Parametric Representations of Signals and Waveforms: Extending the MTSFM by Non-Orthogonal Expansions
conference paper
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
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
Topics
TNO Identifier
969606
Source title
Radar2022 Edinburgh october 2022
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