Filter Design Toolbox

sos

Convert a quantized filter to second-order section form, order, and scale.

Syntax

• Hq2 = sos(Hq) 
  Hq2 = sos(Hq, order) 
  Hq2 = sos(Hq, order, scale)
  

Description

Hq2 = sos(Hq) returns a quantized filter Hq2 that has second-order sections and the dft2 structure. Use the same optional arguments used in tf2sos.

Hq2 = sos(Hq, order) specifies the order of the sections in Hq2, where order is either of the following strings:

• 'down' -- to order the sections so the first section of Hq2 contains the poles closest to the unit circle (L norm scaling)
• 'up' -- to order the sections so the first section of Hq2 contains the poles farthest from the unit circle (L2 norm scaling and the default)

Hq2 = sos(Hq, order, scale) also specifies the desired scaling of the gain and numerator coefficients of all second-order sections, where scale is one of the following strings:

• 'none' -- to apply no scaling (default)
• 'inf' -- to apply infinity-norm scaling
• 'two' -- to apply 2-norm scaling

Use infinity-norm scaling in conjunction with up-ordering to minimize the probability of overflow in the filter realization. Consider using 2-norm scaling in conjunction with down-ordering to minimize the peak round-off noise.

When Hq is a fixed-point filter, the filter coefficients are normalized so that the magnitude of the maximum coefficient in each section is 1. The gain of the filter is applied to the first scale value of Hq2.

sos uses the direct form II transposed (dft2) structure to implement second- order section filters.

Examples

• [A,B,C,D]=butter(8,.5);
  Hq = qfilt('StateSpace',{A,B,C,D},'mode','single');
  Hq1 = sos(Hq)
  

See Also

qfilt, qfilt2tf

setbits

tf2ca