1. Modeling systems using differential equations and solving them to find the impulse response Rachaen Huq. Dept. of EEE, BRACU

2. Why solving DE- s? We already know that LTI systems can be described using a differential relationship between the input and output. We have DE models describing many elements which constitute different systems. For example – inductors, capacitors. We can use those basic relationships to find out the overall DE of a system Solving the DE is “one way” of finding the IR.

8. Because h(t) was :

11. Sampling property of delta

15. Now, can you comment of the system’s causality and stability?

17. Continuous-time necessary and sufficient condition for BIBO stability For a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response be absolutely integrable. ? ∞

18. Practical example DE-s for RLC circuits - e.g. Finding IR, i/p-o/p relations

23. Repeating roots !

24. Homogeneous solution

28. Similarly find out h’’(t) Put all the values in eq-1 Compare coefficients Find out h(t). You will find the complete solution in the midterm and final questions and solutions folder. (fall 2014)

29. Note that – depending on what variety of elements do we have in the system (e.g. circuit), the DE complexity reduces or increases. Complexity of solving DEs depend of the value of M-N to some extent. You can expect exam problems related to this in the midterms (low complexity) and finals (high complexity).