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

 

[alphy]

The difference between the two waveforms conceptually lies in the representation of the signal. In the first plot, the waveform is an impulse train which is a series of delta functions spaced at regular intervals. Each delta function represents a single impulse at a specific time. On the other hand, in the second plot, the waveform is a single impulse at t=0, with zero values everywhere else. This can be seen as a continuous signal with only one non-zero value at a specific time.

The difference between the two lies in the representation of the signal in the time domain. In the first plot, the signal is represented as a series of impulses at different times, whereas in the second plot, the signal is represented as a single impulse at a specific time.

In terms of frequency, the first plot would have a periodic frequency based on the spacing between the impulses, whereas the second plot would have a single frequency at t=0.

Overall, the difference between the two waveforms lies in the representation of the signal in the time domain and the resulting frequency characteristics. It is important to understand the conceptual differences in order to accurately analyze and interpret signals in different forms.