4.5 Selecting a sampling rate

Problem

Read this section to determine the sampling rate when entering acoustic signals from a device.

Solution

If there is no particular reason, it is sufficient to use the initial 16kHz sampling rate. If that is not the case, use the lowest sampling rate within a range that has no aliasing.

It is necessary to set a sampling rate with a consideration that no aliasing occurs. The frequency that is a half the sampling rate is called the Nyquist frequency. Signals with frequency that exceeds Nyquist frequency are aliased during sampling. Therefore, it is adviced to use the highest possible sampling rate to prevent aliasing in the input signals. The higher the sampling rate, the lower the possibility for aliasing to occur.

On the other hand, when high sampling rate is used, the amount of data to be processed increases, which also increases the calculation cost. Which means that the sampling rate should not be set more than what is 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 the transmission of interpretable audio signals with bandwidths of up to around 5kHz [1] possible. 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.