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Problem 1: Sultan Haboos University Department of Electrical & Computer Engineering College of Engineering ECCE3142 Signals and Systems --- Homework Fall 2023 Sketch the following continuous-time signals: a) \(x(t) = u(t+1) - 2u(t-1) + u(t-3)\) b) \(x(t) = (t+1)u(t+1) - tu(t) - u(t-2)\) c) \(x(t) = 2(t-1)u(t-1) - 2(t-2)u(t-2) + 2(t-3)u(t-3)\) Problem 2: Find constants \(a_1, a_2,\) and \(a_3\) so that the solution to the difference equation \(a_1y[n-1] + a_2y[n] - a_3y[n+1] = \delta[n]\) is equal to the signal \(y[n],\) where, \(y[n] = \begin{cases} 3^n & n < 0\\ 2^{-n} & n \ge 0 \end{cases}\) Problem 3: Determine if the following signal is periodic; if so, find the fundamental period. where. \(x(t) = cos((a + 1)2\pi(t + 4)) + 2sin((b + 1)5\pi t + 30)\) a is the remainder when your student ID is divided by 3. b is the remainder when your student ID is divided by 2. Problem 4: The signal \(x(t)\) is shown in the figure below: Draw the following signals: a) \(x(-3(t-1))\) b) \(x(\frac{t}{3} + 2)\) Problem 5: A system with input \(x(t)\) and output \(y(t)\) can be described by: \(\omega(t) = y(t) + x(t)\) \(y(t) = x(t) - \omega(t)\) Determine the transfer function of the system \(H(s)\). More precisely, also determine numerical values for the constants \(c_1, c_2,\) and the poles \(p_1,\) and \(p_2\). Determine the impulse response \(h(t)\) of the system. What would be \(y(t)\) if \(x(t) = \delta(t) - \delta(t-t)?\) Also plot \(y(t)\) in this case for \(-\infty \le t \le \infty\) clearly labelling both axes and important values.

          Problem 1:
Sultan Haboos University
Department of Electrical & Computer Engineering
College of Engineering
ECCE3142 Signals and Systems --- Homework Fall 2023
Sketch the following continuous-time signals:
a) \(x(t) = u(t+1) - 2u(t-1) + u(t-3)\)
b) \(x(t) = (t+1)u(t+1) - tu(t) - u(t-2)\)
c) \(x(t) = 2(t-1)u(t-1) - 2(t-2)u(t-2) + 2(t-3)u(t-3)\)
Problem 2:
Find constants \(a_1, a_2,\) and \(a_3\) so that the solution to the difference equation
\(a_1y[n-1] + a_2y[n] - a_3y[n+1] = \delta[n]\) is equal to the signal \(y[n],\) where,
\(y[n] = \begin{cases} 3^n & n < 0\\ 2^{-n} & n \ge 0 \end{cases}\)
Problem 3:
Determine if the following signal is periodic; if so, find the fundamental period.
where.
\(x(t) = cos((a + 1)2\pi(t + 4)) + 2sin((b + 1)5\pi t + 30)\)
a is the remainder when your student ID is divided by 3.
b is the remainder when your student ID is divided by 2.
Problem 4:
The signal \(x(t)\) is shown in the figure below:
Draw the following signals:
a) \(x(-3(t-1))\)
b) \(x(\frac{t}{3} + 2)\)
Problem 5:
A system with input \(x(t)\) and output \(y(t)\) can be described by:
\(\omega(t) = y(t) + x(t)\)
\(y(t) = x(t) - \omega(t)\)
Determine the transfer function of the system \(H(s)\). More precisely, also determine numerical
values for the constants \(c_1, c_2,\) and the poles \(p_1,\) and \(p_2\). Determine the impulse response \(h(t)\) of
the system. What would be \(y(t)\) if \(x(t) = \delta(t) - \delta(t-t)?\) Also plot \(y(t)\) in this case for \(-\infty \le t \le \infty\)
clearly labelling both axes and important values.

Problem 1:
Sultan Haboos University
Department of Electrical Computer Engineering
College of Engineering
ECCE3142 Signals and Systems — Homework Fall 2023
Sketch the following continuous-time signals:
a) x(t) = u(t+1) - 2u(t-1) + u(t-3)
b) x(t) = (t+1)u(t+1) - tu(t) - u(t-2)
c) x(t) = 2(t-1)u(t-1) - 2(t-2)u(t-2) + 2(t-3)u(t-3)
Problem 2:
Find constants a1, a2, and a3 so that the solution to the difference equation
a1y[n-1] + a2y[n] - a3y[n+1] = δ[n] is equal to the signal y[n], where,
y[n] = 3^n n < 0
2^-n n ≥ 0
Problem 3:
Determine if the following signal is periodic; if so, find the fundamental period.
where.
x(t) = cos((a + 1)2π(t + 4)) + 2sin((b + 1)5π t + 30)
a is the remainder when your student ID is divided by 3.
b is the remainder when your student ID is divided by 2.
Problem 4:
The signal x(t) is shown in the figure below:
Draw the following signals:
a) x(-3(t-1))
b) x((t)/(3) + 2)
Problem 5:
A system with input x(t) and output y(t) can be described by:
ω(t) = y(t) + x(t)
y(t) = x(t) - ω(t)
Determine the transfer function of the system H(s). More precisely, also determine numerical
values for the constants c1, c2, and the poles p1, and p2. Determine the impulse response h(t) of
the system. What would be y(t) if x(t) = δ(t) - δ(t-t)? Also plot y(t) in this case for -∞≤ t ≤∞
clearly labelling both axes and important values.

Added by William H.

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