Question about filters results

[cedance]

minimal phase + tranfer function

hi,

i recently studied ina book that a filter can be implemented as follows.

i/p signal x given to a system with tranfer function H(Z), results in X(Z) * H(Z). then invert it(time inversion) => X-1(Z) * H-1(Z). again pass thro' a system with transfer function H(Z), => X-1(Z) * H-1(Z) * H(Z). now again invert it. => X(Z) * H(Z) * H-1(Z). here (*) denotes multiplication only.

the final expression is equ to X(Z) *( | H(Z) |) ^2

so, the filter ultimately is independent of phase, thereby leading to no delay and distortion. is this implementable in practice. even there is matlab command for executing this command. but, in hardware will this give reasonable results? pls help me know this....


regards,
Arun.

 

[flatulent]

Re: question in filter !!!

Since you have to store the signal and the run it through the filter in reverse order, this cannot be done in real time. As long as your are going to store the signal, you may as well do a DSP type filter with linear phase (nonrecursive types) and get the filtered signal slightly delayed in sort of real time.

 

[Hero]

Re: question in filter !!!

Hi,

Some linear systems theory explanations:

In linear systems with minimal phase amplitude and phase transfer function are dependant and connected with Hilbert transforms. So in this case when you change amplitude transfer function you automatically change pahse transfer function.

Linear systems with minimal phase are systems which have all zeros on the left s-halfplane.

In linear systems with non-minimal phase amplitude and phase transfer function are not dependant but these systems have zeros on the right s-halfplane.

Also take care with impulse time response of these systems. You can always expect negative undershoot after impulse turn-on time.

In linear discrete systems situation is similar.

Linear discrete systems with non-minimal phase have zeros out side of unit circle in complex Z-plane.

This theory is valid only for linear and time-invariant systems (analog and discrete).

You can not implemented non-causal filters in the real-time with real physical systems beacuse you can not expect time response before time exitation.

In the real life this means that you can not start to crash your car 10 days or 10 minutes before traffic accident in the near future.

This also mean that you exactly need to know what will happen in the future to simulate these systems in the real time.

You can exactly simulate these systems if you know past and future, but not in real-time.

These system can be implemented in the quasi-real-time. If you divide real-time samples in the smal groups of samples and make small delay
you can treat these groups of samples as off-line samples and implemented non-causal filter over them.

This system is not pure real-time system beacuse you always need to have some process delay in system.

Regards