Tim Wescott wrote:> Andor wrote: > >> On 11 Jul., 12:08, Robert Adams <robert.ad...@analog.com> wrote: >> >>> On Jul 11, 2:48 am, Andor <andor.bari...@gmail.com> wrote: >>> >>> >>> >>> >>> >>>> Robert Adams wrote: >>>> >>>>> One method of creating a quadrature signal is to pass an input signal >>>>> through two parallel allpass networks, where the outputs of the two >>>>> networks differ in phase by 90 degrees. Each allpass network is >>>>> typically high-order to obtain reasonable accuracy in terms of holding >>>>> the phase difference over frequency. One advantage of this technique >>>>> compared with the more usual anti-symmetric Hilbert filter is that the >>>>> number of multiplies is smaller for a given accuracy (note that the >>>>> Hilbert filter is perfect for phase accuracy, but suffers from >>>>> amplitude errors and becomes very long if you need a frequency range >>>>> that spans a large portion of the band from 0 to PI, whereas the >>>>> allpass filters are perfect for amplitude accuracy but cannot hold the >>>>> phase difference at frequencies near DC and PI). >>>>> The problem I have is designing the allpass filter networks to hold >>>>> the 90-degree phase difference. In the past I have seen people apply >>>>> non-linear optimizers to the problem. I am trying to solve it with >>>>> Matlab fminsearch, but am having trouble getting a starting point that >>>>> is close enough that it converges to the desired 90-degree phase >>>>> difference. >>>>> Has anyone seen any papers on this?. >>>> >>>> Hi Bob >>>> You could try FDLS for this (at least to get sensible starting values >>>> for the coefficients). Using FDLS for phase compensation was discussed >>>> in the thread "Allpass filter with specific phase response Options" by >>>> the FDLS inventor Greg Berchin. >>>> I'm curious: the two allpass networks you want are supposed to have a >>>> phase shift of 90� with respect to each other. However, does the >>>> output of each network have a constant phase shift? >>>> Regards, >>>> Andor- Hide quoted text - >>>> - Show quoted text - >>> >>> No, it does not. >>> Each allpass network will display increasing phase shift with >>> frequency, but if you were to plot them on the same graph the >>> difference in phase would be 90 degreees. >> >> >> Ah, ok. So you generate a quadrature pair, but neither of the outputs >> is equal to the input ... > > > Right. It's an old method for generating or demodulating SSB signals > for voice communications. Since the ear is relatively insensitive to > phase variations, the overall phase variation of the result doesn't > matter nearly as much as the suppression of the opposing sideband.BTW this method can be used in the opposite way. I.e. the SSB signal can be easily converted into 90-degree shifted versions of the modulation signal. The SSB can be formed by conventional filtering. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com