Operation on continuous Time Signals  Addition, Multiplication
Operations of CT Signals

Amplitude Scaling y(t) = Bx(t)

Addition y(t) = x1(t) + x2(t)

Multiplication y(t) = x1(t)x2(t)

Time Scaling y(t) = x(at)

Time Reversal y(t) = x(t)

Time Shifting y(t) = x(ttd)
There are two variable parameters in general:
 Amplitude
 Time
Addition of Signals:
 Pointbypoint addition of multiple signals
 Move from left to right (or vice versa), and add
the value of each signal together to achieve the
final signal  y(t) = x (t) + x (t)
 Addition of two signals is nothing but addition of their corresponding amplitudes. This can be best explained by using the following example:
This Picture is taken from YouTube lecture of “Neso Academy”
As seen from the diagram above,
 10 < t < 3 amplitude of z(t) = x1(t) + x2(t) = 0 + 2 = 2
 3 < t < 3 amplitude of z(t) = x1(t) + x2(t) = 1 + 2 = 3
 3 < t < 10 amplitude of z(t) = x1(t) + x2(t) = 0 + 2 = 2
Sketch y(t) = u(t) – u(t – 2)
First, plot each of the portions of this signal separately
 x1(t) = u(t) > Simply a step signal
 x2(t) = –u(t2) > Delayed step signal, multiplied by 1
Then, move from one side to the other, and add their instantaneous values
Multiplication of signal
 Pointbypoint multiplication of the values
of each signal  y(t) = x1(t)x2(t)

Multiplication of two signals is nothing but multiplication of their corresponding amplitudes. This can be best explained by the following example:
This Picture is taken from YouTube lecture of “Neso Academy”
Sketch y(t) = u(t)·u(t – 2)
First, plot each of the portions of this signal separately
 x1(t) = u(t) > Simply a step signal
 x2(t) = u(t2) > Delayed step signal
Then, move from one side to the other, and multiply instantaneous values
Amplitude Scaling
 Multiply the entire signal by a constant value
 y(t) = Bx(t) [B is a constant]
Sketch y(t) = 5u(t)
C x(t) is a amplitude scaled version of x(t) whose amplitude is scaled by a factor C
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