Continuous-Time Systems HW

System Properties:

1. Determine if the following systems are time-invariant, linear, causal, and/or memoryless?

a) dy

dt y t x t+ =6 4( ) ( )

b) dy

dt ty t x t+ =4 2( ) ( )

c) y n y n x n[ ] [ ] [ ]+ − = +2 1 1

d) y(t) = sin(x(t))

e) dy

dt y t x t+ =2 ( ) ( )

f) y n y n x n x n[ ] [ ] [ ] [ ]+ + = + −1 4 3 1

g) y t dx

dt x t( ) ( )= +

h) y n x n[ ] [ ]= 2

i) y n nx n[ ] [ ]= 2

j) dy

dt t y t x t+ =sin( ) ( ) ( )4

k) d y

dt

dy

dt y t

dx

dt x t

2

2 10 4 4+ + = +( ) ( )

2. The response of an LTI system to a step input, x(t) = u(t) is y(t) = (1-e-2t)u(t). What is the response to an input of x(t) = 4u(t)-4u(t-1)?