A compression system comprising: a processor; and a computer readable medium storing instructions executable by the processor, the instructions comprising: first computer program code that transforms an audio input signal into a frequency spectrum, separates the frequency spectrum into a number of bins of real and imaginary data, partitions and stores the frequency spectrum of bins of real and imaginary data for a frame into a smaller number of sub-bands than said number of bins; second computer program code that executes a first lossy compression for a first set of the sub-bands, the first lossy compression compressing magnitudes and phases for one or more of said bins corresponding to each sub-band of said first set of the sub-bands into a designated magnitude of one bin of each sub-band of the first set that is representative of that sub-band and a designated phase of one bin of each sub-band of the first set that is representative of that sub-band, wherein the first set includes only those sub-bands having indices that are greater than or equal to a first index; characterized in that it further comprises: third computer program code that executes, subsequent to a frequency spectrum processing of the data for a second set of the sub-bands rendered by the second computer program code, a second lossy compression for said second set of the sub-bands, the second lossy compression compressing a designated magnitude of one bin in each sub-band of the second set that is representative of that sub-band and a designated phase of one bin in each sub-band of the second set that is representative of that sub-band, wherein the second set includes only those sub-bands having indices that are less than the first index and greater than to a second index, wherein the frequency spectrum processing is performed by one of: a. an acoustic echo canceller; b. a noise canceller; or c. a beam former. a processor; and a computer readable medium storing instructions executable by the processor, the instructions comprising: first computer program code that transforms an audio input signal into a frequency spectrum, separates the frequency spectrum into a number of bins of real and imaginary data, partitions and stores the frequency spectrum of bins of real and imaginary data for a frame into a smaller number of sub-bands than said number of bins; second computer program code that executes a first lossy compression for a first set of the sub-bands, the first lossy compression compressing magnitudes and phases for one or more of said bins corresponding to each sub-band of said first set of the sub-bands into a designated magnitude of one bin of each sub-band of the first set that is representative of that sub-band and a designated phase of one bin of each sub-band of the first set that is representative of that sub-band, wherein the first set includes only those sub-bands having indices that are greater than or equal to a first index; first computer program code that transforms an audio input signal into a frequency spectrum, separates the frequency spectrum into a number of bins of real and imaginary data, partitions and stores the frequency spectrum of bins of real and imaginary data for a frame into a smaller number of sub-bands than said number of bins; second computer program code that executes a first lossy compression for a first set of the sub-bands, the first lossy compression compressing magnitudes and phases for one or more of said bins corresponding to each sub-band of said first set of the sub-bands into a designated magnitude of one bin of each sub-band of the first set that is representative of that sub-band and a designated phase of one bin of each sub-band of the first set that is representative of that sub-band, wherein the first set includes only those sub-bands having indices that are greater than or equal to a first index; characterized in that it further comprises: third computer program code that executes, subsequent to a frequency spectrum processing of the data for a second set of the sub-bands rendered by the second computer program code, a second lossy compression for said second set of the sub-bands, the second lossy compression compressing a designated magnitude of one bin in each sub-band of the second set that is representative of that sub-band and a designated phase of one bin in each sub-band of the second set that is representative of that sub-band, wherein the second set includes only those sub-bands having indices that are less than the first index and greater than to a second index, wherein the frequency spectrum processing is performed by one of: a. an acoustic echo canceller; b. a noise canceller; or c. a beam former. a. an acoustic echo canceller; b. a noise canceller; or c. a beam former.