This presentation was an assigned task for group of students to present there paper in nust, college of eme. I help them create this presentation to shear knowledge i am shearing this presentation as public.

2. Title:
IID STOCHASTIC ANALYSIS
OF PWM SIGNALS
GROUP MEMBERS:
AMER AZIZ 172203
SALMAN BASHIR 171228

3. CONTENTS
 To evaluate the basic stochastic characteristics
o Mean and Autocorrelation of PWM signals
o 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

4. Beginning
INTRODUCTION
1
Presenter: Muhammad Salman Bashir

5. INTRODUCTION
 PWM (PULSE WIDTH MODULATION)
 Sampling methodology of input signal
 Types of PWM depending
 Make PWM signal wised sense stationary (WSS)
 Evaluation of stochastic characteristics namely
autocorrelation (ACF) and power spectral density (PSD)
theoretically
 Simulation of autocorrelation (ACF) for PWM signal
 Comparison of theoretically and simulation results
 Conclusion

6. Non Stationary
Randomize
Stating
point
Wide Sense
Stationary
How Work Flow
Mean and
auto
correlation
Simulation

7. What is PWM

8.  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

9. 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

10. Presenter: Amer Aziz

11. 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(τ), for all t1
and t2
WIDE SENSE STATIONARY

12.  Randomizing starting point
by Φ, 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
τ=t-s
CONVERSION IN WIDE SENSE
STATIONARY

13. Leading Edge PWM
Mean is constant
Autocorrelation is function of
time difference

14. Double Edge PWM
Mean is constant
Autocorrelation is function
of time difference
We can also find PSD of
PWM signals.

15. Trailing Edge
COMPARISON OF SIMULATION
AND THEORETICAL RESULTS
We have used an
unbiased discrete
estimator for
autocorrelation
functions RPT E(τ)
and RPLE(τ) with T =
200 and we have
traced the behavior
over 10 cycles

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

17.  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