scalecheck

Check scaling of biquadratic filter

Syntax

s = scalecheck(sysobj,pnorm)

s = scalecheck(sysobj,pnorm,'Arithmetic',arithType)

Description

s = scalecheck(sysobj,pnorm) checks the scaling of the input filter System object™.

s = scalecheck(sysobj,pnorm,'Arithmetic',arithType) checks the scaling of the filter object with the arithmetic specified in arithType.

Examples

Linf-norm scaling of a filter

This example shows how to check the Linf-norm scaling of a filter.

Design an elliptic sos filter in the direct form II structure with default specifications.

EllipII = design(fdesign.lowpass, 'ellip', 'FilterStructure', 'df2sos',...
    'SystemObject',true);

Check the scaling.

scalecheck(EllipII,'Linf')

ans = 2×3

    3.1678   15.0757    1.4974
    4.7360   52.6026    1.0000

Design an elliptic sos filter in the direct form I structure with default specifications.

EllipI = design(fdesign.lowpass('N,Fp,Ap,Ast',10,0.5,0.5,20), 'ellip',...
    'FilterStructure', 'df1sos','SystemObject',true);

Check the scaling.

scalecheck(EllipI,'Linf')

ans = 1×5

    1.7078    2.0807    2.6084    7.1467    1.0000

Input Arguments

sysobj — Input filter object

dsp.BiquadFilter System object | dsp.SOSFilter System object

Input filter, specified as one of the following System objects:

• dsp.BiquadFilter

• dsp.SOSFilter

pnorm — Different types of norm

'l1' | 'l2' | 'linf' | 'L1' | 'L2' | 'Linf'

Discrete-time-domain norm or a frequency-domain norm.

Valid time-domain norm values for pnorm are 'l1', 'l2', and 'linf'. Valid frequency-domain norm values are 'L1', 'L2', and 'Linf'. The 'L2' norm is equal to the 'l2' norm (by Parseval's theorem), but this equivalency does not hold for other norms — 'l1' is not the same as 'L1' and 'Linf' is not the same as 'linf'.

arithType — Arithmetic type

'double' (default) | 'single' | 'Fixed'

Arithmetic type used during analysis, specified as 'double', 'single', or 'fixed'. The function assumes a double precision filter when the arithmetic input is not specified and the filter System object is in an unlocked state.

Output Arguments

s — Filter scaling

scalar | row vector

Filter scaling for a given p-norm. An optimally scaled filter has partial norms equal to one. In such cases, s contains all ones.

For direct-form I (df1sos) and direct-form II transposed (df2tsos) filters, the function returns the p-norm of the filter computed from the filter input to the output of each second-order section. Therefore, the number of elements in s is one less than the number of sections in the filter. This p-norm computation does not include the trailing scale value of the filter, which you can find by entering hd.scalevalue(end) at the MATLAB prompt.

For direct-form II (df2sos) and direct-form I transposed (df1tsos) filters, the function returns a row vector whose elements contain the p-norm from the filter input to the input of the recursive part of each second-order section. This computation of the p-norm corresponds to the input to the multipliers in these filter structures. These inputs correspond to the locations in the signal flow where overflow should be avoided.

When hd has nontrivial scale values, that is, if any scale values are not equal to one, s is a two-row matrix, rather than a vector. The first row elements of s report the p-norm of the filter computed from the filter input to the output of each second-order section. The elements of the second row of s contain the p-norm computed from the input of the filter to the input of each scale value between the sections. For df2sos and df1tsos filter structures, the last numerator and the trailing scale value for the filter are not included when scalecheck checks the scaling.

Data Types: double