lab4.pdf

Transcript

1. Linear system and signals Lab 4 Yulong Yang yulong.yang@rutgers.edu [For section 4&1 only.]
2. Practice 1. find coefficients num and den. 2. draw the signal. (r(t) and u(t) are unit ramp and unit step signal respectively) give me report 3 try your best on this [For section 4&1 only.]
3. Answers 1. find coefficients num and den. 2. draw the signal. num = [1 3] den = [1 2 5 0] [For section 4&1 only.]
4. tips • figures • debug [For section 4&1 only.]
5. How to draw worse “Cut-off” “Squeeze” [For section 4&1 only.]
6. ...and better axis([x_start x_end y_start y_end]) [For section 4&1 only.]
7. Debug better • same name for different variables? • typo? • error when running several programs in one script file? [For section 4&1 only.]
8. Debug better Check the error here Check your variables here [For section 4&1 only.]
9. Lab 4 • part I: system response to basic signals • part II: system response to signals with non-standard analytical form • part IV: zero-input response with initial conditions [For section 4&1 only.]
10. System response •transfer function -> num, den •impulse response •step response •zero-state response to different input signals [For section 4&1 only.]
11. num&den • how to find them? refer to example 4.20 on p169 and our practice before [For section 4&1 only.]
12. Impulse&step response • impulse(num, den) • step(num, den) • no time series • no plot() - both functions will calculate and plot the response at the same time [For section 4&1 only.]
13. zero-state response • input signal • time series! the basis of any signal - t=0:0.1:10 • sine - sin(), exponent - exp() • what is u(t)? what does it bring to the signal, when t<0 and t>=0? • lsim(num, den, f, t) • plot them out along with t [For section 4&1 only.]
14. sample plots for part I part I part I part I part I part I [For section 4&1 only.]
15. System response 2 • decompose the system response • system response to elementary signals • shifting in system response • zero-state [For section 4&1 only.]
16. decompose linearity&time-invariance [For section 4&1 only.]
17. System response to elementary signals • impulse response • impulse(num, den, t) • step response • step(num, den, t) • ramp response, input as r(t) • lsim(num, den, t, t); [For section 4&1 only.]
18. ramp response [For section 4&1 only.]
19. Shifting the system response [For section 4&1 only.]
20. Shifting the system response • instead of creating u(t-3) and then plug in to lsim • shift the system response we already have from step and impulse [For section 4&1 only.]
21. Shifting the system response ystepshift = [zeros(?, ?); ystep(?:?)]; u(t) ystep u(t-3) ystepshift [For section 4&1 only.]
22. Shifting the system response ystepshift = [zeros(?, ?); ystep(1:?)]; row vector? [1 2 3 4 ...] column vector? [1;2;3;4; ...] 1. ystep and ystepshift is 2. in ystepshift, how many zeros? how many “ystep”s? how many in total, 100, 101? [For section 4&1 only.]
23. Finally... when you have them all: y= yrampshift - yramp + ystepshift+ ystep; [For section 4&1 only.]
24. sample plot for part III part III part III part III [For section 4&1 only.]
25. zero-input response • complete system response equation 4.53 on p176 • find coefficients • get response by impulse [For section 4&1 only.]
26. complete system response equations could be found on P166 and P176 [For section 4&1 only.]
27. zero-input response in our case [For section 4&1 only.]
28. Find coefficients Find new coefficients num2 and den2 from I(s) and Delta(s) respectively find an from the transfer function [For section 4&1 only.]
29. Get response •zero-input response is just the impulse response with the new coefficients num2 and den2 •impulse(num2, den2, t) •plot [For section 4&1 only.]
30. sample plot for part IV part IV part IV [For section 4&1 only.]
31. For the report •part I: 4 plots for one impulse response, one step response, 2 zero-state response •part III: one plot for the zero-state response •part IV: one plot for zero-input response •IN YOUR REPORT: analytical theoretical backgrounds for part III and IV [For section 4&1 only.]
32. http://bit.ly/ TsVhzK