System and method for noise reduction using bi-orthogonal modified discrete cosine transform

A method for encoding a stereo input signal having a plurality of channels, comprising the steps of:

• transforming a signal from each of the plurality of channels of the stereo signal into a plurality of BMDCT frequency coefficients using a bi-orthogonal modified discrete cosine transform, wherein transforming a signal from each of the plurality of channels includes performing 2×2 orthogonal transforms on two channels of the stereo signal into independent sets of BMDCT coefficients:
• [ L ′ R ′ ] = [ cos ⁢ ⁢ ( θ ) sin ⁢ ⁢ ( θ ) - sin ⁢ ⁢ ( θ ) cos ⁢ ⁢ ( θ ) ] · [ L R ] ;
• quantizing the BMDCT frequency coefficients to produce a set of integer numbers which represent the BMDCT frequency coefficients generated from each channel;
• and
• losslessly encoding the set of integer numbers into representative symbols to lower the number of bits required to represent the BMDCT frequency coefficients generated from the plurality of channels of the stereo signal.

An apparatus configured to encode a signal, comprising:

• a bi-orthogonal transform module configured to transform the signal into a plurality of BMDCT frequency coefficients using a bi-orthogonal modified discrete cosine transform;
• a quantization module configured-to quantize the BMDCT frequency coefficients to produce a set of integer numbers which represents the BMDCT frequency coefficients;
• and
• a lossless encoder module configured to losslessly encode the set of integer numbers to minimize the number of bits required to represent the BMDCT frequency coefficients;
• and
• a signal analysis module configured to divide the signal into a plurality of different window types based on a characteristic of the signal and analyze the signal to determine a set of noise targets where noise can be transparently introduced into the signal to compress the signal;
• a stereo transform module configured to stereo transform the BMDCT signal frequency coefficients to eliminate all redundant and irrelevant bits from the BMDCT signal frequency coefficients;
• a rate control module configured to use the noise targets received from the signal analysis module and determine the step size required to transparently allocate noise into the BMDCT frequency coefficients to meet a required bit rate per frame;
• and
• a frame packing module configured to pack the losslessly encoded set of integer numbers, a plurality of step sizes, a plurality of transform angles, and the plurality of different window sizes into a frame to produce a formatted signal.

A method for decoding a formatted signal, comprising the steps of:

• decoding the coded quantized BMDCT frequency coefficients to reconstruct a quantized set of integer numbers representing BMDCT frequency coefficients of a signal, the BMDCT frequency coefficients at the decoder being represented at a reduced number of bits of precision and the BMDCT window coefficients at the encoder are configured such that the combination of forward transform and inverse transform substantially perfectly reconstruct the signal;
• inverse quantizing the quantized set of integer numbers to produce the BMDCT frequency coefficients of the signal;
• and
• inverse transforming the BMDCT frequency coefficients of the signal using a bi-orthogonal modified discrete cosine inverse transform module to reproduce the signal.

An apparatus configured to decode a formatted signal, comprising:

• a lossless decoder module configured to losslessly decode the formatted signal to reconstruct a quantized set of integer numbers representing the BMDCT frequency coefficients of a signal;
• an inverse quantization module configured to inverse quantize the quantized set of integer numbers to produce the BMDCT frequency coefficients of the signal;
• an inverse bi-orthogonal modified discrete cosine transform module configured to inverse transform the BMDCT frequency coefficients to reproduce the signal;
• a frame unpacking module configured to separate the formatted bitstream into side information and quantized BMDCT frequency coefficients;
• and
• a stereo transformer configured to inverse stereo transform the BMDCT frequency coefficients from a pair of channels and the transformed side information to produce the BMDCT frequency coefficients of the signal.