Digital Sound & Music: Concepts, Applications, & Science, Chapter 5, last updated 6/25/2013
Figure 5.4 Graph of sine function modeling a 440 Hz sound wave
Figure 5.4 shows eight samples being taken for each cycle of the sound wave. The
samples are represented as circles along the waveform. The sound wave has a frequency of 440
cycles/s (440 Hz), and the sampling rate has a frequency of 3520 samples/s (3520 Hz). The
samples are stored as binary numbers. From these stored values, the amplitude of the digitized
sound can be recreated and turned into analog voltage changes by the DAC.
The quantity of these stored values that exists within a given amount of time, as defined by
the sampling rate, is important to capturing and recreating the frequency content of the audio
signal. The higher the frequency content of the audio signal, the more samples per second
(higher sampling rate) are needed to accurately represent it in the digital domain. Consider what
would happen if only one sample was taken for every one-and-a-quarter cycles of the sound
wave, as pictured in Figure 5.5. This would not be enough information for the DAC to correctly
reconstruct the sound wave. Some cycles have been “jumped over” by the sampling process. In
the figure, the higher-frequency wave is the original analog 440 Hz wave.
Figure 5.5 440 Hz wave undersampled
When the sampling rate is too low, the reconstructed sound wave appears to be lower-
frequency than the original sound (or have an incorrect frequency component, in the case of a
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