Digital sub-band filters

A digital filter arrangement comprising:

• input terminal means for connection to an input signal;
• (a) a low-pass filter means, connected to said input terminal means, for filtering said input signal, said low-pass filter means having a stopband contained in an upper subband and a passband contained in a lower subband, the characteristics of said low-pass filter means being defined by an associated transfer function;
• and
• (b) a high-pass filter means, connected to said input terminal means, for filtering said input signal, said high-pass filter means having a stopband coincident with the passband of the low-pass filter means and a passband coincident with the stopband of the low-pass filter means, the characteristics of said high-pass filter means being defined by an associated transfer function,
• the transfer function of both filters being implemented by pole generating means for generating poles enhancing input signal frequency components in a transition band between the stopband and passband, and zero generating means for generating zeros attenuating input signal frequency components in the filter stopband and poles enhancing input signal frequency components in the filter passband,
• wherein the transfer function of one of said filter means has singularities lying in the z-plane representation at polar coordinates r, .theta. within a polar coordinate system and the transfer function of the other filter means has like singularities lying at polar coordinates r, (.pi.-.theta.) within said polar coordinate system;
• wherein the low-pass and high-pass filter means transfer functions have zeros at coordinates 1, .pi. and 1, .theta., respectively, within said polar coordinate system and the remainder of the singularities of said filter transfer functions occur in groups each possessing a symmetrical delay response about a relative frequency of .pi./2 radians, characterized in that at least one of such groups consists of a pole having, in the z-plane, polar coordinates r, .theta. and a zero having coordinates 1/r, (.pi.-.theta.) within said polar coordinate system.

A digital filter for filtering an input signal having frequency components in upper and lower frequency subbands, said filter comprising:

• low-pass filter means, connected to receive said input signal, for passing input signal frequencies within said lower subband and for blocking input signal frequencies within said upper subband in accordance with a predetermined characteristic transfer function associated therewith, said low-pass filter means having singularity generating means for generating singularities lying in the z-plane representation at polar coordinates r, .theta., including:
• (1) at least one pole causing enhancement of signal frequencies within said lower subband, (2) at least one zero, lying at z-plane polar coordinates 1, .pi., within a polar coordinate system causing attenuation of signal frequencies within said upper subband, and (3) at least one further pole causing enhancement of signal frequencies within a transition frequency subband situated between said upper and lower subbands;
• and
• high-pass filter means, connected to receive said input signal, for passing input signal frequencies within said upper subband and for blocking input signal frequencies within said lower subband in accordance with a predetermined characteristic transfer function associated therewith, said high-pass filter means transfer function having singularities lying at polar coordinates r, (.pi.-.theta.) within said polar coordinate system, including:
• (1) at least one pole causing enhancement of signal frequencies within said upper subband (2) at least one zero, lying at z-plane polar coordinates 1, Q, within said polar coordinate system causing attenuation of signal frequencies within said lower subband, and (3) at least one further pole causing enhancement of signal frequencies within said transition frequency subband
• wherein said poles and any additional zeros of the transfer function of said digital filter occur in groups possessing a symmetrical delay response about a relative frequency of .pi./2 radians, and at least one such group comprises a pole having z-plane coordinates r, .theta. and a zero having z-plane coordinates 1/r (.pi.-.theta.) within said polar coordinate system.

A digital filter for filtering an input signal having frequency components in first and second frequency subbands, said filter having an associated predetermined characteristic transfer function, said filter comprising:

• means, connected to receive said input signal, for introducing poles into said transfer function causing enhancement of signal frequencies within said first subband;
• means, connected to receive said input signal, for introducing poles into said transfer function causing enhancement of signal frequencies within a transition frequency subband situated between said first and second subbands;
• and
• means, connected to receive said input signal, for introducing zeros into said transfer function causing attenuation of signal frequencies within said second subband,
• wherein said filter transfer function has a pole which, in the z-plane representation, lies on the real axis at unit radius, the singularities of said filter transfer function occur in groups possessing a symmetrical delay response about a relative frequency of .pi./2 radians, and at least one of said groups comprises a pole having z-plane polar coordinates r, .theta., with a polar coordinate system and a zero having z-plane polar coordinates 1/r, (.pi.-.theta.) within said polar coordinate system.