Waveform Design using Multi-Tone Feedback Frequency Modulation

TL;DR

This paper presents a novel waveform design method called Multi-Tone Feedback Frequency Modulation (MT-FFM), which generalizes single oscillator feedback FM by using multiple harmonically related oscillators to create richer modulation functions.

Contribution

It introduces the MT-FFM framework, derives its Kapteyn series representation, and demonstrates its application through a waveform design example, expanding the capabilities of feedback FM techniques.

Findings

MT-FFM enables richer modulation functions than single oscillator feedback FM.

The waveform's modulation function is expressed as a Kapteyn series of Generalized Bessel Functions.

The method is demonstrated with a practical waveform design example.

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, 1981]. 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.