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Operation on continuous Time Signals | Addition, Multiplication

Operations of CT Signals

 

We will look at several common continuous-time signals and also operations that may be performed on them

There are two variable parameters in general:

  • Amplitude
  • Time

Addition of Signals:

  • 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:

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(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:

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(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

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