Periodic Signals

[learningcreature]

Why a periodic signal need to be start from t=-∞ ?
It is stated in "Linear Systems And Signals" By B.P.Lathi (2nd Edition) page no. 18.

 

[cjb]

In practice, it does not need to.

However, it is typical to describe a periodic waveform as a function with a Fourier series representation. Hence rather than having to use a Fourier transform to manipulate a wavetrain, one can use the far easier to analyse series.

 

[dknguyen]

Why a periodic signal need to be start from t=-∞ ?
It is stated in "Linear Systems And Signals" By B.P.Lathi (2nd Edition) page no. 18.

Because that's the definition of true periodic. It's theoretical though (obviously). It also goes to T = +∞. It simplifies things by making it so you know there are no sudden unexpected changes anywhere in the past or anywhere in the future.

 

[learningcreature]

Pay attention to my Question

Hi!

Regarding your answers, friends if you study the book "Linear Systems And Signals" by B.P.Lathi, you will find that the author has said :

"By definition, a periodic signal x(t) remains unchanged when time-shifted by one period.For that reason a periodic signal must start at

t= - infinity: if it starts at some finite instant, say t=0, the time-shifted signal

x(t+T) would start at t= - T 0 ( - T naught) and x(t+ T0) would not be the same as x(t)."



Now I think that there is some solid reason because of which the author is using the word "must" .

Find that if you can and tell me again.I also try to find that reason

 

[dknguyen]

Hi!

Regarding your answers, friends if you study the book "Linear Systems And Signals" by B.P.Lathi, you will find that the author has said :

"By definition, a periodic signal x(t) remains unchanged when time-shifted by one period.For that reason a periodic signal must start at

t= - infinity: if it starts at some finite instant, say t=0, the time-shifted signal

x(t+T) would start at t= - T 0 ( - T naught) and x(t+ T0) would not be the same as x(t)."



Now I think that there is some solid reason because of which the author is using the word "must" .

Find that if you can and tell me again.I also try to find that reason

It's for the same reason. If I time shift by one period into the past/future, then another, then another, then another, all the way to infinite it's still the same. That means the signal is the same at negative infinity (or positive infinity). If it wasn't the same, the signal would be eventually appear as something differently at the "present time" if I eventually change if I time shifted it by enough.