A “STAC Codec” provides lossless audio compression and decompression by processing an audio signal using integer-reversible modulated lapped transforms (MLT) to produce transform coefficients. Transform coefficients are then encoded using a backward-adaptive run-length Golomb-Rice (RLGR) encoder to produce losslessly compressed audio signals. In additional embodiments, further compression gains are achieved via an inter-block spectral estimation and data sorting strategy. Further, compression in the transform domain allows the bitstream to be partially decoded, using the corresponding RLGR decoder, to reconstruct the frequency-domain coefficients. These frequency-domain coefficients are then directly used to speed up various transform-domain based applications such as transcoding media to lossy or other formats, search, identification, visualization, watermarking, etc. In other embodiments, near-lossless compression is achieved by right-shifting transform coefficients by some number of bits such that quantization errors are not perceived as distortion in the decoded audio signal.