A sub-band audio signal synthesizer produces a digital audio signal from a sub-band coded audio signal having a predetermined number of sub-bands. A memory stores predetermined samples. A memory controller controls read and write operations of the memory. An adder adds the signal read out of the memory to a new window signal produced on the sub-band coded audio signal to synthesize a digital audio signal. A buffer memory stores and outputs the synthesized digital audio signal and an interpolation signal of the digital audio signal. During normal synthesis, the memory-controller cyclically reads the samples stored in the memory beginning from an address shifted by a predetermined number of samples every time a new cycle of reading is started. The memory-controller writes a result of the addition by the adder back into the memory, thereby producing cumulatively added samples of the window signals. The output circuit outputs, from among the cumulatively added samples, a predetermined number of samples which have been subjected to a predetermined number of cumulative additions, the sample being outputted every time the addition is performed. During interpolation, the memory-controller prevents the result of the addition from being written into the memory, and repeatedly reads the cumulatively added samples from the memory. The output circuit outputs the cumulatively added samples read from the memory as the interpolation signal of the digital audio signal.