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Signals Basic Operations



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

    -3

    3

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

    -3

    3

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

    -3

    3

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|

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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