Minimum Phase and All Pass Systems (c)

[@Signalprocessing-c8y]

Thank you for the lecture. you explained it very well.

[@saigunaranjanPelluri]

Sir,you mentioned that in trying to factor H(z) as a minimum phase component and an all phase component there should not be any zero on the unit circle.Is it because if there is a zero on the unit circle then we would have to introduce a pole also on the unit circle to make an all pass component and this could lead to an unstable all pass component?Also is there any restiction that H(z) should have/have not any pole on the unit circle? also how can we comment on the stability of an all pass filter?

[@elpintoelpinto2253]

Great lecture!

[@HalJordan18]

thanks a lot for the explanation, very useful

[@scatteringparameters.4167]

And how do we rove that added phase distortion due to all pass

[@tedsheridan8725]

You do a bit of sleight-of-hand when showing the all-pass filter has unity gain. If you use a more standard (z-zero)/(z-pole) formulation, there is a non-unity gain, though it is the same for all frequencies. The way you wrote it cleverly hides the gain constant so the gain is indeed one. But I was racking my brain trying to figure out how any point on the unit circle could be equidistant to a reciprocal conjugate pair. Maybe you could mention that there is a constant needed to account for the difference in distances to the pole and the zero?

[@ahmedmuhammed6905]

That is very good explanation

[@deahyeonyu5434]

reallt really great lecure thank you sir

[@linkmaster959]

Still not sure why you would need to factor out that (-Beta) term... ive seen examples say all pass systems are just reciprocal zeros and poles... such as (1+3z^-1)/(1+1/3z^-1)

[@scatteringparameters.4167]

Poles and zeroes are always added in time constant form. DC Gain factor is preserved

[@rachelstokes1340]

this is amazing, thank you so much