Question

(4 points) Consider a system H that takes a signal x(t) as input and returns the even part of x(t) as output, i.e., xe(t) = H(x(t)) where xe(t) is the even part of x(t). Is it time invariant? Is it stable? (c) (5 points) Consider the following three systems:
S1 : w(t) = x(t/2) S2 : z(t) =Zt −∞ w(τ)dτ S3 : y(t) = S3(z(t)) The three systems are connected in series as illustrated here:
Choose the third system S3, such that overall system is equivalent to the following system: y(t) =Zt−1 −∞ x(τ)dτ

(b) (4 points) Consider a system H that takes a signal x(t) as input and returns the evern part of x(t) as output, i.e., xe(t) = H (x(t)) where xe(t) is the even part of r(t). Is it time invariant? Is it stable? (c) (5 points) Consider the following three systems: Si : w(t)- x(t/2) Sq : y(t) = Sq(z(t)) The three systems are connected in series as illustrated here: w(t) 2 r(t) y(t) 3 Choose the third system S3, such that overall system is equivalent to the following svstem:

Answer 1