Digital audio signals stored on compact digital discs (CDs) are sampled at 44.1kHz 44.1 kHz , while those stored on digital audio tapes (DATs) are sampled at 48kHz 48 kHz . Conversion from CD to DAT requires an exchange rate of Q=4800044100=160147 Q 48000 44100 160 147 Assuming that the audio signal is bandlimited to 20kHz 20 kHz , we design our master lowpass filter with transition bands ∀k,k∈ℤ: 2k+2022.05π1602k+1-2022.05π160 k 2 k 20 22.05 160 2 k 1 20 22.05 160 k Keeping the passband and stopband ripple levels below -96dB -96 dB requires a filter with a length N≈10000 N 10000 , implying that the standard polyphase resampler will require about NM=1.5million N M 1.5 million multiplication per output, or 70billion 70 billion multiplications per second! If the equivalent polyphase implementation is used instead, we require only NL≈62 N L 62 multiplies per output, or 3million 3 million multiplications per second.