StudyWithGenius Operation on continuous Time Signals | Addition, Multiplication

#### Operations of CT Signals

• ###### Time Shifting               y(t) = x(t-td)

There are two variable parameters in general:

• Amplitude
• Time

• Point-by-point 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:  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(t-2)        ->  Delayed step signal, multiplied by -1

Then, move from one side to the other, and add their instantaneous values

#### Multiplication of signal

• Point-by-point 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: ###### 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(t-2)             -> 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 ### 1 thought on “Operations on Continuous Time Signals | Addition Subtraction”

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