<Definetions
δ == impulse signal
Π == unit impulse signal
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let say we have a function δ(t) which is accurately defined as below :
[math]δ_Δ = \left\{ \begin {array} {cc} \frac 1Δ & 0 \leq t \leq Δ \\ 0 & anything-else \end {array} \right.[/math]
but we will considering it like following:
[math]δ = \left\{ \begin {array} {cc} 1 & t = 0 \\ 0 & anything-else \end {array} \right.[/math]
and other functions like Π(t) is exist
[math]Π(t) = \left\{ \begin {array} {cc} 1 & |t| \leq \frac 12 \\ 0 & t > 1 \frac 12 \end {array} \right.[/math]
how we can prove that δ can be defined by Π like below :
[math] δ(t) = \frac 1T \lim_{T \to 0} Π(\frac tT)[/math]
And thanks for your help
δ == impulse signal
Π == unit impulse signal
/>
let say we have a function δ(t) which is accurately defined as below :
[math]δ_Δ = \left\{ \begin {array} {cc} \frac 1Δ & 0 \leq t \leq Δ \\ 0 & anything-else \end {array} \right.[/math]
but we will considering it like following:
[math]δ = \left\{ \begin {array} {cc} 1 & t = 0 \\ 0 & anything-else \end {array} \right.[/math]
and other functions like Π(t) is exist
[math]Π(t) = \left\{ \begin {array} {cc} 1 & |t| \leq \frac 12 \\ 0 & t > 1 \frac 12 \end {array} \right.[/math]
how we can prove that δ can be defined by Π like below :
[math] δ(t) = \frac 1T \lim_{T \to 0} Π(\frac tT)[/math]
And thanks for your help