Download presentation

Presentation is loading. Please wait.

Published byRita Dinning Modified over 3 years ago

1
Complex exponentials as input to LTI systems h(t) h[n] H(e j ) e j n e j t e j n H(j ) e j t Cos as input… use Euler formula

2
LCC Differential equation 1 st order: y(t) + a y(t) = x(t) Homogenous solution/ zero input / natural response: y h (t) = -ay h (t) y h (t) = e -at Solution to x(t) = (t), with zero initial condition y(t) = h(t) = e -at u(t) What is initial rest condition: x(t) = 0, for t <= t 0 y(t) = 0, for t <= t 0 If zero initial condition (initially at rest) is imposed: equation is describing LTI and causal system.

3
LCC Difference equation 1 st order: y[n] - a y[n-1] = x[n] Homogenous solution/ zero input / natural response: y h [n] = ay h [n-1] y h [n] = a n Solution to x[n] = [n], with zero initial condition y[n] = h[n] = a n u[n] Use initial rest condition to find particular solution: x[n] = 0, for n <= n 0 y[n] = 0, for n <= n 0 If zero initial condition (initially at rest) is imposed: equation is describing LTI and causal system.

4
LCC Differential equation N th order: 1 st order: y(t) + a y(t) = b x(t) Homogenous solution/ zero input / natural response: y h (t) = -ay h (t) y h (t) = e -at Solution to x(t) = (t), with zero initial condition: y(t) = h(t) = b e -at u(t) (t) is changing the output instantaneously. Zero initial condition: x(t) = 0, for t <= t 0 y(t) = 0, for t <= t 0 If zero initial condition (initially at rest) is imposed: equation is describing LTI and causal system.

5
LCC Difference equation N th order: 1 st order: y[n] - a y[n-1] = x[n] Homogenous solution/ zero input / natural response: y h [n] = ay h [n-1] y h [n] = a n Solution to x[n] = [n], with zero initial condition y[n] = h[n] = a n u[n] Initial rest condition: x[n] = 0, for n <= n 0 y[n] = 0, for n <= n 0 If zero initial condition (initially at rest) is imposed: equation is describing LTI and causal system.

Similar presentations

OK

Ch 3.4: Complex Roots of Characteristic Equation Recall our discussion of the equation where a, b and c are constants. Assuming an exponential soln leads.

Ch 3.4: Complex Roots of Characteristic Equation Recall our discussion of the equation where a, b and c are constants. Assuming an exponential soln leads.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Powerpoint ppt on spinal injuries Ppt on power sharing in indian and other countries Ppt on video teleconferencing software Ppt on superstition in indian culture Ppt on beer lambert law problems Ppt on toyota production system Ppt on sustainable tourism practices Ppt on world book day dress Ppt on online shopping in php Blood vessel anatomy and physiology ppt on cells