diamondback 1.0.25

Diamondback Digital Signal Processing ( DSP ) package including commons, filters, interfaces, models, and transforms.

### Description

Diamondback is a Python package which provides Digital Signal Processing ( DSP ) solutions, organized in the form of commons, filters, interfaces, models, and transforms.

Diamondback was designed to complement Artificial Intelligence ( AI ) frameworks, by defining components which analyze, filter, extract, model, and transform data into forms which are useful in applications including pattern recognition, feature extraction, and optimization.

Diamondback was also designed to provide utility in the context of classical signal processing solutions including communications, modeling, signal identification and extraction, and noise cancellation.

Documentation is provided in HTML form, extracted from docstrings in the diamondback package source, and a Jupyter notebook is provided to dynamically construct and exercise diamondback components to facilitate experimentation and visualization.

### Details

An extensible factory design pattern is expressed in many components, and a mix-in design pattern is extensively employed in property definition. Complex or real types, in adaptive or static forms, are supported as appropriate. Data collections are consistently expressed in native types, including tuples, sets, lists, and dictionaries, with vector and matrix types expressed in numpy arrays.

Diamondback is defined in subpackages :

• [commons](https://larryturner.github.io/diamondback/diamondback.commons)

• [filters](https://larryturner.github.io/diamondback/diamondback.filters)

• [interfaces](https://larryturner.github.io/diamondback/diamondback.interfaces)

• [models](https://larryturner.github.io/diamondback/diamondback.models)

• [transforms](https://larryturner.github.io/diamondback/diamondback.transforms)

#### [commons](https://larryturner.github.io/diamondback/diamondback.commons)

• [Log](https://larryturner.github.io/diamondback/diamondback.commons#module-diamondback.commons.Log) singleton instance which formats and writes log entries, electively using the logger package or directly to a specified stream. Log entries are prefaced with an ISO-8601 datetime and log level, and enhancements are made to the formatting of datetime, exception, and collection data types. Dynamic stream redirection and log level specification are supported.

• [Serial](https://larryturner.github.io/diamondback/diamondback.commons#module-diamondback.commons.Serial) singleton instance which encodes and decodes an instance or collection with JSON text, or base-64 encoded gzip JSON binary format.

#### [filters](https://larryturner.github.io/diamondback/diamondback.filters)

• [ComplexBandPassFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.ComplexBandPassFilter) instances adaptively extract or reject signals at a normalized frequency of interest, and may be employed to dynamically track magnitude and phase or demodulate signals.

• [ComplexExponentialFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.ComplexExponentialFilter) instances synthesize complex exponential signals at normalized frequencies of interest with contiguous phase.

• [ComplexFrequencyFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.ComplexFrequencyFilter) instances adaptively discriminate and estimate a normalized frequency of a signal.

• [DerivativeFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.DerivativeFilter) instances estimate discrete derivative approximations at several filter orders, through extensible factory construction.

• [FirFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.FirFilter) instances realize discrete difference equations of Finite Impulse Response ( FIR ) form, in adaptive or static solutions. A factory electively constructs instances based on type, classification, normalized frequency, order, cascade count, and complement. Filters may be readily extended to support new types and functionality, while retaining factory support. Root extraction, group delay, and frequency response evaluation are defined.

• [GoertzelFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.GoertzelFilter) instances efficiently evaluate a Discrete Fourier Transform ( DFT ) at a normalized frequency, based on a window filter and normalized frequency.

• [IirFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.IirFilter) instances realize discrete difference equations of Infinite Impulse Response ( IIR ) form, in adaptive or static solutions. A factory electively constructs instances based on type, classification, normalized frequency, order, cascade count, and complement. Filters may be readily extended to support new types and functionality, while retaining factory support. Root extraction, group delay, and frequency response evaluation are defined.

• [IntegralFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.IntegralFilter) instances estimate discrete integral approximations at several filter orders, through extensible factory construction.

• [PidFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.PidFilter) instances realize discrete difference equations of Proportional Integral Derivative ( PID ) form.

• [PolynomialRateFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.PolynomialRateFilter) instances approximate a signal evaluated at an effective frequency equal to the product of the normalized frequency and a rate greater than zero, supporting decimation and interpolation through localized polynomial approximation with no group delay.

• [PolyphaseRateFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.PolyphaseRateFilter) instances approximate a signal evaluated at an effective frequency equal to the product of the normalized frequency and a rate greater than zero, supporting decimation and interpolation through construction and application of a polyphase filter bank, a sequence of low pass filters with a common frequency response and a fractional sample difference in group delay. An appropriate stride is determined to realize the specified effective frequency without bias and with group delay based on order.

• [RankFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.RankFilter) instances define nonlinear morphological operators, which define functionality based on rank and order, including dilation, median, and erosion, and may be combined in sequences to support close and open.

• [WindowFilter](https://larryturner.github.io/diamondback/diamondback.filters#module-diamondback.filters.WindowFilter) instances realize discrete window functions useful in Fourier analysis, based on type, classification, order, and normalization, through extensible factory construction.

#### [interfaces](https://larryturner.github.io/diamondback/diamondback.interfaces)

• [IA](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IA), [IB](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IB), [IClear](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IClear), [IData](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IData), [IDateTime](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IDateTime), [IDuration](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IDuration), [IEncoding](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IEncoding), [IEqual](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IEqual), [IFrequency](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IFrequency), [IInterval](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IInterval), [ILatency](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.ILatency), [IPath](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IPath), [IPeriod](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IPeriod), [IPhase](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IPhase), [IQ](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IQ), [IRate](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IRate), [IReset](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IReset), [IResolution](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IResolution), [IRotation](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IRotation), [IS](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IS), [IState](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IState), [ITimeZone](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.ITimeZone), [IUpdate](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IUpdate), and [IVersion](https://larryturner.github.io/diamondback/diamondback.interfaces#module-diamondback.interfaces.IVersion) interfaces facilitate mix-in design.

#### [models](https://larryturner.github.io/diamondback/diamondback.models)

• [DiversityModel](https://larryturner.github.io/diamondback/diamondback.models#module-diamondback.models.DiversityModel) instances select and retain a state extracted to maximize the minimum distance between state members based on classification and order, through extensible factory construction. An opportunistic unsupervised learning model typically improves condition and numerical accuracy and reduces storage relative to alternative approaches including generalized linear inverse.

• [PrincipalComponentModel](https://larryturner.github.io/diamondback/diamondback.models#module-diamondback.models.PrincipalComponentModel) instances are supervised learning models which analyze an incident signal to learn a mean vector, standard deviation vector, and a collection of eigenvectors, and produce a reference signal which is a candidate for dimension reduction, in which higher order dimensions are discarded, reducing the order of the reference signal, while preserving significant and often sufficient information.

#### [transforms](https://larryturner.github.io/diamondback/diamondback.transforms)

• [ComplexTransform](https://larryturner.github.io/diamondback/diamondback.transforms#module-diamondback.transforms.ComplexTransform) is a singleton instance which converts a three-phase real signal to a complex signal, or a complex signal to a three-phase real signal, in equivalent and reversible representations, based on a neutral condition.

• [FourierTransform](https://larryturner.github.io/diamondback/diamondback.transforms#module-diamondback.transforms.FourierTransform) is a singleton instance which converts a real or complex discrete-time signal to a complex discrete-frequency signal, or a complex discrete-frequency signal to a real or complex discrete-time signal, in equivalent and reversible representations, based on a window filter and inverse.

• [PowerSpectrumTransform](https://larryturner.github.io/diamondback/diamondback.transforms#module-diamondback.transforms.PowerSpectrumTransform) is a singleton instance which converts a real or complex discrete-time signal to a real discrete-frequency signal which estimates a mean power density of the signal, based on a window filter.

• [WaveletTransform](https://larryturner.github.io/diamondback/diamondback.transforms#module-diamondback.transforms.WaveletTransform) instances realize a temporal spatial frequency transformation through construction and application of analysis and synthesis filters with complementary frequency responses, combined with downsampling and upsampling operations, in equivalent and reversible representations. A factory constructs instances based on type, classification, and order. Filters may be readily extended to support new types and functionality, while retaining factory support.

• [ZTransform](https://larryturner.github.io/diamondback/diamondback.transforms#module-diamondback.transforms.ZTransform) is a singleton instance which converts continuous s-domain to discrete z-domain difference equations, based on a normalized frequency and application of bilinear or impulse invariant methods.

### Dependencies

Diamondback depends upon external packages :

• [jsonpickle](https://github.com/jsonpickle/jsonpickle)

• [numpy](https://github.com/numpy/numpy)

• [scipy](https://github.com/scipy/scipy)

Diamondback Jupyter notebook depends upon additional external packages :

• [ipython](https://github.com/ipython/ipython)

• [ipywidgets](https://github.com/jupyter-widgets/ipywidgets)

• [jupyter](https://github.com/jupyter/notebook)

• [matplotlib](https://github.com/matplotlib/matplotlib)

• [pillow](https://github.com/python-pillow/pillow)

### Installation

Diamondback is a public repository hosted at PyPI and GitHub.

pip install diamondback

pip install git+https://github.com/larryturner/diamondback.git

### Demonstration

A Jupyter notebook defines cells to create and exercise diamondback components. The notebook serves as a tool for visualization, validation, and demonstration of diamondback capabilities.

A Jupyter notebook may be run on a remote server without installation with Binder, which dynamically builds and deploys a Docker container from a GitHub repository, or installed from GitHub and run on a local system.

Remote

[](https://mybinder.org/v2/gh/larryturner/diamondback/master?filepath=jupyter%2Fdiamondback.ipynb)

Local

git clone https://github.com/larryturner/diamondback.git

cd diamondback

pip install –requirement requirements.txt

jupyter notebook .jupyterdiamondback.ipynb

Restart the kernel, as the first cell contains common definitions, find cells which exercise components of interest, and manipulate widgets to exercise and visualize functionality.

### Documentation

Diamondback documentation is generated from the source, indexed, and searchable from GitHub.

[](https://larryturner.github.io/diamondback/)

### Tests

A simple pytest solution is provided to exercise and verify diamondback components.

py.test –capture=no –verbose .tests

### Author

[Larry Turner](https://github.com/larryturner)

### License

[BSD-3C](https://github.com/larryturner/diamondback/blob/master/license)

### Release

[Version](https://github.com/larryturner/diamondback/blob/master/version)

Copyright (c) 2018, Larry Turner, Schneider Electric. All rights reserved.