6.2 Lab 5: prelab  (Page 2/4)

Once our magnitude response has been selected, we need to perform group delay equalization to yield approximatelyconstant group delay. This can be done using the iirgrpdelay command in the FD Toolbox. Again, note that a least- $p$ th algorithm is used and that we can constrain the radius of the poles. Theresulting all-pass filter can be connected in series with the nonlinear phase low-pass filter created with iirlpnormc to complete the entire system.

The FD Toolbox can also aid in analyzing quantization effects. We suggest using FDATool , a convenient GUI for interacting with the FD Toolbox, to carryout the analysis. See the internet documentation for more information on the functions available. Of course, you maychoose to do this by scaling and rounding as you have done in previous labs. Note that even though MATLAB useshigh-precision arithmetic you may find that for long IIR filters MATLAB has difficulty rendering frequency responses,etc. Thus, you may find it useful to design a filter that has half the passband ripple, half the stop-bandattenuation, etc. and implement it twice in your code to meet the specification.

Note that FDAtool and the filter design toolbox ( qfilt function) can be used to analyze quantization effects on various filter structures,as well as on the FFT. The quantization parameters can be chosen and optimized in FDAtool . Also, FDAtool (with or without the filter design toolbox) can compute correct scaling to avoidoverflow.

Implementation structures

There are several ways to implement an IIR filter. One of these, a cascade of second-order systems, we have alreadyseen. An alternative is placing these second-order sections in parallel. Another common implementation is a latticestructure (see any standard DSP textbook), which tends to be more resistant to finite word-length effects and may be morecomputationally efficient. To examine your choices, as a starting point you should examine the MATLAB functionslisted as "Linear System Transformations" when you type help signal at the command prompt (does not require the FDToolbox).

One of the difficult aspects of an IIR lattice is that although the lattice coefficients are in the interval(-1,1), the internals of the lattice can grow to be prohibitively large. To compensate for this, an m-file( latcfiltn.m ) has been created that performs normalization after each lattice section to preventoverflow. If you are interested in exploring a lattice implementation you may want to copy this m-file to your owndirectory and modify it to suit your needs. Note that there are comments within the file to indicate where you might addchecks for overflow conditions.

We suggest the use of FDAtool and dfilt for structure transformations. The function dfilt works also without the Filter Design Toolbox. It is also useful for evaluatingcascade or parallel connections of sub-filters. The MATLAB command fvtool can be used to quickly evaluate frequency response of various filter structures.