I.I.D. stochastic analysis of PWM signals

Sevuktekin, Noyan C.; Singer, Andrew C.

doi:10.1109/acssc.2014.7094796

2014 48th Asilomar Conference on Signals, Systems and Computers 2014

DOI: 10.1109/acssc.2014.7094796

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I.I.D. stochastic analysis of PWM signals

Noyan C. Sevuktekin

Andrew C. Singer

Abstract: A stochastic analysis for pulse width modulation (PWM) is given. Under a discrete random generator process with independent identically distributed (i.i.d.), continuous, rangelimited samples, stochastic models for different PWM signals are proposed. Using randomization of the signal starting point, wide sense stationarity (WSS) of proposed PWM signals are shown. Autocorrelation functions and their corresponding power spectrum densities (PSD) are derived in terms of the modified complementary cumulative distrib… Show more

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Cited by 2 publications

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“…Introduction: There has been much interest in random modulation schemes for power converters, with reduced electromagnetic interference (EMI) as one of the main benefits [1][2][3][4]. To date all of the analyses of power converters driven by random modulation schemes have involved auto-correlation functions and power density spectra.…”

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confidence: 99%

Generalised random switching circuits: A time‐domain technique

Naude

Hofsajer

2016

Electron. lett.

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A probabilistic solution of the time-domain performance of an arbitrary switching circuit driven by a generalised random switching sequence is presented. A generalised random switching sequence is the superset of all clock-based random pulse-width modulation schemes and has the best possible spectral spreading. The switching circuits considered are linear and time invariant, have a constant DC input and contain at least one ideal switch. The mean of the probability density updates exactly like a discrete time solution to state-space averaging, with probability replacing the duty cycle. The covariance matrix of the probability density updates using a difference equation. The value of this work is in the prediction of the statistics of transients for randomly switched power converters. A boost converter is presented as an example.

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confidence: 99%

Generalised random switching circuits: A time‐domain technique

Naude

Hofsajer

2016

Electron. lett.

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Spectrum analysis of digital UPWM signals generated from random modulating signals

Kaleris,

Psarakis,

Mourjopoulos

2024

Sci Rep

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This work studies the spectrum of discrete-time Uniform-sampling pulse width modulation (UPWM) signals originating from stochastic input signals. It demonstrates that for ergodic input sequences of independent and identically distributed random variables, the Discrete Fourier Transform (DFT) of the UPWM signals can be directly estimated from the input signal’s statistics. Consequently, it is shown that if the input signal can be modeled as such a random sequence, only statistical information of the sequence is required for the accurate estimation of the DFT of the UPWM signal. This is achieved here by proving that the DFT estimators obtained by observation of the input sequence within a time window are consistent estimators of the DFT coefficients of the underlying random process. Moreover, for signals whose generalized probability density functions can be expressed as functions of a small number of parameters, the DFT coefficients can be estimated or even calculated via closed-form expressions with linear complexity. Examples are given for input signals derived from symmetric and asymmetric distributions. The results are validated by comparison with evaluations of the UPWM signal’s DFT via the Fast Fourier Transform (FFT). The proposed method provides a mathematical framework for the analysis and design of UPWM systems whose inputs have known statistical properties.

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I.I.D. stochastic analysis of PWM signals

Cited by 2 publications

References 8 publications

Generalised random switching circuits: A time‐domain technique

Generalised random switching circuits: A time‐domain technique

Spectrum analysis of digital UPWM signals generated from random modulating signals

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