An electrical control signal can be described using the function as 3, 0≤t<1 f(t)=4-t, 1≤t<4 (a) 0, t≥4 (i) Sketch the signal variation with time. (i) Show that the signal can be expressed as f(t)=3U(t)-(t-1)U(t-1)+(t-4)U(t-4) where U(t), U(t − 1) and U(t-4) are unit step functions. (iii) Determine £{f(t)}.

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An electrical control signal can be described using the function as
3, 0≤t<1
f(t)=4-t, 1≤t<4
(a)
0,
t≥4
(i) Sketch the signal variation with time.
(i)
Show that the signal can be expressed as
f(t)=3U(t)-(t-1)U(t-1)+(t-4)U(t-4)
where U(t), U(t − 1) and U(t-4) are unit step functions.
(iii)
Determine £{f(t)}.
Transcribed Image Text:An electrical control signal can be described using the function as 3, 0≤t<1 f(t)=4-t, 1≤t<4 (a) 0, t≥4 (i) Sketch the signal variation with time. (i) Show that the signal can be expressed as f(t)=3U(t)-(t-1)U(t-1)+(t-4)U(t-4) where U(t), U(t − 1) and U(t-4) are unit step functions. (iii) Determine £{f(t)}.
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