Waveform Design using Multi-Tone Feedback Frequency Modulation

Abstract

This paper introduces a waveform design method using Multi-Tone Feedback Frequency Modulation (MT-FFM), a generalization of the single oscillator feedback FM method developed by Tomisawa [1]. The MT-FFM utilizes a collection of K harmonically related oscillators each governed by a design parameter z k which are utilized as a discrete set of parameters that may be modified to generate a richer set of modulation functions than in the single oscillator case. The resulting modulation function is represented using a form of Kapteyn series composed of Generalized Bessel Functions. This paper describes the structure of the MT-FFM waveform, derives the Kapteyn series representation of the waveform's modulation function, and demonstrates the design method with a waveform design example.

Generalized Bessel Functions and Their Use in Bremsstrahlung and Multi-Photon Processes

“…During the sixties of XX-th century, Reiss rediscovered elementary examples of GBF while investigating problems in light-light and non-dipolar scattering [6,7]. More substantive applications started some years later and they have been employed in Classical/Quantum Electromagnetic Processes [8,9], laser physics [10], Sonar and Radar [11,12], Crystallography [13] . .…”

Transmit waveform design using Multi-Tone Sinusoidal Frequency Modulation

“…Recently, the author introduced the Multi-Tone Sinusoidal Frequency Modulated (MTSFM) waveform model [13], [14] and its variants [14], [15] as a constant amplitude and spectrally efficient adaptive waveform design method. The MTSFM's modulation function is represented as a finite Fourier series where the Fourier coefficients are utilized as a discrete set of parameters.…”