The invention discloses a finite impulse response (FIR) filter for processing a digital input signal to generate a digital output signal. The FIR filter has a tap amount N and a decimation ratio D. The FIR filter includes a first memory, a multiplier, and an accumulation module. For each input sample of the digital input signal, the first memory provides N/D corresponding tap coefficients from a plurality of tap coefficients in turn. The multiplier multiplies the input sample with the N/D corresponding tap coefficients in turn to generate N/D product values. The accumulation module adds the N/D product values to N/D previous accumulation values to generate N/D renewed accumulation values respectively. If one of the accumulation values has already accumulated N product values, the accumulation module outputs the accumulation value as an output sample of the digital output signal.