Some embodiments relate to techniques for encoding an audio signal represented by a plurality of frames including a first frame. The techniques include using at least one computer hardware processor to perform: obtaining an initial discrete spectral representation of the first frame; obtaining a primary discrete spectral representation of the initial discrete spectral representation at least in part by estimating a phase envelope of the initial discrete spectral representation and evaluating the estimated phase envelope at a discrete set of frequencies; calculating a residual discrete spectral representation of the initial discrete spectral representation based on the initial discrete spectral representation and the primary discrete spectral representation; and encoding the residual discrete spectral representation using a plurality of codewords.