Sampling rate
When sound enters a digital hearing aid, it has to be converted into a sequence of numbers to render it processible.
The conversion of sound into numbers is done by measuring the sound pressure at certain intervals. A measurement of the sound pressure is called a sample, and the frequency with which the measurements are done is called the sampling rate or sampling frequency.
In a Widex hearing aid, samples of the sound pressure are taken 32,000 times per second – in other words, we have a sampling rate of 32,000 Hz.
Why the sampling rate is important
The sampling rate is important in terms of getting an accurate picture of a given change.
Imagine measuring the temperature over 24 hours to get an idea of how it changes. Normally it will be higher in the middle of the day than in the middle of the night. If the temperature is sampled once every hour, this change will be clearly visible from the measurements.
Even if only two measurements are performed, one in the day and one in the night, they will reveal that the temperature changes during the 24 hours.
One measurement per day, on the other hand, will indicate a constant temperature, even if it is repeated over a week.
Nyquist Sampling Theorem
This fact is described in the Nyquist Sampling Theorem, which is a fundamental signal processing theorem.
The Nyquist Sampling Theorem provides a prescription for the sampling interval required to accurately reconstruct the signal.
More specifically, the theorem states that a signal must be sampled twice as fast as the bandwidth of the signal in order to obtain an accurate representation of the signal; otherwise high-frequency components will be mistaken for lower-frequency components in the analysis.
Original:
The original wave shows a continuous variation in level with respect to time
Sampled at low frequency:
With more than two samples per period the original can be reproduced correctly. In this example the 4 samples per period allows the reproduction to follow the original curve.
Sampled at higher frequency:
With less than two samples per period the original will not be reproduced correctly. The example shows that with only one sample per period the reproduction will fail to follow the original curve. The result will be a signal of much lower frequency than the original. | 
