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If the ratio of the two sample rates is (or can be approximated by) [A] [4] a fixed rational number L/M: generate an intermediate signal by inserting L − 1 zeros between each of the original samples. Low-pass filter this signal at half of the lower of the two rates. Select every M-th sample from the filtered output, to obtain the result. [5]
The selection of the sample rate was based primarily on the need to reproduce the audible frequency range of 20–20,000 Hz (20 kHz). The Nyquist–Shannon sampling theorem states that a sampling rate of more than twice the maximum frequency of the signal to be recorded is needed, resulting in a required rate of greater than 40 kHz.
The sampling frequency or sampling rate, , is the average number of samples obtained in one second, thus = /, with the unit samples per second, sometimes referred to as hertz, for example 48 kHz is 48,000 samples per second.
The DVD format uses the 48 kHz sampling rate, and its doublings. In digital audio, 48,000 Hz (also represented as 48 kHz or DVD Quality) is a common sampling rate. It has become the standard for professional audio and video. 48 kHz is evenly divisible by 24, a common frame rate for media, such as film, unlike 44.1 kHz. [i]
The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing.
High-resolution audio (high-definition audio or HD audio) is a term for audio files with greater than 44.1 kHz sample rate or higher than 16-bit audio bit depth. It commonly refers to 96 or 192 kHz sample rates. However, 44.1 kHz/24-bit, 48 kHz/24-bit and 88.2 kHz/24-bit recordings also exist that are labeled HD audio.
For instance, to implement a 24-bit converter, it is sufficient to use a 20-bit converter that can run at 256 times the target sampling rate. Combining 256 consecutive 20-bit samples can increase the SNR by a factor of 16, effectively adding 4 bits to the resolution and producing a single sample with 24-bit resolution. [3] [a]
Private international cartels (those with participants from two or more nations) had an average price increase of 28 percent, whereas domestic cartels averaged 18 percent. Less than 10 percent of all cartels in the sample failed to raise market prices.