A signal processing device has a program memory for storing program code transferred from an external source under the control of an access control unit having an address counter. The transferred program code is executed by a computational unit having a program counter. The access control unit controls the transfer of the program code according to the values of both the address counter and the program counter, thereby enabling the computational unit to start executing the program code before the entire program has been transferred. Program initialization can therefore be completed quickly, and the program can promptly begin producing audible or visible results.