What is the difference in the shown waveforms conceptually?

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The discussion centers on the conceptual differences between an impulse train represented by δ(t) and a unit spike at t=0. The key distinction is that δ(t) is undefined at t=0, while the unit spike has a defined value of 1 at that point. Understanding these differences is crucial for analyzing the area under the waveforms and performing Fourier transforms. Practically, spectrum analyzers cannot display infinite pulses of zero width, so they represent these as limited amplitude pulses, with their area reflecting energy. The spectrum of a Dirac comb, which consists of these delta functions, is also a Dirac comb, emphasizing the relationship between time and frequency representations.
dexterdev
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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...
 

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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.
 
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?
 
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
 

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