this can be accomplished by designing low pass all pass filter by connecting the input to an R-C passive low ass filter whose output is connected yo the noninverting amplifier input. The filter input is connected at the same time to a feedback potential divider with equal resistor.

It results in a transfer function having the following form:

H(s)= (S-Z0)/(S+P), eqn 1

where z0 is a zero and P is a pole.

both Z0 an P are real. Also Z0and P are equal in magnitude.

It results that the gain of the filter is eqaul to 1 at all the pass band frequencies.

Using binomial transformations to transform H(s) to H(z), one can can get the equivalent low pass all pass filter design.

The binomial transformation are:

s= (z-1)/(z+1),

the analog frequency wa= tanh wd/2

wd= 2 pi fc/fs

fc is the cut off frequency

and fs is the sampling frequency

fc= p/2 pi

Using these expressions you can transform eqn 1 to H(z) form which are digitally implementable.

For more information please follow the handouts in the link:Presentation Infinite Impulse response digital filter design-Handouts

By searching the web you can get a digital implementation of such circuit. Best wishes

Yes. Easiest way:

1) do FFT on signal x(t)

2) do filter F(omega) = exp(j*phi(omega)), signal Y(omega)=F(omega)*X(omega), where phi(omega) is your frequency dependent phase function.

3) inverse FFT to recover time domain signal y(t)

Cheers!

this can be accomplished by designing low pass all pass filter by connecting the input to an R-C passive low ass filter whose output is connected yo the noninverting amplifier input. The filter input is connected at the same time to a feedback potential divider with equal resistor.

It results in a transfer function having the following form:

H(s)= (S-Z0)/(S+P), eqn 1

where z0 is a zero and P is a pole.

both Z0 an P are real. Also Z0and P are equal in magnitude.

It results that the gain of the filter is eqaul to 1 at all the pass band frequencies.

Using binomial transformations to transform H(s) to H(z), one can can get the equivalent low pass all pass filter design.

The binomial transformation are:

s= (z-1)/(z+1),

the analog frequency wa= tanh wd/2

wd= 2 pi fc/fs

fc is the cut off frequency

and fs is the sampling frequency

fc= p/2 pi

Using these expressions you can transform eqn 1 to H(z) form which are digitally implementable.

For more information please follow the handouts in the link:Presentation Infinite Impulse response digital filter design-Handouts

By searching the web you can get a digital implementation of such circuit. Best wishes

Please search the online literature. You will even find online filter design software.

All pass filter is wight noise.

System band is part of this wight noise.

Please read my book

Communication Engineering Laboratories in Universities of England (part 1)