Signals Basic Operations

There are two variable parameters in general:

Ampptude

Time

The following operation can be performed with ampptude:

Ampptude Scapng

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

Addition

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

As seen from the diagram above,

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

-3 < t < 3 ampptude of z(t) = x1(t) + x2(t) = 1 + 2 = 3

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

Subtraction

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

As seen from the diagram above,

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

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

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

Multippcation

Multippcation of two signals is nothing but multippcation of their corresponding ampptudes. This can be best explained by the following example:

As seen from the diagram above,

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

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

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

Time Shifting

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

x (t + t₀) $ o$ negative shift

x (t - t₀) $ o$ positive shift

Time Scapng

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

|A| > 1 $ o$ Compression of the signal

|A| < 1 $ o$ Expansion of the signal

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

Time Reversal

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