A sub-band processing system that reduces computational complexity and memory requirements includes a processor and a local or distributed memory. Logic stored in the memory partitions a frequency spectrum of bins into a smaller number of sub-bands. The logic enables a lossy compression by designating a magnitude and a designated or derived phase of each bin in the frequency spectrum as representative. The logic renders a lossless compression by decompressing the lossy compressed data and providing lost data based on original spectral relationships contained within the frequency spectrum.