Abstract: A digital synthesis technique provides pulse shaping in accordance with predetermined time domain and frequency domain constraints. In the technique, the informational content of a binary bit stream is used by an access circuit (12) to form address words for accessing a read-only-memory (13). The digital representations stored in the ROM (13) represent a superposition of temporally-displaced truncated impulse time functions, each weighted by the discrete transmission symbol levels of the analog output signal. The digital representations from two ROMs (13-1 and 13-2) are toggled by a sequencng circuit. In other embodiments of the invention, different memory arrangements ranging from a signal ROM (142) to an array of ROMS (163-1 through 163-3 and 164-1 through 164-3) are respectively used to decrease circuit complexity. In a digital radio transmission application of the technique, this arrangement is economical, readily reproducible and stable since it obviates the need for conventional complex analog filters.

Abstract: Compensation for arbitrary combinations of linear and nonlinear distortion is provided by altering a received symbol value by a preselected amount. This amount is based on an estimate of the sequence of transmitted symbol values represented by the received symbol value at a sampling time and a number of received symbol values at other sampling times. The altered symbol value is then compared with the closest one of the possible transmitted symbol values to determine the difference, if any, therebetween. The closest one of the possible transmitted symbol values is then outputted if the difference meets a prescribed criterion. If not, the received symbol value is altered by a different amount in response to another estimate until the recited difference meets the prescribed criterion. In the disclosed embodiments, the foregoing technique is incorporated in a memory-based canceler or transversal filter.