6. Signal x()- exp(-t) u() and signal ho) is as shown. (a) Express h(t) in terms of ramp functions only 2 O2 3 4 (b) Find y(t) x(t)*h(t) 0) 6. Signal x()- exp(-t) u() and signal ho) is as sh...
(b) The signal f(t) is shown in the figure below 3 2 f(t) _ 0 I 1 -4 -3 -2 -1 0 1 2 3 4 5 6 7 t and is given by 21 (1) + 3A (132), where A is the triangle function defined as 10-{ It a It <a It > a 0 Write the Fourier transform F [A(t)] (s) of f(t) exploiting the fact that FA(t)](s) = sinc-(s) where sin(TTS) sinc(s) ITS and the theorem for...
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions. (c) Evaluate the gain and phase (in degrees) of H(f) at 0.2 Hz from each expression. 3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions. (c) Evaluate the gain and phase (in degrees)...
Express the waveform shown below in terms of the unit step function or the ramp function. 1. x(t) 0 2 4 t(sec) -10 Answer: x(t)= Express the waveform shown below in terms of the unit step function or the ramp function. 2. xt) 5 0 2 4 t(sec) -5 Answer: x(t)= LC 10 Express the waveform shown below in terms of the unit step function or the ramp function. 1. x(t) 0 2 4 t(sec) -10 Answer: x(t)= Express the...
*Note: Please answer all parts, and explain all workings. Thank you! 3. Consider the follo 2 lu The boundary conditions are: u(0,y, t) - u(x, 0,t) - 0, ou (a, y, t) = (x, b, t) = 0 ay The initial conditions are: at t-0,11-4 (x,y)--Yo(x,y) . ot a) Assume u(x,y,t) - X(x)Y(y)T(t), derive the eigenvalue problems: a) Apply the boundary conditions and derive all the possible eigenvalues for λι, λ2 and corresponding eigen-functions, Xm,Yn b) for any combination of...
wi() (V) 3 2 1 1 234 56 7 t (ms) 4. Express the signal above (a) in terms of unit step and ramp functions, and (b) in terms of puls functions. (c) Show that your answers to (a) and (b) are equivalent.
7 Draw the continuous time signal. x(t)={r(t)-r(t-2)-r(t-4)+r(t-6)}+{u(t+4)-2u(t+2)+2u(t)-u(t-6)} where [u(t) is unit step signal and r(t) is unit ramp signal]. And sketch the following i. yl(t)=x[-1-2) ii. y2(t)=x[3-t] 15 Marks
1. Use combinations of STEP FUNCTIONS to describe each continuous-time signal shown below. f(t) 0 2 4 6 0 1 2 3 0 1 2 3 4 2. Sketch the following signals: (a) x (t)=1 [u(t+2)-u(t-1)] (c) X(t)=\fety (b) X(t)=t.e (d) x (t) = u(t) u(t-1).ult-2).u(t-3) 3. Determine whether the systems below are linear and time invariant. Justify your answer! (a) y(t) = x(31) (b) y(t)= 2x(1-t) y(t)=cos(x(t)] 4. Simplify the expressions: (a) y(t)=1.8(t+2)+(t +1) 8(1-1)+(t+3). 8(t) (b) y(t) =...
An LT-I system with the following differential equation y’(t) + 3 y(t) = x(t) has a Zero State Response of yzsr(t) = -2 exp(-5t) u(t) + 2 exp(-3t) u(t) when an input signal: x(t) = 4 exp(-5t) u(t) is applied to the system. What is the Zero State Response of the following system beginning at time t = 0 seconds, y’(t) + 3 y(t) = x’(t) -2 x(t) if the same input signal is applied to the system, and it...
compute the energy Ex of signal x(t) of x(t) = exp(t*(1+j*2*pi))u(-t), y(t) = Re{2x *((-5-t)/2)}
compute the energy (Ey) of signal y(t) given x(t) = exp(t*(1+j*2*pi))u(-t), y(t) = Re{2x *((-5-t)/2)}