Title:

IID STOCHASTIC ANALYSIS OF PWM SIGNALSGROUP MEMBERS: AMER AZIZ 172203 SALMAN BASHIR 171228

CONTENTSTo evaluate the basic stochastic characteristics Mean and Autocorrelation of PWM signals Power Spectral Density (PSD)

Conversion of non stationary PWM signals into simple wide sense stationary using different sampling techniques

For I.I.D uniformly distributed, the proposed autocorrelation functions are tested with simulation

BeginningWITHINTRODUCTION

1Presenter: Muhammad Salman Bashir

The second rule is: Spread ideas and move people.4

INTRODUCTIONPWM (PULSE WIDTH MODULATION)Sampling methodology of input signalTypes of PWM depending Make PWM signal wised sense stationary (WSS) Evaluation of stochastic characteristics namely autocorrelation (ACF) and power spectral density (PSD) theoreticallySimulation of autocorrelation (ACF) for PWM signalComparison of theoretically and simulation resultsConclusion

How Work Flow

What is PWM

Trailing Edge PWM Lead edge of trigger signal is modulated.

Leading Edge PWM Trail edge of trigger signal is modulated.

Double Edge PWM Pulse center is fixed and both edges are modulated.

Types of PWM

Trailing Edge PWM

Mean of TEPWM Leading Edge PWM

Mean of LEPWM

Double Edge PWM

Mean of DEPWM

NON STATIONARY PWM Signal with fixed starting point

WSS

WideSenseStationaryPresenter: Amer Aziz

So there are the rules.10

A discrete-time or continuous-time random process X(t) is wide-sense stationary (WSS)Mean is constant mX(t) = m

For all t Autocorrelation of X(t) is function of time difference (t2-t1) RX(t1, t2) = RX(), for all t1 and t2

WIDE SENSE STATIONARY

Randomizing starting point by , uniformly distributed over [0,T]

Limiting input signal amplitude(bk) over sample interval [0,1] uniformly and using sampling methodology WSS and IID PWM signal

Trailing Edge PMW Mean is constant Autocorrelation is function of difference as =t-s

CONVERSION IN WIDE SENSE STATIONARY

Leading Edge PWM

Mean is constant

Autocorrelation is function of time difference

Double Edge PWM

Mean is constant

Autocorrelation is function of time difference

We can also find PSD of PWM signals.

Trailing Edge

COMPARISON OF SIMULATION AND THEORETICAL RESULTS

We have used an unbiased discreteestimator for autocorrelation functions RPT E() and RPLE() with T = 200 and we have traced the behavior over 10 cycles

I.I.D uniform, construction, RPT E() = RPLE() even if Trailing Edge And leading edge PWM signals are different

Leading Edge

Double Edge

PWM signal with a fixed starting point is not necessarily wide sense stationary

PWM signal with randomized starting point and I.I.D pulse widths over a symbol interval is necessarily WSS

Using the autocorrelation functions, derived the power spectrum densities (PSD) easily

For I.I.D. uniform distribution case, we have shown the accuracy of our results with simulations.

CONCLUSION