Audio Sample Rate Converter

Sample rate sets the temporal resolution of a digital audio stream, and the Nyquist frequency - exactly half the sample rate - is the highest frequency the stream can represent without ambiguity. At 44.1 kHz that limit is 22.05 kHz, at 48 kHz it is 24 kHz, and at 96 kHz it is 48 kHz. Converting between rates changes the sample count in proportion to the ratio of target to source, and for uncompressed PCM the file size follows directly: sample rate times bit depth times channels times duration, divided by 8 for bytes. A stereo 16-bit minute occupies about 10.1 MB at 44.1 kHz and about 22 MB at 96 kHz. The direction of conversion determines the risk. Downsampling requires a low-pass anti-aliasing filter applied before decimation, because any energy above the new Nyquist frequency folds back into the audible band as inharmonic aliasing distortion; going from 96 kHz to 48 kHz means everything above 24 kHz must be removed first. Upsampling has the opposite problem: interpolation invents intermediate samples but adds no frequency content that was not captured, so the extended Nyquist range above the original limit is empty. The awkward case is 44.1 kHz to 48 kHz, a ratio of 147 to 160 rather than a clean integer, which forces the converter into a long polyphase or sinc-based structure. Quality tracks the length of the interpolation kernel, and that length is also latency - a 64-tap sinc filter needs about 32 samples of lookahead, roughly 0.67 ms at 48 kHz.

The theoretical foundation was laid by Harry Nyquist at Bell Labs in 1928, who determined the signalling rate a channel of given bandwidth can carry, and by Claude Shannon, whose 1948 and 1949 papers stated the sampling theorem in the form used today. Vladimir Kotelnikov had published an equivalent result in the Soviet Union in 1933, and the theorem is sometimes named for all three. Digital audio recording became practical in the 1970s once converters and storage were fast enough, with early professional systems from Soundstream and 3M operating at rates near 50 kHz. The specific rates in use are artifacts of the storage media of the period. The 44.1 kHz figure comes from recording digital audio onto videotape using a PCM adaptor: it is the number of samples that fit into the active video lines of both NTSC and PAL frames, 245 lines times 3 samples times 60 fields per second for NTSC. Sony and Philips carried it into the Red Book Compact Disc specification published in 1980, and it remains the music distribution standard. The 48 kHz rate was chosen for professional and broadcast use because it divides cleanly against video frame rates, and it was carried into DAT, DVD, and digital television. Higher rates of 88.2, 96, and 192 kHz followed with DVD-Audio and later high-resolution download formats, and the AES has published standards and information documents covering sample rate conversion practice for interchange between these families.