Signals And Systems Homework Help

1) For signal x(t) below, generate the corresponding graph using the following operation: y(t) = x(2t - 4)

Suppose A is a 3 by 3 matrix. Consider a linear system that outputs y = Ar where x R³ is the input signal. To be more precise, x is a column vector of dimension 3, and y E R³ is the output column vector of dimension 3. Further, we know that • when ₁ = (1, 0, 0), the output is y₁ = (1, 2, 3). • when x2 = (0, 1,0), the output is y2 = (3, —2, 1)¹. • when x3 = (0, 0, 1), the output is y3 = (2,-1,-3). What is the output y = Ar when the input is x = (2,2, 4)T? (Hint: Use the linearity of the system.)

Suppose -π/2 ≤ a ≤0, π ≤ B ≤ 3π/2, Compute the following values: (i) cos(a +ß) (ii) sin(a -ß)

Consider a function f(t) such that f(t) = -2 if t≥ 1 and f(t) = 0 otherwise. Find the expression of where a is a constant that is strictly larger than zero.

Further review of calculus and arithmetics Question 13: [Basic] Consider two functions f(t) and g(t) described as follows.

Determine the expression for the Fourier transform of y(t) = x(t)p(t).

find discrete-time systems zero input response Example 3 (E²-1.56E+0.81)y[n]=(E+3)x[n], y [-1]=2, v. [-2]=1.

Q5. SSB AM: A message signal m(t) = cos(2000mt) + 2 cos(4000mt) modulated the carrier c(t) 100 cos(2π fet) where fe = 1 MHz to produce the DSB-SC signal m(t)e(t). Determine and sketch the spectrum of the upper sideband (USB) signal.

Q4. DSB-SC AM: The message signal m(t) = 2 cos(400t) + 4 sin(500+) modulates the carrier signal c(t) = A cos(8000rt), using double sideband suppressed carrier (DSB-SC) amplitude modulation. Find the time domain and frequency domain representation of the modulated signal and plot the spectrum (Fourier transform) of the modulated signal.

Q1. Modulation: Let z(t) be a signal which has Fourier Transform X(f) as shown below. Find theFourier Transform of y(t), where y(t) is shown below. Assume that fe 2 W. What happens when fe<W?