Abstract: A process for processing a digital signal comprises constructing a fractional order control system that models a desired frequency response by assembling filter components from a filter component library. The filter components are defined by Laplace functions that include a non-integer control order having a variable fractional scaling exponent. Then, the fractional order control system is adjusted by applying an altitude exponent to the fractional order control system, and the altitude exponent changes a magnitude of the frequency response without changing a width of a transition band of the frequency response. An input signal in the digital frequency domain is received and processed based upon the fractional order control system to generate a digital output that is conveyed.

Abstract: A process for processing a digital signal comprises constructing a fractional order control system that models a desired frequency response by assembling filter components from a filter component library. The filter components are defined by Laplace functions that include a non-integer control order having a variable fractional scaling exponent. Then, the fractional order control system is adjusted by applying an altitude exponent to the fractional order control system, and the altitude exponent changes a magnitude of the frequency response without changing a width of a transition band of the frequency response. An input signal in the digital frequency domain is received and processed based upon the fractional order control system to generate a digital output that is conveyed.

Abstract: A method for processing a digital signal comprises identifying a desired frequency and/or phase response that is represented in a frequency domain representation. A fractional order control system that models the desired frequency and/or phase response is constructed by assembling a first filter component from a filter component library and a second filter component from the filter component library. At least one filter component of the filter component library is defined by a Laplace function that includes a non-integer control order having a variable fractional scaling exponent and a value for the non-integer, variable fractional scaling exponent of the second filter component is based on a value of the non-integer, variable fractional scaling exponent of the first filter component. An input in the digital frequency domain is received and processed based upon the fractional order control system to generate a digital output. The output is then conveyed to a user.

Abstract: A digital signal synthesizer for generating a frequency and/or phase modified digital signal output comprises an input buffer, a transform module, a processing module, and an output buffer. The input buffer receives a digital input that is represented in a frequency domain representation. The transform module stores a fractional order control system that models a desired frequency and/or phase response defined by an assembly of at least one filter component. Each filter component is defined by a Laplace function that is modified to include a non-integer control order having a variable fractional scaling exponent. The processing module multiplies or divides the digital input with the fractional order control system stored in the transform module. Moreover, the output buffer stores a synthesized output of the input, which is modified in the frequency domain, the phase domain, or both according to the desired frequency and/or phase response by the processing module.

Abstract: A method for processing a digital signal comprises identifying a desired frequency and/or phase response that is represented in a frequency domain representation. A fractional order control system that models the desired frequency and/or phase response is constructed by assembling a first filter component from a filter component library and a second filter component from the filter component library. At least one filter component of the filter component library is defined by a Laplace function that includes a non-integer control order having a variable fractional scaling exponent and a value for the non-integer, variable fractional scaling exponent of the second filter component is based on a value of the non-integer, variable fractional scaling exponent of the first filter component. An input in the digital frequency domain is received and processed based upon the fractional order control system to generate a digital output. The output is then conveyed to a user.

Abstract: Generation of standardized noise signals that provide mathematically correct noise with no errors and no loss of data, and can generate the noise of specific environments based on the transfer function of that environment are discussed. Various embodiments can generate synthetic data sets based on natural data sets that have similar scaling behavior. Fractional scaling digital filters, containing the fractional scaling characteristics of one or more of the eleven fundamental forms of basic building block transfer functions which incorporate the scaling exponent, can be encoded on FPGA devices or DSP chips for use in digital signal processing. Fractional Scaling Digital Filters allow fractional calculus, and thus fractional filtering (e.g.

Abstract: A digital signal synthesizer for generating a frequency and/or phase modified digital signal output comprises an input buffer, a transform module, a processing module, and an output buffer. The input buffer receives a digital input that is represented in a frequency domain representation. The transform module stores a fractional order control system that models a desired frequency and/or phase response defined by an assembly of at least one filter component. Each filter component is defined by a Laplace function that is modified to include a non-integer control order having a variable fractional scaling exponent. The processing module multiplies or divides the digital input with the fractional order control system stored in the transform module. Moreover, the output buffer stores a synthesized output of the input, which is modified in the frequency domain, the phase domain, or both according to the desired frequency and/or phase response by the processing module.

Abstract: Generation of standardized noise signals that provide mathematically correct noise with no errors and no loss of data, and can generate the noise of specific environments based on the transfer function of that environment are discussed. Various embodiments can generate synthetic data sets based on natural data sets that have similar scaling behavior. Fractional scaling digital filters, containing the fractional scaling characteristics of one or more of the eleven fundamental forms of basic building block transfer functions which incorporate the scaling exponent, can be encoded on FPGA devices or DSP chips for use in digital signal processing. Fractional Scaling Digital Filters allow fractional calculus, and thus fractional filtering (e.g.