other optimizations

The joint optimization technique was developed initially for the approximation of linear phase and equiripple group delay lowpass filter characteristics. It was later applied to other areas of interest.

These include:


~~~~~ return to the home page

bandpass filters
There are applications where a flat group delay within the passband of a bandpass filter is required. Rather than cascade an allpass equalizer it has been found advantageous to re-optimize a new system having the desired overall characteristic. This, as in the lowpass filter case, results in a system of the same or lower order, but with lower pole Qs, simplifying the realization.

~~~~~ to top of page

linear phase crossover networks
Crossover networks are used in the audio (HIFI) industry to split a wideband audio signal into two (or more) channels for feeding speakers encompassing different frequency ranges. A desirable characteristic is that the phase response of the system be linear. That is to say, there is a frequency-independent time delay between any component of the wideband (electrical) input signal to the crossover network, and the audio (acoustic) signal received from the split speaker system at a remote point.

These networks have been realized in both passive (high level) and active (low-level) form, and received with considerable acclaim by 'golden ear' aficionados. Unfortunately funding was not available at the time for their commercial exploitation, and other developments have since taken precedence.

~~~~~ to top of page

time domain optimizations and Nyquist I responses
The joint optimization technique lends itself naturally to the control of responses in both amplitude and time. Typically it is the characteristic of the step response which is of interest. Pulse shaping filters have been developed with controlled overshoots, and with uniformly spaced zero crossings (Nyquist I response).

It might seem natural that the second response under control would be that of the amplitude, in both the passband and the stopband. But this produces un-necessary conflicts between the amplitude and time domain requirements. Far preferable is to maintain a defined slotband, and let the passband response find its own shape.

The technique has been successfully employed in commercial data communication systems.

~~~~~ to top of page

linear phase QPS
One of the methods of generating a single sideband (SSB) signal is known as the phasing method. This uses a wideband quadrature phase splitter (QPS) network. The original applications of SSB were for speech, and so phase response was of little importance.

Joint optimization techniques have been used to develop a QPS which enables implementation of the phasing method of SSB generation, but with a flat group delay characteristic (between message in at the transmitter to message out at the receiver). This has applications when SSB is used for data transmission.

In the 'digital age' it might seem that the need for this analog method of SSB generation no longer exists. However, there remain applications where digital realizations are hampered by high frequency (speed) constraints. Here the humble analog QPS - linear phase or otherwise - can provide the solution. We can offer approximations to meet your most demanding requirements.

~~~~~ to top of page

outboard equalization
A common practice for group delay equalization is to cascade an existing system (which needs delay equalization) with an outboard allpass equalizer. Commercially available software exists for designing these networks.

The joint optimization software being exploited by this site is capable of producing an add-on network which can modify both the group delay and the amplitude response of the cascaded system. Typically this would reduce further any amplitude ripple, and 'flatten' the group delay characteristic.

~~~~~ to top of page

z-plane optimizations
There are well known analytical methods for transforming a filter characteristic from the s-plane to the z-plane. These preserve the amplitude response, but not the phase response - thus they have their limitations.

All of the networks optimized in the s-plane can be re-optimized in (transformed into) the z-plane, whilst preserving their amplitude and phase (or delay) characteristics. This ability has been exploited in some optimizations of cascaded analog and digital filters.

Could anyone out there use this ability, or has it since been achieved analytically?

~~~~~ to top of page

return to the home page.