# Time reversal transformation

Discussion in 'General Electronics Discussion' started by Jawad, Jun 8, 2018.

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Jun 8, 2018
Please, I am looking for an electronic circuit which allows the time reversal transformation of a signal f(ωt) (i.e from f(ωt) to f(-ωt)).
Thank you

2. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
Over what period of time?

You can't do this in real time because that requires you know the state of the waveform in the future.

Perhaps you could go with sampling and replaying in reverse.

9
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Jun 8, 2018
my wave is either a sin or a cos and the transformation must be done in a time less than 2 periods

4. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
How about a piece of wire? A sine wave in reverse is a sine wave.

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Jun 8, 2018
besides I do not know if it was a cos or a sin. my circuit must work for the both
besides I do not know if it was a cos or a sin. my circuit must work for the both.

6. ### Alec_t

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Jul 7, 2015
An xxxxxxxxxxxx is one option.
Is this homework?

7. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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A piece of wire will so it for a time delay = pi/ω for sin and 0 for cos.

They are periodic waveforms, so a delay of the appropriate length (essentially aaphase change) wil result in exactly the same as -ωt.

Now, if you want both functions to be reversed and delayed the same amount... You'll have to go back to your maths and look at identities.

The answer is a little more difficult, but is essentially a simple mathematical relation applied to that piece of wire

8. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
I expect it is.

9
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Jun 8, 2018
that's just my problem
If I consider a circle of radius 1 and I have a transformation which is a symmetry with respect to a central axis of radius π / 8 with respect to the axis Ox. So this symmetry will transform my initial signal which is sin (ωt) into sin (-ωt + π / 4). the problem is that if I want to apply this transformation more than twice in succession. Moreover if I apply it twice I have to find the identity (ie sin (-ωt + π / 4) gives sin (-ωt))

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Jun 8, 2018
No it is a project of License

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Jun 8, 2018
Excuse me i have error
Moreover if I apply it twice I have to find sin (ωt) (ie sin (-ωt + π / 4) gives sin (ωt))

12. ### Harald KappModeratorModerator

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Nov 17, 2011
Makes absolutely no sense to me: sin (-ωt + π / 4) <> sin (ωt))
Do you mean find f(x) such that f(sin (-ωt + π / 4)) = sin (ωt) ? (I don't have a solution for that at hand.)

13. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
I think the problem is, for the equations
1. Sin(a + x) = f( sin(-x) )
2. Cos(a + x) = f( cos(-x) )
Find a and f() such that 0 <= a <= 2π and f() can be implemented as an electronic circuit.

I think I have done half the work by laying out the equations. There problem is more of a test of understanding of mathematics than of electronics.

@Jawad was on the right track using a unit circle. I don't know where π/4 came from, and I encourage him to keep trying.

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Jun 8, 2018
I apologize for this delay because I was testing other alternatives. This is almost the equations you quoted steve and which are exactly:
1. Sin(π / 4 - x) = f( sin(x) )
2. Cos(π / 4 - x) = f( cos(x) )
but the problem is that I have not found a circuit which allows the time reversal transformation to achieve this transformation

15. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
Try something else that will make the function obvious.

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Jan 21, 2010
17. ### Harald KappModeratorModerator

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What is the input to the function sought? Is it "x" or is it "sin(x)".
I assume the latter: a sinewave of frequency f and angular frequency w = 2*pi*f -> sin(wt). If so, is the frequency f fixed or variable? For a fixed frequency you can generate sin(π / 4 - x) by a simple phase shift circuit (e.g. by a low-pass filter or an all-pass filter) and an inverting amplifier using the identity sin(-x) = -sin(x).
Note that the output of such a circuit will be frequency dependent and will fulfill the equation for one fixed frequency only.

18. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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He is required to produce a "time reversed" signal for a sin or cos input signal.

If the input is sin(x) then a time reversed signal is sin (--x). Three bug hint I'd that the circuit is permitted to have a time lag.

The question is more about a basic understanding of the various trig identities. I have the basic form of the identity above.

For some reason @Jawad is stuck on pi/4 for some reason.

Once he finds the trivial identity (which applies equally to sin and cos) then the function he had to provide in hardware becomes obvious and trivial.

There is a deleted post earlier in this thread where the answer was given. @Harald Kapp if you're able to guide Jawad to the answer without giving it to him, be my guest.

Edit: not deleted, but an edited post by @Alec_t

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Jun 8, 2018
it's not a choice of pi / 4 but I have just transformed my basic function that are:
1. (sqr(2)/2)*(sin(x)-cos(x)) = f( sin(x) )
2. (sqr(2)/2)*(sin(x)+cos(x)) = f( cos(x) )

20. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

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Jan 21, 2010
At the risk of sounding like a broken record, look for a set of identities written pretty much exactly in the form I have given. You won't find f() around anything, but you will find exactly the same mathematical transformation applied.

When you find that pair of identities, you can determine what f() is and make a circuit to do it.

This stuff is simple high school mathematics, and is one of the extremely simple cases that can be derived by inspection from the unit circle.

The other option is to go through that wiki page identity by identity until you find equations roughly in the form I gave you. To make it easy, look for all the identities that involve just sin and just cos, and have a change in sign of the angle on opposite sides of the identity. Look for all of them, because I can tell you that you will find a couple that won't work before you find the ones that obviously will.