Which one of the following relations is not correct?

Concept:

Unit Impulse function:

A continuous-time unit impulse function δ(t), also called a Dirac delta function is defined as:

δ (t) = ∞ , t = 0

= 0,  otherwise

The unit impulse function is represented by an arrow with the strength of  ‘1’ which represents its area.

Properties of Delta function:

Scaling Property:

Multiplication Property:

X(t).δ(t – t₀) = x(t₀)δ(t – t₀)

Sampling Property:

Important Expressions:

 X(t).δ(t) = x(0)δ(t)

Explanation:

From the concept part we can find that:

option(1) is true

From option (2)

This option is false

As

Both options (3) and (4) follow delta function properties,

Hence they are true.

Important Points

Differentiation Property:

Even Signal property:

δ(-t) = δ(t)

Convolution Property:

Integration Property:

 for  (t₁ < t₂)

0, otherwise.