Is it possible to obtain the transfer function of a signal that has a variable delay?

For instance, I have a signal consisting of 10 samples: 0,1,1,1,1,0,0,0,0,1

If I would apply a unit delay to the signal, the transfer function would be z^-1 and the signal is now:


What would be the effect e.g. transfer function if I delay the rising edge of the pulse by 1 delay as above, but the falling edge would be delayed by 2 samples? The signal then would be:


Could this be derrived as a combination of z^(-1) and z^(-2) or this transfer function is non-linear?

Thank you for your answers.


A (discrete-time) system with a variable delay must be time-varying, and for this reason it cannot be described by a transfer function of the form


where $h[n]$ is the impulse response of the system. Only linear time-invariant (LTI) systems can be described by a transfer function as given in $(1)$.

  • $\begingroup$ Thanks for your answer Matt L. Is it possible to describe the change as a transfer function in linear time-variant system? $\endgroup$ – aurado Dec 11 '18 at 11:41
  • $\begingroup$ @aurado: No, "change" and "time-invariant" are not compatible. A time-varying system doesn't have a transfer function in the conventional sense. $\endgroup$ – Matt L. Dec 11 '18 at 11:43
  • $\begingroup$ Thanks again Matt L. So, to clarify it is not possible to obtain the FFT of the last signal through a linear modification of the FFT of the first signal? $\endgroup$ – aurado Dec 11 '18 at 11:48
  • $\begingroup$ @aurado: You're right, that's not possible. $\endgroup$ – Matt L. Dec 11 '18 at 11:54
  • $\begingroup$ Thanks for clarification, I'm accepting the answer to mark as closed. $\endgroup$ – aurado Dec 11 '18 at 12:03

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