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Today in our signals and systems lecture we were going through a particular problem then our professor took a signal and broke into its constituent parts he drew this diagram------

Horribly out of scale and sorry for thatI didn't understood how the highlighted portion was missing in the output(That vertical line from (0,1) to (1,1)..) i asked him but he further confused me...

Is his diagram even correct?

Where does that part go?How to visualize it ?

enter image description here

Horribly out of scale and sorry for that*

EDIT-----------------------------------

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Below i posted an image about composition/decomposition of a signal

1>> What my professor drew in the class.

2>> What i think is correct intuitively.

enter image description here

Which one is correct?One of them is wrong,why?

What basic concept am i missing in the composition/decomposition of a signal?

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    \$\begingroup\$ About the edit: It's still ambiquous in terms of math. You simply have no method to show exact values where the curve jumps. I added something about it to my answer. \$\endgroup\$ – user287001 Apr 10 '18 at 8:21
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Actually all those images are wrong because at t=1 (and t=2,too) a voltage cannot have infinitely many simultaneous values. Be it 0 or 1 or 2 - that's up how the author says, but not 0 and 1 and all values between them at the same time.

That's math. If a math student draws vertical graphs for y=f(x) where f is a function, the teacher judges the drawing straight away to be invalid. In electronics we have used to draw vertical voltage and current graphs anyway. That means we let it be unclear what is the actual value at t=1. That's because in actual circuits an erratic voltage at single strictly zero wide time moment means nothing. It has no time cause any response due the nature of the laws of the electromagnetism. Those laws are rules for gradually changing fields, voltages and currents.

ADD: One method to make non-ambiquous graphs for functions which have here and there separate discontinuity points:

enter image description here

The black dot indicates the actual value where the curve jumps. The leftmost and the mid graph are two pulses and the rightmost is their sum.

NOTE: It's well possible to have tailless black spots without making any errors.

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  • \$\begingroup\$ I have added an extra part to this question kindly look and help me up \$\endgroup\$ – Paran Bharali Apr 10 '18 at 2:46
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    \$\begingroup\$ The answer is augmented. \$\endgroup\$ – user287001 Apr 10 '18 at 10:06
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I believe that is a simple signal addition: You have signal 1 on the left with amplitude 1 between time 0 and 1, and amplitude 0 afterward. And then you have signal 2 in the middle with an amplitude 0 before time 1, amplitude 2 between time 1 and 2, and amplitude 0 afterward.

By adding both signals 1 and 2, you get the result signal on the right: Between time=0 and time=1, the amplitude is the sum of both original signals, Amplitude=1+0=1, between time=1 and time=2 the amplitude is the sum 0+2=2. After time=2 you have amplitude 0+0=0.

At the instant time=1, the resulting signal goes from amplitude=1 to amplitude=2, it doesn't go to zero, apparently.

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  • \$\begingroup\$ I have added an extra part to this question kindly look and help me up \$\endgroup\$ – Paran Bharali Apr 10 '18 at 2:47

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