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can anybody define delta function clearly?

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define delta difference

The delta function is a DISTRIBUTION. This means that many functions like sinc , tri etc can be thought to be delta functions in the limit. The delta function is defined as any function that satisfies the following properties

\int_{-\infty}^\int{infty} \delta t dt = 1

\int_{-\infty}^{\infty} f(t) \delta(t-\tau) dt = f(\tau)
\]
 

define deltas

Hi,
Delta function has different definition in mathematics and in communication engineering. In mathematics δ(t) is a pulse at t = 0 and 0 elsewhere. In communication also it is the same. But the difference is, mathematically the hieght of the pulse is infinity so that the area under the delta pulse is non-zero. In communication it is only a spike of unity value. The earlier one is used a lot in electromagnetism in vector form, called Dirac Delta function. There are many more analytcal expression of the deta function in terms of other functions. Any good communication book can help I guess.
 

delta function

delta function is a pulse whose area is 1 and height is theoritically infinity.

In notation when you say delta(t)=5 what you mean is its area is 5 and not its height. 5 is called the strenght of the delta function.
 

height of the delta function

You are correct. Thanx. But when you write 5δ(t) and graphically represent it, it is represented as a spike of hieght 5 at t = 0. Similarly for a function 10δ(t) the amplitude of the pulse is 10. So in comunication the delta function is taken as unit impulse function whose value is equal to the strength of the function. The area under the curve 5δ(t) is 5 when δ(t) is infinity at t = 0. But then the area is not a function of t as the area is
∫ 5δ(t)dt = 5 where the limits are t = -∞ to t = +∞. So there is no point representing the area 5 as a spike at t = 0.
 

define: delta

As Ddkrishna points out, delta is not a function but a distribution, although it is common to speak about the "delta function",

Delta is well defined by this property:
For any function f(t) continuous at t=0:
[integral (from -Inf to Inf) delta(t)*f(t)*dt] = f(0)

From this, the two conditions of Ddkrishna follow (in the second, f(t) must be continuous at t=tau).

Regards

Z
 

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