1. The problem statement, all variables and given/known data

Solvinf the unit time step equation mathematically.
2. Relevant equations

x(t) = u(t+1) - 2u(t) + u(t-1)
3. The attempt at a solution
How can i solve this signal mathemtically and using plotted signals , i couldn't understand,
here is my approach and i'm not sure it is correct,
i simply wrote the coordiantes of each signal,
u(t+1) = (-1,1)
-2ut = (0,-2)
u(t-1) = (1,1)
and then added them which give answer = '0'
is this the way of solving the signals ?
please help

 

Give values to t, 0 1 2 3 and so on.

At each value evaluate each term in the equation. If t in u(t) is equal or greater than zero then u(t) equals 1.

Remember the definition of a step signal.

 

i wanna solve it without putting a value for t,

what my teacher did is , he simply draw those three signals and cancelled out the opposite signals , the remaining signal is the answer ! what the hell was that ???
is that a way of solving a signal ?
he said there is no mathematical approach to solve signals (btw we have just started signals n system and this was my 2nd lecture),
i wonder how the hell there is no way to solve the above equation mathematically.
there must be a way which my teacher doesn't aware about,

can you draw the output waveform of this signal and approach of solving it without assigning a value of t ?

 

i wanna solve it without putting a value for t,

what my teacher did is , he simply draw those three signals and cancelled out the opposite signals , the remaining signal is the answer ! what the hell was that ???
is that a way of solving a signal ?
he said there is no mathematical approach to solve signals (btw we have just started signals n system and this was my 2nd lecture),
i wonder how the hell there is no way to solve the above equation mathematically.
there must be a way which my teacher doesn't aware about,

can you draw the output waveform of this signal and approach of solving it without assigning a value of t ?

Yes, you can plot each u() component of x(t) individually and then sum them up.

Assume the component u(t+1):

set t+1=0 and solve for t

t=-1

Thus, at t=-1 the signal rises from 0 t 1 (step)

Do the same for all u() components.

 

i already did that as i mentioned in my first post , re-read the first post please.

but how to solve further,
after this step ??
look at this,

u(t+1) = (-1,1)
-2ut = (0,-2)
u(t-1) = (1,1)

you said exactly what i've already posted.

can i solve it like

u(t+1) - 2u(t) + u(t-1)

(-1,1) + (0,-2) + (1,1) = 0

is this correct ? if not then how to solve it ?

 

i already did that as i mentioned in my first post , re-read the first post please.

but how to solve further,
after this step ??
look at this,

u(t+1) = (-1,1)
-2ut = (0,-2)
u(t-1) = (1,1)

you said exactly what i've already posted.

can i solve it like

u(t+1) - 2u(t) + u(t-1)

(-1,1) + (0,-2) + (1,1) = 0

is this correct ? if not then how to solve it ?

Draw the three signals on the same sheet and sum them up.

 

i already did that as i mentioned in my first post , re-read the first post please.

but how to solve further,
after this step ??
look at this,

u(t+1) = (-1,1)
-2ut = (0,-2)
u(t-1) = (1,1)

you said exactly what i've already posted.

can i solve it like

u(t+1) - 2u(t) + u(t-1)

(-1,1) + (0,-2) + (1,1) = 0

is this correct ? if not then how to solve it ?

The three functions are not continuous over the region from t=-∞ to t=+∞ and cannot be summed as you propose.

Your summation only holds true for either t<-1 or t>=1.