A method and apparatus for compressing signal samples uses block floating point representations where the number of bits per mantissa is determined by the maximum magnitude sample in the group. The compressor defines groups of signal samples having a fixed number of samples per group. The maximum magnitude sample in the group determines an exponent value corresponding to the number of bits for representing the maximum sample value. The exponent values are encoded to form exponent tokens. Exponent differences between consecutive exponent values may be encoded individually or jointly. The samples in the group are mapped to corresponding mantissas, each mantissa having a number of bits based on the exponent value. Removing LSBs depending on the exponent value produces mantissas having fewer bits. Feedback control monitors the compressed bit rate and/or a quality metric. This abstract does not limit the scope of the invention as described in the claims.