4.5 Selecting a sampling rate

Problem

Read this section if you do not know how to determine a sampling rate in entering acoustic signals from a device.

Solution

In the absence of particular indications, 16kHz is a sufficient sampling rate. If there are particular indications, use the lowest sampling rate within the range at which alias does not occur. The frequency that is a half the sampling rate is called the Nyquist frequency. Alias occurs in signals with frequency components greater than the Nyquist frequency. Therefore, to prevent alias in input signals, it is preferable to use as high a sampling rate as possible. At the highest sampling rate, alias is infrequent. When the sampling rate is increased, however, the amount of data to be processed increases, increasing calculation costs. Therefore, when setting a sampling rate, it is better not to increase it by more than the amount necessary.

Discussion

Speech energy reaches over 10kHz in bandwidth, with much of the energy present as low frequency components. Therefore, consideration of low frequency bands is often sufficient for most purposes. For example, for telephones, sampling ranges from around 500 Hz to 3,500 Hz , making possible the transmission of interpretable audio signals with bandwidths of up to around 5kHz [1] . For 16kHz sampling, frequency components $\leq$ 8kHz can be sampled without alias, making it useful for speech recognition.

[1] Acoustic analysis of speech, by Ray D Kent and Charles Read, translation supervised by Takayuki Arai and Tsutomu Sugawara, Kaibundo, 2004.