Hello, if you have any need, please feel free to consult us, this is my wechat: wx91due
EEE 203 Signals and Systems
PRACTICE MIDTERM
1. (Signal Transformation) For x(t) shown below, plot the following functions
(a) a(t) = x(2t)
(b) b(t) = x(一t + 1)
(c) c(t) = x(t)[u(t) 一 u(t 一 2)]
(d) d(t) = x(t)δ(t 一 1)
2. (Signal Property) Under what condition is a discrete-time signal x[n] or a continuous-time signal x(t) periodic? Determine whether or not the following signals are periodic. If the signal is periodic, determine the fundamental period. Justify your answer.
(a) x(t) = 5sin(3t + 1)
(b) x[n] = 
3. (System Properties) Consider a discrete-time system with input signal x[n] and corresponding output signal y[n] = x[一n] + 3. Determine whether the system is
(a) Memoryless
(b) Time invariant
(c) Linear
(d) Causal
(e) Stable
In each case, write down the definition of each property and justify your answer.
4. (Convolution) The impulse response of an LTI system is given by 
What is the output y(t) when the input is x(t) = u(t) 一 u(t 一 2)?
5. (Convolution) Consider the following interconnection of LTI systems. Here h1 [n] = u[n] 一u[n 一 2]and h2 [n] = u[n + 1] 一 u[n 一 1].
(a) What is the impulse response h[n] of the overall system?
(b) What is the output y[n] when the input is x[n] = anu[n], 0 < a < 1?
6. (System Properties) For a continuous-time or discrete-time LTI system to be causal or stable, what is the requirement on the impulse response h(t) or h[n]? The followings are the impulse response of LTI systems. Determine whether each system is 1) causal, 2) stable. Justify your answers.
(a) h[n] = (0.9)nu[n + 1]
(b) h(t) = e一3tu(1 — t)
7. (Fourier Series) Compute the Fourier series coefficients ofthe periodic signal x(t) = 1 + cos(t)sin(2t).
8. (Fourier Series)
(a) What are the Fourier series coefficients ofthe period signal 
with period N = 6?
(b) The Fourier series coefficients of a periodic signal y[n] with period N = 6 is a0 = 1, a1 = a一1 = 2. What is y[n]?
(c) What are the Fourier series coefficients ofthe periodic signal 
with period N = 2?
9. (Fourier Series) Consider an LTI system with an impulse response 
(a) What is the frequency response H(ejw)?
(b) If the Fourier series coefficients ofthe input x[n] are 
and 
what is the Fourier series coefficients ofthe output y[n]?
(c) What is the Fourier series representation of output y[n]?