However, if the the same wave form  (F = 1/2 Fs) were (miraculously) encoded at 90 degrees "out of sync" with the occurence  of the sampling measurement, itself, then all excursion would occur only in between the samples, and the reconstructed wave form would be silence, as illustrated below.

     The odds that a "1/2 Fs" analog signal wave form will be 90 degrees out of sync with the sampling event is Fs : 1.  Therefore, to avoid the infrequent, but inevitable "lost" wave form, a higher value (i.e., more than 2x Nyquist) must be clocked in order for all desired frequencies to be reconstructed "without error" at all times.
     How close can a frequency be to 1/2 Fs without being plagued with the sampling interval pitfall?   This concern is rather academic, and, provided that the sampling frequency is at least 44.1k, the odd disappearance of a 1/2 Fs sound wave (22.05 kHz) would not be noticed, anyway, by most listeners.  In fact, the presence of a low pass filter that is necessary in the reconstruction of PCM audio into analog would lower the audible bandwidth of the 44.1 kHz Fs digital audio down to no more than about 20 kHz.

     Anti-aliasing filters are implemented at the analog to digital conversion, as well as at the digital to analog conversion, so that the echoes of the signal, which occur at multiples of the sampling frequency, will be silenced.  This requires some bandwidth above the highest needed frequency component of the encoded signal.  The more available bandwidth above the highest desired frequency (say, 20 kHz), the more gentle the slope possible for the anti-aliasing filter(s).  The more gentle their slope, the less phase distortion will affect the high frequency component of the reconstructed signal.  Therefore, a sampling frequency even much greater than 48 kHz, such as 88.2 kHz, or higher, may be selected, even though the encoded signals, in themselves, do not need the extra information stored with such high sampling frequencies in order to carry all the information it was presented at frequencies above which anybody can hear.  Also, according to Dan Lavry, precision in the encoding of the samples is compromised, especially at lower frequencies, when the sampling rate is doubled.

     Below is a picture of an analog signal wave form (green), and its digitization events (white).   The sampling frequency is more than 2F (roughly 2.7 F).

      At 44.1 kHz Fs, the image above would represent less than 1/6,300 second.
      Basically, the DAC's job is to "connect the dots," but don't take that metaphor literally.  The DAC's output signal is produced by summing together many electrical pulses, each centered at a particular sample, and also scaled by the amplitude of the sample.  Sync pulses may be rectangular, triangular, or truncation sync pulses (see Fourier transform).  An interpolated wave form is produced after these quick "look-ahead" calculations are made.  The analog output is continuous, even though the digital information represents discrete moments in time, with gaps in data for the moments in time unmeasured as immaterial to the perfect reconstruction of the original signal as are the omission of trisodium phosphate to the incoming clocked stream of bits.)

A Fourier transform sync pulse:

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Explanation of CD sampling rate (44.1 kHz Fs)

(from the page http://www.cs.columbia.edu/~hgs/audio/44.1.html,
edited by Henning Schulzrinne)
 

"Explanation of 44.1 kHz CD sampling rate

"The CD sampling rate has to be larger than about 40 kHz to fulfill the Nyquist criterion that requires sampling at twice the maximum analog frequency, which is about 20 kHz for audio. The sampling frequency is chosen somewhat higher than the Nyquist rate since practical filters needed to prevent aliasing have a finite slope.  Digital audio tapes (DATs) use a sampling rate of 48 kHz.  It has been claimed that their sampling rate differs from that of CDs to make digital copying from one to the other more difficult. 48 kHz is, in principle, a better rate since it is a multiple of the other standard sampling rates, namely 8 and 16 kHz for telephone-quality audio.  Sampling rate conversion is simplified if rates are integer multiples of each other.

"From John Watkinson, The Art of Digital Audio, 2nd edition, pg. 104:

     "In the early days of digital audio research, the necessary bandwidth of about 1 Mbps per audio channel was difficult to store. Disk drives had the bandwidth but not the capacity for long recording time, so attention turned to video recorders. These were adapted to store audio samples by creating a pseudo-video wave form which would convey binary as black and white levels. The sampling rate of such a system is constrained to relate simply to the field rate and field structure of the television standard used, so that an integer number of samples can be stored on each usable TV line in the field. Such a recording can be made on a monochrome recorder, and these recording are made in two standards, 525 lines at 60 Hz and 625 lines at 50 Hz.  Thus it is possible to find a frequency which is a common multiple of the two and is also suitable for use as a sampling rate.   [see Nyquist and A.T.H.]
     "The allowable sampling rates in a pseudo-video system can be deduced by multiplying the field rate by the number of active lines in a field (blanking lines cannot be used) and again by the number of samples in a line. By careful choice of parameters it is possible to use either 525/60 or 625/50 video with a sampling rate of 44.1KHz.
     "In 60 Hz video, there are 35 blanked lines, leaving 490 lines per frame or 245 lines per field, so the sampling rate is given by :
     "60 X 245 X 3 = 44.1 KHz .
     "In 50 Hz video, there are 37 lines of blanking, leaving 588 active lines per frame, or 294 per field, so the same sampling rate is given by
     "50 X 294 X3 = 44.1 Khz.
     "The sampling rate of 44.1 KHz came to be that of the Compact Disc. Even though CD has no video circuitry, the equipment used to make CD masters is video based and determines the sampling rate.

"(Reference provided by Kavitha Parthasarathy.)"
 

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