Print Email Facebook Twitter Parametric Representations of Signals and Waveforms Title Parametric Representations of Signals and Waveforms: Extending the MTSFM by Non-Orthogonal Expansions Author Bekers, D.J. Publication year 2022 Abstract In this paper we revisit and generalize the Multi-Tone Sinusoidal Frequency Modulation (MTSFM), which has been used in the past decade for various Radar and Sonar applications including optimal transmit waveform design, modelling non-linear frequency modulation, high-duty cycle sensors . In its original form, the MTSFM describes a phase modulated signal or pulse by Fourier expansions of its phase and instantaneous frequency. These expansions exhibit orthogonal sinusoidal functions. In this work we extend the MTSFM to support also non-orthogonal expansion functions by introducing periodicities different from the pulse width. For a simple example of an up-chirp we specify its expansions for three different periodicities, which by definition incorporate also the symmetric chirp. The expansions have different convergence rates and differentiability characteristics when considered as Fourier series. Also, we derive tangible expressions for the RMS bandwidth induced by the non-orthogonal expansions and its derivatives, potentially to be used in gradient-based optimizers. We validate the RMS bandwidth expressions, both analytically and numerically, using the three expansions with different periodicities Subject Mult-tone sinusoidal frequency modulationSignal representationNon-orthogonal Fourier expansionsRMS bandwidthPhase modulation To reference this document use: http://resolver.tudelft.nl/uuid:70c2512a-80ec-46a7-b0c2-a5d0cfe735a1 TNO identifier 969606 Source Radar2022 Edinburgh october 2022 Document type conference paper Files To receive the publication files, please send an e-mail request to TNO Library.