Help me find x(t) from x(-2t+1) !

[baby_1]

Hello
here is the x(-2t+1). i want to know how can find the x(t) diagram from this picture?

 

[albbg]

From the graphic you can say:

from the abscissa axis you have three points in time:

0, where the function is 0
1, where the function is 1
2, where the function is 1

that is:

x(-2*t1+1) = 0 = x(0)
x(-2*t2+1) = 1 = x(1)
x(-2*t3+1) = 1 = x(2)

then:

-2*t1+1 = 0 ==> t1 = 1/2
-2*t2+1 = 1 ==> t2 = 0
-2*t3+1 = 2 ==> t3 = -1/2

So x(1/2) = 0
x(0) = 1
x(-1/2) =1

 

[p.0774023179]

Hello
here is the x(-2t+1). i want to know how can find the x(t) diagram from this picture?

What about the following symbolic approach?

The function in image is described by:
x(-2t+1) = t for t in (0,1]
x(-2t+1) = 1 for t in (1,2)
x(-2t+1) = 0 for t = 2

Then by proceding with a variable substitution such as t=-1/2*(t-1) you have
x(t) = -1/2*(t-1) for t in (0, 1/2)
x(t) = 1 for t in (-1/2, 0)
etc...

The previous answer is correct but now you have the analytical expressions too

 

[jeffrey samuel]

do all the process you did in the reverse order

first shift the signal by -1 t thus you will get the signal x(-2t)

then the rotation part comes replace -2t by 2t thus you get x(2t)

then compress the signal that is divide the time into 2 that will give you x(t)

 

[Chips & Chips]

I thought I knew something about math, but I do not understand the meaning of X(-2t+1). The function appears to be a discontinuous one and I understand that, but what is the significance of labeling the vertical axis with that expression instead of using just a single variable, like X? And where would this kind of notation be used?

 

[jeffrey samuel]

this is not exactly math this is a representation of a continuous signal mathematically

 

[Chips & Chips]

And this explains what?

So, exactly what does the vertical axis show in this graph? I can't help but wonder if the real problem here is just muddy thinking as illustrated by this axis label.

I mean, looking back to the original question, the graph shown DOES show x as a function of t or x(t) as is requested. The only real confusion, in my mind, is the labeling of the vertical axis which seems to make no sense. To me it should be simply labeled x or x(t). So I ask what is the significance of labeling it X(-2t+1). If there is a reason for this label, I would like to know what it is. What it means or represents.

this is not exactly math this is a representation of a continuous signal mathematically

 

[jeffrey samuel]

I think you are a newbie in DSP terminologies the one here is a most common way of representing a signal in te form of math notation that is it

and all the operation are performed on the basic signal which is given by x(t)

Here the x(t) has underwent
a time scaling(2t)
a reflection(-2t)
a delay (-2t+1)

If the above methods are done in the reverse order then the resultant wave front is x(t)

x(t) is not 0 if you are assuming so my pal

 

[Chips & Chips]

I think you are a newbie in DSP terminologies the one here is a most common way of representing a signal in te form of math notation that is it

and all the operation are performed on the basic signal which is given by x(t)

Here the x(t) has underwent
a time scaling(2t)
a reflection(-2t)
a delay (-2t+1)

If the above methods are done in the reverse order then the resultant wave front is x(t)

x(t) is not 0 if you are assuming so my pal

Perhaps I am a "newbie" in this area. That is why I am asking about it. "representing a signal in te form of math notation that is it"? I am sorry, but that makes no sense to me.

Still none of what you are saying has told me what the vertical axis actually represents in the original sketch. So, as you suggested, I have performed the reverse operations to get back to the original x(t) (or am I saying this correctly?):

So what does this tell me? A function has been converted by several transformations. Why? To make the math easier? To make it easier to write some computer code about it? Just for fun? Why and why would anybody who understands this notation ask the original question? I mean, the reverse transformation seems to be so simple. And finally, does this reverse transformation tell me anything about what the vertical axis in the original drawing actually represents? I don't see it.

I am just trying to understand.

 

[jeffrey samuel]

You applied pure math relations here pal they are not suitable in this signal flow analysis the procedures i will work it out for you



- - - Updated - - -

You applied pure math relations here pal they are not suitable in this signal flow analysis the procedures i will work it out for you

 

[Er.abdulrehman]

By using 3 steps you can solve the problem:
1) Take "-" sign out and invert the waveform about x-axis, so the equation will become "x(2t-1)",the inverted wave will now have time period "-1" and "-2" instead of "1" and "2" i.e.mirror image about x-axis.

2) Take 2 outside and make time scaling, so the time period of waveform will get deivided by 2, so the equation become
"t-1/2", the time period will get divided by 2.

3) Now shift the complete waveform right for 1/2 period, so the final waveform have the amplitude of 1 and it starts from -1 and ends at 1.

 

[jeffrey samuel]

By using 3 steps you can solve the problem:

3) Now shift the complete waveform right for 1/2 period, so the final waveform have the amplitude of 1 and it starts from -1 and ends at 1.

N number of solutions is there for this problem and the time axis is from -1/2 to 1/2

I think so cos of the time scaled down event

 

[Marvel_tronix]

Perhaps I am a "newbie" in this area. That is why I am asking about it. "representing a signal in te form of math notation that is it"? I am sorry, but that makes no sense to me.

Still none of what you are saying has told me what the vertical axis actually represents in the original sketch.

x(t) may represent any signal for e.g. a voltage, current, a sound wave, a television or mobile signal, a video signal which will be played by a pc on a monitor, daily closing of stock market, seismic wave (wave of energy that travel through the Earth), etc..
Signal processing, as it name simply states, is a subject related to processing of signals of interest.
In the initial part of the subject, one has to study the various amplitude and time based transformations (like shifting, scaling).
As u may have got from the e.g.s of a signal I have given, this subject is very important as it forms base for many other subjects like linear system theory, communication engg., etc..
Hope u would have got an idea!!!