Multiplierless 2-band perfect reconstruction quadrature mirror filter (PR-QMF) banks
First Claim
1. A multiplierless filter bank to be used in the sub-band coding of various types of signals, said multiplierless filter bank comprising at least one pair of finite impulse response filters connected in parallel, said finite impulse response filters in each said pair of finite impulse response filters having non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, said finite impulse response filters in each said pair of finite impulse response filters being Multiplierless Quadrature Mirror Filters which satisfy the perfect reconstruction requirement, ##EQU3## wherein Q is an integer normalization factor, wherein
(k)=1 for K=0
space="preserve" listing-type="equation">δ
(k)=0 for all other kwherein N+1 is the order of said Multiplierless Quadrature Mirror Filters, wherein ##EQU4## wherein
space="preserve" listing-type="equation">n=0, 1, . . .,Nwherein
space="preserve" listing-type="equation">k.sub.n.sup.(i) =integersand wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said Multiplierless Quadrature Mirror Filters.
1 Assignment
0 Petitions
Accused Products
Abstract
The Multiplierless Quadrature Mirror Filter concept is used in the design of analysis and synthesis filter banks to be used for the sub-band coding of various types of signals. The individual filters in the analysis and synthesis filter banks are designed to be near linear in phase, non-symmetrical in time, and to have equal bandwidth frequency responses. These multiplierless filters are relatively easy to implement in hardware and allow for the sub-band coding of signals with minimal computational complexity so as to result perfect signal reconstruction. Furthermore, these filters are particularly well suited for configuration in hierarchical sub-band structures.
119 Citations
22 Claims
- 1. A multiplierless filter bank to be used in the sub-band coding of various types of signals, said multiplierless filter bank comprising at least one pair of finite impulse response filters connected in parallel, said finite impulse response filters in each said pair of finite impulse response filters having non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, said finite impulse response filters in each said pair of finite impulse response filters being Multiplierless Quadrature Mirror Filters which satisfy the perfect reconstruction requirement, ##EQU3## wherein Q is an integer normalization factor, wherein
- space="preserve" listing-type="equation">δ
(k)=1 for K=0
space="preserve" listing-type="equation">δ
(k)=0 for all other kwherein N+1 is the order of said Multiplierless Quadrature Mirror Filters, wherein ##EQU4## wherein
space="preserve" listing-type="equation">n=0, 1, . . .,Nwherein
space="preserve" listing-type="equation">k.sub.n.sup.(i) =integersand wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said Multiplierless Quadrature Mirror Filters. - View Dependent Claims (2, 3, 4, 5)
- space="preserve" listing-type="equation">δ
-
6. A sub-band coding system for various types of signals, said sub-band coding system comprising:
-
a first multiplierless filter bank for analyzing each of said various types of signals into a plurality of sub-band signals, wherein said first multiplierless filter bank comprises at least one pair of finite impulse response filters having non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, wherein said finite impulse response filters in each said pair of finite impulse response filters in said first multiplierless filter bank are Multiplierless Quadrature Mirror Filters which satisfy the perfect reconstruction requirement, ##EQU5## wherein Q is an integer normalization factor, wherein
space="preserve" listing-type="equation">δ
(k)=1 for k=0
space="preserve" listing-type="equation">δ
(k)=0 for all other kwherein N+1 is the order of said Multiplierless Quadrature Mirror Filters, wherein ##EQU6## wherein
space="preserve" listing-type="equation">n=0, 1, . . .,Nwherein
space="preserve" listing-type="equation">k.sub.n.sup.(i) =integersand wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said Multiplierless Quadrature Mirror Filters; and a second multiplierless filter bank, connected in, series with said first multiplierless filter bank, for synthesizing each of said various types of analyzed signals from said plurality of sub-band signals, wherein said second multiplierless filter bank comprises at least one pair of finite impulse response filters having non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, wherein said finite impulse response filters in each said pair of finite impulse response filters in said second multiplierless filter bank are Multiplierless Quadrature Mirror Filters which satisfy the perfect reconstruction requirement, ##EQU7## wherein Q is an integer normalization factor, wherein
space="preserve" listing-type="equation">δ
(k)=1 for k=0
space="preserve" listing-type="equation">δ
(k)=0 for all other kwherein N+1 is the order of said Multiplierless Quadrature Mirror Filters, wherein ##EQU8## wherein
space="preserve" listing-type="equation">n=0, 1, . . .,Nwherein
space="preserve" listing-type="equation">k.sub.n.sup.(i) =integersand wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said Multiplierless Quadrature Mirror Filters. - View Dependent Claims (7, 8, 9, 10, 11, 12, 13)
-
-
14. A sub-band coding system for various types of signals, said sub-band coding system comprising:
-
at least one pair of finite impulse response Multiplierless Quadrature Mirror Filters (M-QMF'"'"'s) for analyzing each of said various types of signals into a plurality of analyzed sub-band signals, wherein said finite impulse response M-QMF'"'"'s in each said pair of analyzing M-QMF'"'"'s have non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, wherein said finite impulse response M-QMF'"'"'s in each said pair of analyzing M-QMF'"'"'s satisfy the perfect reconstruction requirement, ##EQU9## wherein Q is an integer normalization factor, wherein
space="preserve" listing-type="equation">δ
(k)=1 for k=0
space="preserve" listing-type="equation">δ
(k)=0 for all other kwherein N+1 is the order of said M-QMF'"'"'s, wherein ##EQU10## wherein
space="preserve" listing-type="equation">n=1, 1, . . .,Nwherein
space="preserve" listing-type="equation">k.sub.n.sup.(i) =integersand wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said M-QMF'"'"'s; means for decimating each of said analyzed sub-band signals; means for coding each of said decimated sub-band signals; means for decoding each of said coded sub-band signals; means for interpolating each of said decoded sub-band signals; at least one pair of finite impulse response Multiplierless Quadrature Mirror Filters (M-QMF'"'"'s) for synthesizing each of said analyzed sub-band signals from said plurality of interpolated sub-band signals, wherein said finite impulse response M-QMF'"'"'s in each said pair of synthesizing M-QMF'"'"'s have non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, wherein said finite impulse response M-QMF'"'"'s in each said pair of synthesizing M-QMF'"'"'s satisfy the perfect reconstruction requirement, wherein Q is an integer normalization factor, wherein ##EQU11##
space="preserve" listing-type="equation">δ
(k)=1 for k=0
space="preserve" listing-type="equation">δ
(k)=0 for all other kwherein N+1 is the order of said M-QMF'"'"'s, wherein ##EQU12## wherein
space="preserve" listing-type="equation">n=0, 1, . . .,Nwherein
space="preserve" listing-type="equation">k.sub.n.sup.(i) =integersand wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said M-QMF'"'"'s; and means for summing said synthesized analyzed sub-band signals so as to perfectly reconstruct each of said various types of analyzed signals. - View Dependent Claims (15, 16, 17)
-
- 18. A multiplierless filter bank, said multiplierless filter bank comprising at least one pair of finite impulse response filters connected in parallel, said finite impulse response filters in each said pair of finite impulse response filters having non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, said finite impulse response filters in each said pair of finite impulse response filters being Multiplierless Quadrature Mirror Filters which satisfy the perfect reconstruction requirement, ##EQU13## wherein Q is an integer normalization factor, wherein
- space="preserve" listing-type="equation">δ
(k)=1 for k=0
space="preserve" listing-type="equation">δ
(k)=0 for all other kwherein N+1 is the order of said Multiplierless Quadrature Mirror Filters, wherein ##EQU14## wherein
space="preserve" listing-type="equation">n=0, 1, . . .,Nwherein
space="preserve" listing-type="equation">k.sub.n.sup.(i) =integersand wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said Multiplierless Quadrature Mirror Filters. - View Dependent Claims (19, 20, 21, 22)
- space="preserve" listing-type="equation">δ
Specification