The Essential Guide to Digital Signal Processing by Richard G. Lyons D. Lee Fugal & D. Lee Fugal

Author:Richard G. Lyons,D. Lee Fugal & D. Lee Fugal
Language: eng
Format: epub
Publisher: Pearson Education Limited (US titles)
Published: 2014-04-08T16:00:00+00:00

Figure 5-20 Hypothetical analog music signal: (a) original music signal spectrum; (b) digital signal spectrum showing overlapped spectral replications; (c) contaminated spectrum of the analog playback signal from a CD.

Because the fs = 8 kHz sample rate is less than twice the highest-frequency spectral content of the analog signal (that is, less than 12 kHz), a spectral alias overlaps the original signal spectrum as shown by the cross-hatched area on the left side of Figure 5-20(b). In this scenario, we have violated the Nyquist sampling criterion, which results in a digital signal whose low-frequency spectrum is contaminated. As such, if we put that compact disc in a CD player to listen to the music, the audio signal we hear will have the spectrum shown in Figure 5-20(c). The digital signal’s overlapped spectral components cause the final analog audio playback signal to have an unpleasant underwater, or gurgling, sound.

Audio engineers who record music on CDs solve the overlapped spectrum problem described above by merely increasing the fs sample rate of the digital signal obtained from the original analog music signal. Because analog music signals can have frequencies almost as high as 20 kHz, as shown in Figure 5-21(a), the sample rate of the digital music signals recorded on music CDs must be greater than 40 kHz. For a variety of engineering reasons, the industry standard sample rate for music compact discs is 44.1 kHz as shown in Figure 5-21(b). In that figure, we see that the fs = 44.1 kHz sample rate results in no spectral overlap and the CD’s analog playback signal will be undistorted as shown in Figure 5-21(c).

Figure 5-21 Analog music signal: (a) original music signal spectrum; (b) digital signal spectrum showing no overlapped spectral replications; (c) spectrum of the analog playback signal from a CD.

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