Why the amplitude of the 90 shifted phase signal when use the analytic signal block is not equal to the original signal?

I could manage to shift the phase of signal by 90 by using analytic signal block. But, the problem is that its amplitude is not equal to the original one. Can anyone please explain it?

[Walter Roberson]

Could you confirm that you are using https://www.mathworks.com/help/dsp/ref/analyticsignal.html ?

How are you measuring the amplitude?

[saleh shlimet]

yes I used this block

[saleh shlimet]

the amplitude is change with the frequency. and according to hilbert trabsform theory the amplitude must be the same

[Walter Roberson]

I see what you mean, but at the moment I have no idea why that is happening. :(

[saleh shlimet]

Dear Walter do you know another method to shift the phase of the signal by 90 degrees?

[Walter Roberson]

I wonder if it would be practical to implement in terms of laplace transform?

https://math.stackexchange.com/questions/933207/laplace-transforms-phase-delay

[saleh shlimet]

I tried but it does not work

[Walter Roberson]

Sorry, I do not know.

Answer 1

[Jyotsna Talluri]

You can try variable phase shift block in simulink.

https://www.mathworks.com/help/simrf/ug/variable-phase-shift.html

[saleh shlimet]

Thank you Talluri for your reply I tried this example but when I enter 90 degrees instead of 180 the output becomes zero.

[Jyotsna Talluri]

What is the input signal you are considering?From the figure you attached,I see it is a sine wave and you can specify the phase,you want to shift in the block parameters itself

[saleh shlimet]

Yes you can shift the signal from the block itself. But you cannot do that with a signal you receive in a telecommunications system for example and you want to shift it by 90 degrees.

[Jyotsna Talluri]

The other option I could think of is transport delay block where we can specify the time delay corresponding to a phase shift of 90 degrees as per the equation

phase shift (in deg) = 360*time delay/period of signal.

Refer to the below link

https://www.mathworks.com/help/simulink/slref/transportdelay.html

[saleh shlimet]

this is a good idea if the frequency is constant, but in my case the frequency is changing.

[Walter Roberson]

Suppose you leave the program running for two weeks. Then a frequency as low as one cycle per week could be detected, mathematically. That frequency has to have its phase shifted by 90 degrees, just like all the other frequencies do.Is it mathematically possible for something like a hilbert transform to properly predict when to make the appropriate output adjustments before the system has seen one cycle of the wave? Nyquist would say NO.

I would argue that it is therefore not possible to do what you want in a real-time system, unless

1. You put a lower-frequency boundary for detection (upper frequency is according to sampling frequency); and
2. You have a transport delay corresponding to one cycle of that low frequency.