What is the difference in the shown waveforms conceptually?

[dexterdev]

Hi guys ,
My present doubt is regarding the waveforms shown in the image. The first plot is a impulse train. what is the difference having δ(t) in one plot and 1 at t=0, (0 else where) in a second case. whether time or frequency is the case...

 

[Simon Bridge]

what is the difference having δ(t) in one plot and 1 at t=0, (0 else where) in a second case.

You mean the difference between a train of shifted delta functions and that of unit spikes?

In the second one, at t=0, f(t)=1. In the first one, f(t=0) is undefined.
It will probably help you understand if you consider the situations you'd have to find the area under the train in each case ... or do a Fourier transform.

 

[dexterdev]

Sir , thanks for the eye opener... But how does this concept do apply practically...for example when viewing spectrum analyzer of a periodic signal, the frequency domain we see is what mathematically?Is it impulse functions or spikes...? How do we treat this impulses practically?

 

[Baluncore]

A spectrum analyser cannot represent infinite pulses of zero width so we see each as a limited amplitude pulse with an area determined by energy. A train of Dirac delta pulses is a Dirac comb.
The spectrum of a Dirac comb is itself a Dirac comb.
Take a look at... https://en.wikipedia.org/wiki/Dirac_comb