In this article, we revisit and generalize the multitone sinusoidal frequency modulation (MTSFM) expansion, which has been used in the past decade for various radar and sonar applications, such as optimal transmit waveform design and modeling nonlinear frequency modulation. In its original form, the MTSFM describes a phase-modulated signal on a time interval $T$ by the Fourier expansion of its instantaneous frequency or modulation function. The period of this expansion is chosen equal to $T$ resulting in the sinusoidal expansion functions being orthogonal on $T$. In this article, we extend the MTSFM to expansions with arbitrary periods and, hence, nonorthogonal sinusoidal expansion functions. When applied to represent a specific signal, these expansions have different convergence rates and differentiability characteristics and, hence, result in signals with different spectral compactness and efficiency. Also, we expand the time-dependent phase of the signal instead of the instantaneous frequency or modulation function, which allows classically (in $L_{2}$ sense) for the representation of less smooth signals. We will illustrate these aspects by three examples of representing a classical MTSFM expansion, an up-chirp, and a pseudorandomly phase-modulated pulse by generalized MTSFM expansions, for which we calculate quantities such as root-mean-square (RMS) bandwidth, frequency response, autocorrelation function, and approximation accuracy. Also, we provide tangible examples of using the generalized expansions in a gradient-based optimizer to synthesize signals for optimal integrated sidelobe ratio under RMS bandwidth constraint. To this end, we derive general and easy-to-use expressions for the derivatives of the objective and constraint functions.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Extending the Multitone Sinusoidal Frequency Modulation Signal Model by Fourier Expansions With Arbitrary Periods


    Contributors:


    Publication date :

    2025-04-01


    Size :

    4728060 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Optical frequency comb optimization for satellite payload applications based on multitone phase modulation

    Stratakis, Ioannis / Avraam, Chrysovalantis / Kastritsis, Dimitrios et al. | British Library Conference Proceedings | 2023



    Impact of Nonlinear LED Transfer Function on Discrete Multitone Modulation: Analytical Approach

    Neokosmidis, I. / Kamalakis, T. / Walewski, J.W. et al. | British Library Online Contents | 2009


    Discrete Multitone Format for Repeater-Less Direct-Modulation Direct-Detection Over 150 km

    Liu, Z. / Kelly, B. / O Carroll, J. et al. | British Library Online Contents | 2016