System and method for low-resolution signal rendering from a hierarchical transform representation

A method for generating reduced resolution versions of a signal encoded via a hierarchical cascade of lapped biorthogonal transforms (LBT), comprising using a computing device to:

• decode blocks of transform coefficients from the encoded signal up to a highest current hierarchical level not exceeding a desired signal resolution;
• and
• for desired signal resolutions not directly corresponding to the current hierarchical transform level, using the computing device for:
• scaling the decoded blocks of transform coefficients,
• lowpass filtering the scaled decoded blocks of transform coefficients in the transform domain,
• applying an inverse transform to the filtered scaled decoded blocks of transform coefficients, and
• downsampling the resulting signal to generate an output signal having the desired resolution.

A computer readable medium having computer executable instructions for generating reduced resolution versions of a signal encoded via a hierarchical cascade of lapped biorthogonal transforms (LBT), comprising:

• decoding blocks of transform coefficients of the encoded signal up to a highest current hierarchical level not exceeding a desired signal resolution;
• for desired signal resolutions not directly corresponding to the current hierarchical transform level:
• scaling the decoded blocks of transform coefficients,
• lowpass filtering the scaled decoded blocks of transform coefficients in the transform domain,
• applying an inverse transform to the filtered scaled decoded blocks of transform coefficients, and
• downsampling the resulting signal to generate an output signal having the desired resolution;
• and
• for desired signal resolutions directly corresponding to the current hierarchical transform level:
• grouping DC coefficients of the decoded blocks of transform coefficients,
• scaling the grouped DC coefficients to generate an output signal having the desired resolution, and
• lowpass filtering the output signal in the signal domain to remove high frequency aliasing in the output signal.