1.14 Cd to dat conversion

Example: cd to dat rate conversion

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