptive/Augmented hearing

• Music Synthesis/Processing

• Radio

• Television

• Medical Data (EEG, MEG, fMRI)

• Economic Data (stock market algorithms)

• Environmental Data (temperature)

• Bionics/Prosthetics

sNRL BUILT AND ESTABLISHED FOUNDATIONS FOR SUCCESS

• We have developed a foundational set of FC toolbox libraries in MATLAB, hold key patents in fractional calculus algorithms, and have more patents ready to file.
• We built and maintain our own infrastructure which includes an internal communications network, a video conferencing platform, and a code repository, enabling us to begin building commercially viable FC solutions immediately upon investment while protecting the security of our technology.

PROVEN MARKET-READY SOLUTIONS ACROSS INDUSTRIES

• With validated and successful proof of concepts in fields such as borehole telemetry, audio, and neuroscience, we know our fractional calculus solutions work.
• With your investment, we can launch our FC libraries from the laboratory into commercially viable enterprise solutions across a vast and diverse industrial, medical, and technological market, unlocking substantial growth potential for our business and significant returns for our investors.

RAPID TRANSITION TO COMMERCIALIZATION

• Our expedited path to market positions us strategically ahead of competitors.
• Investment will serve as the catalyst to accelerate the development of APIs, SDKs, and comprehensive FC toolbox libraries for seamless integration into AI and other applications.
• With a clear path to market and the groundwork already laid, we are also poised to initiate the development of our SCaLiNG Layered Matrix Network (SLMN) AI.

PARTNERING FOR A TRANSFORMATIVE FUTURE

• By investing in sNRL, you become a key partner in our mission to advance science and expand the boundaries of technology. Together, we will harness fractional calculus to redefine industry standards, introduce entirely new technologies, and reshape the future of AI.
• Together, by leveraging the power of fractional calculus, we can drive a technological revolution that opens new scientific frontiers and creates a lasting impact across multiple markets to meet the demands of tomorrow—today. Your investment will not only contribute to this momentum but also position you alongside us at the forefront of a paradigm shift in the technological landscape through the integration of fractional calculus, capitalizing on our advanced position in the industry.
  

Building the Algorithms that Shape Our World

The TIME is NOW:

Emerging Fields in Frontier Science:

Fractional Calculus is emerging as a significant field of mathematics while Artificial Intelligence is experiencing exponential growth, both of which have profound applications in all related fields of science and engineering. Only recently in the past 15 years have researchers and academics really begun to explore Fractional Calculus as an applied discipline, as advancements in computer processing power and sensor technologies have made possible the handling of the breadth of calculations which had previously precluded any serious application of the subject.

Integration of Fractional Calculus

Into Deep Learning and AI Algorithms:

Likewise, these same advances in computer processing power have led to an explosion in Artificial Intelligence technologies, with new discoveries occurring on an almost daily basis.  Still, while AI is thought of as the next frontier, AI is still in its early stages of development. Furthermore, dedicated research and development of Fractional Calculus currently exists only in a few rarefied universities and laboratories.

In order to push the envelope of Frontier Science, AI must be given access to the power, accuracy, robustness, and efficiency of fractional calculus.

Fractional Calculus and Artificial Intelligence Institute:

R&D Think Tank and Educational Institute

Fractional Scaling

Digital Signal Processing

Licensing Information:
The sNoise Research Laboratory has intellectual property rights relating to technology described in this document. In particular, and without limitation, these intellectual property rights include the algorithms and methods of Fractional Scaling Digital Signal Processing, Fractional Scaling Digital Filters, and Fractional Order Control Systems which are covered by one or more patents or pending patent applications. Commercial use of algorithms and methods of Fractional Scaling Digital Signal Processing, Fractional Scaling Digital Filters, and/or Fractional Order Control Systems is strictly prohibited without a licensing agreement obtained through the sNoise Research Laboratory Technology Office (tech@snoiselab.com). Other uses of this document, including reproduction and distribution, selling or licensing copies, or posting to personal, institutional, or third party websites are prohibited.

sNoise®™ is a registered trademark of the sNoise Research Laboratory.

Patented and Patent Pending Technology:

• U.S. Patent No. 9,740,662 issued August 22, 2017 claiming priority to U.S. Provisional Patent Applications Nos. 61/870,052 and 61/870,064 filed on August 26, 2013 and No. 62/039,684 filed on August 20, 2014.

• U.S. Patent No. 10,164,609B2 issued December 25, 2018; US version of International Patent Application No. PCT/US15/46184

• International Patent Application No. PCT/US15/46184 filed on August 20, 2015 claiming priority to U.S. Provisional Patent Application No.62/039,684 filed on August 20, 2014.

• International Patent Application No. PCT/US17/44257 filed on July 27, 2017 claiming priority to U.S. Provisional Patent Application No. 62/367,464 filed on July 27, 2016.

• U.S. Patent No. 10,169,293B2 issued January 1, 2019; filed on August 21, 2017, Continuation of U.S. Patent No. 9,740,662.

• U.S. Patent No. 10,727,813B2 issued July 28, 2020; filed on July 27, 2017.

CONTACT:
For All Licensing Inquires: tech@snoiselab.com
For Scientific Inquiries: Jeffrey.Smigelski@snoiselab.com

v18.14DEC2024

sNoise Research Laboratory
13719 23 Mile Road #116, Shelby Township, MI 48315
sNRL@snoiselab.com

Dr. Jeffrey R. Smigelski, Ph.D.
Jeffrey.Smigelski@snoiselab.com

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