increase equivalent to n additional bits of resolution, a signal must be oversampled by For example, a 14-bit ADC can produce 16-bit 48 kHz audio if operated at 16× oversampling, or 768 kHz. Oversampled PCM, therefore, exchanges fewer bits per sample for more samples in order to obtain the same resolution. Dynamic range can also be enhanced with oversampling at signal reconstruction, absent oversampling at the source. Consider 16× oversampling at reconstruction. Each sample at reconstruction would be unique in that for each of the original sample points sixteen are inserted, all having been calculated by a digital reconstruction filter. The mechanism of increased effective bit depth is as previously discussed, that is, quantization noise power has not been reduced, but the noise spectrum has been spread over 16× the audio bandwidth. Historical note—The compact disc standard was developed by a collaboration between Sony and Philips. The first Sony consumer unit featured a 16-bit DAC; the first Philips units dual 14-bit DACs. This caused confusion in the marketplace and even in professional circles, because 14-bit PCM allows for 84 dB SNR, 12 dB less than 16-bit PCM. Philips had implemented 4× oversampling with first order noise shaping which theoretically realized the full 96 dB dynamic range of the CD format. In practice the Philips CD100 was rated at 90 dB SNR in the audio band of 20 Hz–20 kHz, the same as Sony's CDP-101. Noise shaping Oversampling a signal results in equal quantization noise per unit of bandwidth at all frequencies and a dynamic range that improves with only the square root of the oversampling ratio. Noise shaping is a technique that adds additional noise at higher frequencies which cancels out some error at lower frequencies, resulting in a larger increase in dynamic range when oversampling. For nth-order noise shaping, the dynamic range of an oversampled signal is improved by an additional 6n dB relative to oversampling without noise shaping. For example, for a 20 kHz analog audio sampled at 4× oversampling with second-order noise shaping, the dynamic range is increased by 30 dB. Therefore, a 16-bit signal sampled at 176 kHz would have a bit depth equal to a 21-bit signal sampled at 44.1 kHz without noise shaping. Noise shaping is commonly implemented with delta-sigma modulation. Using delta-sigma modulation, Direct Stream Digital achieves a theoretical 120 dB SNR at audio frequencies using 1-bit audio with 64× oversampling. Applications Bit