Method of designing families of boost and cut filters, including treble and bass controls and graphic equalizers

A method of designing a family of cut filters, each cut filter having a transfer function H(z) and a different selected gain gd, comprising:

• designing a first filter using conventional methods, the first filter having one of the selected gains gd and denominator polynomial A0(z) and numerator polynomial B0(z);
• decomposing the first filter into a circuit having an active region gain g0 and containing a series combination of a nominal filter having a transfer function Hm(z) and an amplifier having a gain ga;
• and
• i) calculating gain ga for each said cut filter in the family, where
• ga=(g0−g0gd)/(gd−g0gd)
• ii) calculating the transfer function H(z) of each said cut filter, where
• H(z)=B0(z)/[B0(z)+ga(A0(z)−B0(z)].

A method of designing a family of filters, each filter having a transfer function H(z) and a different selected gain gd, comprising:

• designing a first filter using conventional methods, the first filter having one of the selected gains and denominator polynomial A0(z) and numerator polynomial B0(z);
• decomposing the first filter into a circuit having an active region gain g0 and containing a series combination of a nominal filter having a transfer function Hm(z) and an amplifier having a gain ga;
• and
• a) calculating gain ga for each filter in the family, where
• (i) ga=(gd−1)/(g0−1) in the case of a boost filter family, and
• (ii) ga=(g0−g0gd)/(gd−g0gd) in the case of a cut filter family,
• b) calculating the transfer function H(z) of each filter, where
• (i) H(z)=[A0(z)+ga(B0(z)−A0(z)]/A0(z) in the case of a boost filter family, and
• (ii) H(z)=B0(z)/[B0(z)+ga(A0(z)−B0(z)] in the case of a cut filter family.

An adjustable boost filter, comprising:

• a first boost filter having a selectable gain gd and derived from a standard filter having gain gd and having denominator polynomial A0(z) and numerator polynomial B0(z);
• the first boost filter being adapted to be decomposed into a circuit having an active region gain g0 and two parallel branches, the first branch directly applying an input signal to a signal summer, the second branch being applied to the signal summer and containing a series combination of a nominal filter having a transfer function Hm(z) and an amplifier having a gain ga;
• and
• a) wherein the first boost filter selectable gain gd is defined by the equation:
• ga=(gd−1)/(g0−1);
• and
• b) wherein the first boost filter has a transfer function H(z), where:
• H(z)=[A0(z)+ga(B0(z)−A0(z)]/A0(z).

An adjustable cut filter having a selectable gain gd and derived from a standard filter having a transfer function

• 12 H ⁡ ( z ) = B 0 A 0 ,
• said standard filter first being decomposed into a filter having an active gain g0 and a loop gain ga, wherein:
• a) the first cut filter selectable gd is defined by the equation:
• ga=(g0−g0gd)/(gd−g0gd);
• and
• b) the first cut filter has a transfer function H(z), where:
• H(z)=B0(z)/[B0(z)+ga(A0(z)−B0(z)];
• wherein:
• A0 is the denominator polynomial of standard filter;
• and
• B0 is the numerator polynomial of standard filter.

An adjustable filter derived from a standard filter, the adjustable filter having a transfer function H(z) and a selectable gain gd, wherein the standard filter has one of the selected gains gd and denominator polynomial A0(z) and numerator polynomial B0(z);

• wherein the standard filter is decomposed into a circuit having an active region gain g0 and two parallel branches, the first branch directly applying an input signal to a signal summer, the second branch applied to the signal summer and containing a series combination of a nominal filter having a transfer function Hm(z) and an amplifier having a gain ga;
• where:
• a) gain ga for each filter is:
• (i) ga=(gd−1)/(g0−1) in the case of a boost filter, and
• (ii) ga=(g0−g0gd)/(gd−gogd) in the case of a cut filter,
• b) where the transfer function H(z) of the adjustable filter is:
• (i) H(z)=[A0(z)+ga(B0(z)−A0(z)]/A0(z) in the case of a boost filter, and
• (ii) H(z)=B0(z)/[B0(z)+ga(A0(z)−B0(z)] in the case of a cut filter;
• the adjustable filter further being coupled to a normalization filter having having a transfer function HT(z), comprising:
• an input having a plurality of input branches summed by a signal summer, the input branches having coefficients of bo, b1, . . . bn;
• and
• an output having a plurality of output branches from the signal summer, the output branches having coefficients 1/ao, a1 . . . an, whereby coefficient a0 is the first coefficient of the numerator of the transfer function HT(z).