Signals Basic Operations


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There are two variable parameters in general:

  1. Amplitude
  2. Time

The following operation can be performed with amplitude:

Amplitude Scaling

C x(t) is a amplitude scaled version of x(t) whose amplitude is scaled by a factor C.

Amplitude scaling

Addition

Addition of two signals is nothing but addition of their corresponding amplitudes. This can be best explained by using the following example:

Amplitude addition

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

Subtraction

subtraction of two signals is nothing but subtraction of their corresponding amplitudes. This can be best explained by the following example:

Amplitude subtraction

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 = -1

    3 < t < 10 amplitude of z (t) = x1(t) + x2(t) = 0 - 2 = -2

Multiplication

Multiplication of two signals is nothing but multiplication of their corresponding amplitudes. This can be best explained by the following example:

Amplitude multiplication

As seen from the diagram above,

    -10 < t < -3 amplitude of z (t) = x1(t) ×x2(t) = 0 ×2 = 0

    -3 < t < 3 amplitude of z (t) = x1(t) ×x2(t) = 1 ×2 = 2

    3 < t < 10 amplitude of z (t) = x1(t) × x2(t) = 0 × 2 = 0

The following operations can be performed with time:

Time Shifting

x(t $\pm$ t0) is time shifted version of the signal x(t).

    x (t + t0) $\to$ negative shift

    x (t - t0) $\to$ positive shift

Time shifting

Time Scaling

x(At) is time scaled version of the signal x(t). where A is always positive.

    |A| > 1 $\to$ Compression of the signal

    |A| < 1 $\to$ Expansion of the signal

Time scaling

Note: u(at) = u(t) time scaling is not applicable for unit step function.

Time Reversal

x(-t) is the time reversal of the signal x(t).

Time reversal

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