Lattice phase equaliser

A lattice filter is a type of the electronic filter having a grating structure. In the German literature, the term conductor structure is also used as an alternative for it. The filter structure goes back to works from the 1920s by Otto Julius Zobel and George Ashley Campbell.

General

This filter structure is used as an analog filter circuitry and in the digital signal processing of a digital filter, and has the advantage that it is easy to check for stability: If all the coefficients with a value of less than 1, the overall system is stable. A digital filter structure, either in the filter with a finite impulse response ( FIR) filter or as an infinite impulse response (IIR) can be realized.

The characteristic impedance Z0 of an analog base element consisting of the single complex impedances Z, as shown in the illustration, is given as:

Having the transfer function H ( ω ):

Digital realization

The following figure shows a lattice filter 3rd order in FIR structure as a digital filter. Supplied from the left sequence x [k] is converted into the output sequence y [ k]. The values ​​α0, α'0, ... represent the filter coefficients per stage represents the blocks labeled z -1 delay elements by a sampling:

The next image is a lattice filter in the form of an IIR structure. This structure is referred to as English all pole structure, since the transfer function has only poles and no zeros. The feedback is implemented in the lower row.

Applications

These filters are mainly used in the field of speech coding and synthesis. As used for example mobile radio telephones, which operate according to the GSM standard, in the IIR filter lattice structure.

For the calculation of the filter coefficients are comprehensive software packages available, such as the software package MATLAB latcfilt.m with its functions and tf2latc.m.