Nonuniform oversampled filter banks for audio signal processing

An arrangement comprising:

• an n1 plurality of analysis filters i, where i=0, 1, . . . n1−1, each developing an output signal and each coupled to a circuit that subsamples the associated output signal by a factor of K1, where each filter i has a transfer function
• V
• 1
• (
• ⅇ
• j
• ⁡
• (
• ω
• -
• 2
• ⁢
• π
• N
• 1
• ⁢
• i
• )
• )
• ,
• symmetric about ω=0, where n1 is a first constant, N1 is a second constant, and V1 is a first preselected window filter function;
• an (N2/2)−n2 plurality of analysis filters k where k=n2+1, n2+2, . . . N2/2, each developing an output signal and each coupled to a circuit that subsamples the associated output signal by a factor of K2, where each filter k has a transfer function
• V
• 2
• (
• ⅇ
• j
• ⁡
• (
• ω
• -
• 2
• ⁢
• π
• N
• 2
• ⁢
• i
• )
• )
• ,
• symmetric about ω=0, where n2 is a third constant, N2 is a fourth constant, and V2 is a second preselected window filter function;
• and
• a transition analysis filter that develops an output signal, coupled to a circuit that subsamples said output signal of said transition filter by a factor of K1 or K2, having a bandpass transfer function that fills-in a gap frequencies that are passed by said n1 plurality of filters and frequencies that are passed by said (N2/2)−n2 plurality of filters.

An arrangement comprising:

• an n1 plurality of upsampling circuits, each responsive to an associated input signal and upsampling its input signal by a factor of K1;
• an n1 plurality of synthesis filters i where i=0, 1, . . . n1−1, each responsive to an associated one of said n1 plurality of upsampling circuits, where each filter i has a transfer function
• V
• _
• 1
• (
• ⅇ
• j
• ⁡
• (
• ω
• +
• 2
• ⁢
• π
• N
• 1
• ⁢
• i
• )
• )
• ,
• symmetric about ω=0, n1 is a first constant, N1 is a second constant, and {tilde over (V)}1 is a first preselected window filter function;
• an (N2/2)−n2 plurality of upsampling circuits, each responsive to an associated input signal port and upsampling its input signal by a factor of K2;
• an (N2/2)−n2 plurality of synthesis filters k where k=n2+1, n2+2, . . . N2/2, each responsive to an associated one of said (N2/2)−n2 plurality of upsampling circuits, where each filter k has a transfer function
• V
• _
• 2
• (
• ⅇ
• j
• ⁡
• (
• ω
• +
• 2
• ⁢
• π
• N
• 1
• ⁢
• k
• )
• )
• ,
• symmetric about ω=0, n2 is a third constant, N2 is a fourth constant, and V2 is a second preselected window filter function;
• a transition upsampling circuit, responsive to an associated input signal port that oversamples its input signal by a factor of K1 or K2;
• a transition synthesis filter responsive to said transition upsampling circuit, having a bandpass transfer function that fills-in a gap frequencies passed by said n1 plurality of filters and frequencies passed by said (N2/2)−n2 plurality of filters;
• and
• an addition circuit that combines output signals of said n1 plurality of filters, said transition filter, and said (N2/2)−n2 plurality of filters, to develop an output signal.