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Signals and Systems - Engineering

Q1:

The waveform shown in the given Figure can be written as

A v(t) = u(t - 1) + u(t - 2) + u(t - 3) + u(t -4)

B v(t) = u(t - 1) + u(t - 2) + u(t - 3) + u(t -4) - u(t - 5)

C v(t) = u(t - 1) + u(t - 2) + u(t - 3) + u(t -4) - 4u(t - 5)

D v(t) = u(t - 1) + u(t - 2) + u(t - 3) + u(t -4) + 4u(t - 5)

ANS:C - v(t) = u(t - 1) + u(t - 2) + u(t - 3) + u(t -4) - 4u(t - 5)

Trick:

Final value - Initial value.

Suppose here the graph shows that 0 to 1 increasing,

So 1-0=1.

=>>>1.u(t-1).

1 to 2.

So 2-1=1.

=>>>1.u(t-2).

And so on...

At last 4 to 0 decreasing.

So 0-4=-4.

=>>-4.u(t-5).

If any one know other trick please post.