(a)
Sketch the functions over the range
(a)
Explanation of Solution
Given data:
The given function is:
The range of
Calculation:
The unit-step forcing function as a function of time which is zero for all values of its argument less than zero and which is unity for all positive values of its argument.
Here,
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The different value of the function
The sketch of the function over the range
Conclusion:
Thus, the sketch for the function over the range
(b)
Sketch the functions over the range
(b)
Explanation of Solution
Given Data:
The function is
The range of
Calculation:
The unit-step forcing function as a function of time which is zero for all values of its argument less than zero and which is unity for all positive values of its argument.
Here,
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The different value of the function
The sketch of the function over the range
Conclusion:
Thus, the sketch for the function over the range
(c)
Sketch the functions over the range
(c)
Explanation of Solution
Given data:
The function is
The range of
Calculation:
The unit-step forcing function as a function of time which is zero for all values of its argument less than zero and which is unity for all positive values of its argument.
Here,
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The different value of the function
The sketch the function over the range
Conclusion:
Thus, the sketch for the function over the range
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Chapter 8 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
- Compute and roughly sketch y(t) = x(t) * h(t), where x(t) = e[U(t) – U(t – 1)] and h(t)= 2U(t) – U(t+1) – U(t – 1). Please, show all steps.arrow_forward2. Sketch the following convolutions: a(t) = rect b(t) = ("C"- = ("(), 0arrow_forwardDetermine y(t) for −1 < t < 0 given the following: x(t) = u(t) — u(t − 1) + r(t − 2) – r(t − 3) – u(t − 3) h(t) = r(t + 1) − 2r(t) + r(t − 1) - ○ a. y(t) = ² +t+0.5 t² O b. y(t) +t+1.5 2 y(t) = 2 + t y(t) = 0.5 ○ c. O d. =arrow_forwardWhich of the following equations would match the graph ofxt)? x(t) -1 1 A) x(t) = u(t + 1) + u(t – 2) B) x(t) = -u(t + 1) – u(t – 2) C) x(t) = -u(t 1) + u(t + 2) %3D D) x(t) = u(t + 1) – u(t + 2) E) x(t) = u(t + 1) – u(t – 2) 2)arrow_forwardCompute the convolution y(t) = x(t) * h(t) of the following pairs of signals 1, 0≤t < 1 -1, 1≤t<2. 0, otherwise Determine the output y(t) via convolution of x(t) and h(t). h(t) = e-t[u(t) — u(t – 2)] and x(t)arrow_forward4) Sketch the following signals - a) w(t) = u(t) — u(t – 1) where u(t) is the unit step function. b) p(t) = sin(2πt)w(t) - P(t - 2n) 8(t = n) d) n=-∞ e) a[n], where the (complex) discrete time signal ∞ f) Za[n] g) x(t)]², where r(t) = 2-¹jt h) Zx(t) a[n] = j n 2 n‡0 n = 0arrow_forwardFind the f(t) for the signal shown in the figure below: -2 -1 3 2 0 f(t) 1 Time (t) 2 3 Select one: a. f(t)=u(t-1)+2u(t)-u(t+1)-u(t+2)-u(t+3) O b. f(t)=u(t+1)+2u(t)-u(t-1)-u(t-2)-u(t-3) O c. f(t)=-u(t+1)+2u(t)-u(t-1)-u(t-2)-u(t-3) O d. f(t)=-u(t-1)+2u(t)-u(t+1)-u(t+2)-u(t+3) 4arrow_forwardSketch the following signals. (a) x(t) = u(t-3) u(t +2) (b) x(t) = 1 + 2 u(t/2-1) (c) x(t) = u(-2t + 3) + r(t-1)arrow_forwardDetermine y(t) for −1 < t < 0 given the following: x(t) = u(t) — u(t − 1) + r(t − 2) – r(t − 3) − u(t – 3) h(t) = r(t + 1) − 2r(t) + r(t − 1) a. y(t) = 1/2+1+0.5 O b. y(t) = +1 t c._y(t) = ½ + t + 1.5 O d. y(t) = 0.5arrow_forwardb)For a LTI system given h(t+1) as below i) is the system causal (justify your answer ) ii) find and draw the output to the system if x(t)=4u(t) that is find y(t)=x(t)*h(t) h(t+1)=1 – t? in the interval {-1, 1} h(t+1) 1 2arrow_forwardNE The system described by y(t) = S x(1) dt has impulse response A) h(t) = u(t – 2) B) h(t) = 8(t – 2) C) h(t) = 8(t – 2) + u(t – 2) D) h(t) = u(t) %3D E) h(t) = u(t) – 2 %3Darrow_forwardCompute the convolution y(t)=x(t)*h(t) of the following signals. a. x(1)=e"u(t+5); b. x(1)=(+1)[u(t+1)-u(t)]+ (-t+1)[u(t)-u(t-1)]; h(t)=u(t)-u(t-2)+e²*&t-3). h(t)=e"u(-2t).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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