In a pulse searching arrangement (65) of a multi-pulse voice encoder comprising a linear prediction residual signal producing arrangement (61), a pitch period is predicted in a cross-correlation domain in each subframe of a frame of an input voice signal. For this purpose, a local signal producing circuit comprises a first cross-correlator (66) for producing a first cross-correlation signal related to a linear prediction residual signal. A buffer memory (32) produces an output cross-correlation signal from subframe to subframe. Supplied with a sum signal and controlled by a pitch period signal representative of pitch periods of the input voice signal, a pitch synthesizing filter (71) produces a synthesized signal, which is added to provide the sum signal to a signal representative of excitation pulses. Responsive to the synthesized signal, a second cross-correlator (67) produces a second cross-correlation signal, which is subtracted from the output cross-correlation signal to provide the local signal. Supplied with an autocorrelation signal, a pulse searcher (44) searches the excitation pulses in the local signal.