An electronic system with audio capability may generate an acoustic signal to which a human may listen. For example, a television may generate an acoustic signal that includes the voices of people in a scene, and that includes other sounds (e.g., a car horn, a slamming door) associated with the scene. And an MP3 player may generate an acoustic signal that includes instrumentals and vocals. An acoustic signal typically includes frequencies that are within a range of approximately 10 Hz-25 KHz, which is considered to be the approximate range of frequencies that a normal human ear is able to perceive.
Such an electronic system typically generates an acoustic signal from an analog electronic audio signal having the same frequency content as the acoustic signal, and having an amplitude proportional to the amplitude of the acoustic signal (typically the system amplifies the audio signal to generate the acoustic signal).
Although direct sources (e.g., a microphone) of analog audio signals exist, in many applications an analog audio signal is stored for subsequent playback. For example, a production company may record a television show in a studio, and store the resulting audio and video signals on magnetic tape or on a digital versatile Disk (DVD) for subsequent playback; and, a band may record music in a studio, and store the resulting audio signal in an electronic file or on a CD for subsequent playback.
Analog audio signals, are typically stored in digital form, i.e., as a file of digital values. Storing an analog audio signal in digital form may provide advantages such as allowing easy copying of the digital file without degradation of the played-back acoustic signal, allowing electronic transfer of the digital file (e.g., over the internet), reducing the amount of noise added to the stored analog audio signal during the storing process, and allowing use of a higher-density storage medium (e.g., a CD vs. a vinyl LP).
The overwhelming majority of today's electronic systems with the ability to receive and store an analog audio signal do so by sampling the amplitude of the analog audio signal and converting the samples into respective digital values.
FIG. 1A is a timing diagram of an original analog audio signal 10 (here a sinusoid, which represents an acoustic pure tone) having a frequency F and period T=1/F.
FIG. 1B is a timing diagram of a sampling clock 12 having a frequency Fs=4F and a period
      T    s    =      T    4  
Referring to FIGS. 1A and 1B, at each rising edge 14 of the clock 12, a circuit (not shown in FIGS. 1A and 1B) samples the instantaneous amplitude of the analog audio signal 10, and holds this sampled amplitude until the next rising edge of the clock. For example, at a time t1, the circuit samples and holds the amplitude of the signal 10 at a point 16.
Next, an analog-to-digital converter (ADC) (not shown in FIGS. 1A-1B) converts the sampled amplitude into a corresponding digital value, for example a twenty-four bit binary number. This digital value represents the digitized amplitude of the analog audio signal 10 at the point 16.
Then, an electronic memory or other storage device (not shown in FIGS. 1A-1B) stores this digital value on a digital storage medium as part of a digital audio file.
The sample-and-hold circuit, the ADC, and the memory (none shown in FIGS. 1A-1B) continue this procedure until the entire signal 10 is digitized, and the resulting digital values are stored on the storage medium as part of the digital audio file.
An audio playback system may then reconstitute the original audio signal 10 and playback a resulting acoustic signal by streaming the stored digital values to a digital-to-analog converter (DAC) (not shown in FIGS. 1A-1B), which generates the reconstituted audio signal, and by then providing the reconstituted audio signal to a transducer (e.g., a speaker), which converts the reconstituted audio signal into the resulting acoustic signal.
Unfortunately, the above-described amplitude sampling technique may introduce distortion and other undesirable artifacts into the reconstituted audio signal, and thus into the resulting acoustic signal.
For example, still referring to FIGS. 1A-1B, jitter in the sampling clock 12 may introduce distortion into the reconstituted audio signal, and thus may introduce distortion into the resulting acoustic signal. Because jitter is a form of noise, and is thus random and unpredictable, the durations between the sampling edges of the sampling clock 12 are likely to be different than the durations between the corresponding edges of the DAC clock (not shown in FIGS. 1A-1B), which ideally has the same frequency and phase (relative to the analog audio signal 10) as the sample clock; and jitter in the DAC clock may exacerbate this problem. Therefore, the DAC may generate the points 16 of the reconstituted audio signal at different positions relative to the original audio signal 10. Consequently, the amplitude of the reconstituted audio signal may be distorted relative to the amplitude of the original audio signal 10, and this distortion may cause noticeable distortion, and thus a noticeable loss of fidelity, in the resulting acoustic signal.
Furthermore, according to Nyquist's theorem, the frequency Fs of the sampling clock 12 must be at least twice the highest frequency in the original audio signal 10. If the audio signal 10 contains frequencies that are higher than Fs/2, a phenomenon called aliasing may occur, and aliasing may introduce aliasing distortion into the reconstituted audio signal, and thus into the resulting acoustic signal.
Many of today's audio systems that digitize analog audio signals according to the above-described amplitude-sampling technique use a sampling clock having a frequency Fs of 44.1 KHz.
To limit aliasing, before an audio system samples an analog audio signal it typically filters the audio signal to remove all frequencies above 22.05 KHz (44.1 KHz/2). Therefore, this filtering preserves all but the highest frequencies in the audio-frequency range of approximately 10 Hz-25 KHz.
But even though this filtering may limit the introduction of aliasing distortion into the reconstituted audio signal and into the resulting acoustic signal, this filtering may introduce other types of distortion into these signals.
For example, this filtering may introduce Tartani distortion into the reconstituted audio signal and into the resulting acoustic signal.
It is theorized that the human ear processes audio signals in a non-linear manner. For example, if frequencies f1 and f2 occur simultaneously in an acoustic signal, then the human ear may perceive not only the frequencies f1 and f2, but may also perceive the sum (f1+f2) and difference (|f2−f1|) frequencies. These sum and difference frequencies are often called Tartani tones, which are named after their discoverer. The most noticeable of the Tartani tones is often the difference frequency |f2−f1|. Because, in the above example, the anti-aliasing filter cuts out all frequencies above 22.05 KHz, some of the natural Tartani frequencies that a human ear may have perceived in the original acoustic signal may not be perceivable in the resulting acoustic signal generated from the reconstituted audio signal. For example, suppose that the original acoustic signal is music from a live band, and the band's drummer crashes a symbol to produce simultaneous frequencies at 10 KHz, 20 KHz, and 25 KHz. Because the anti-aliasing filter cuts out the 25 kHz frequency from the original analog audio signal prior to its being sampled, this 25 KHz frequency is not present in the reconstituted audio signal, and, therefore, is not present in the resulting acoustic signal. Consequently, the Tartani frequencies at 15 kHz (25 KHz-10 KHz) and at 5 kHz (25 KHz-20 KHz), which were perceivable in the original acoustic signal, are not perceivable in the resulting acoustic signal. Therefore the absence of these Tartani frequencies causes Tartani distortion in the resulting acoustic signal.
One potential technique for reducing or eliminating Tartani distortion in the resulting acoustic signal is to use a sampling frequency that is greater than 44.1 KHz.
But increasing the sampling frequency may increase the cost and complexity of an audio system, and may also be impractical for other reasons. For example, increasing the sampling frequency may increase the complexity and cost of the sample-and-hold circuit and ADC. Furthermore, many of today's audio players, including CD players, DVD players, and MP3 players, are designed for digital audio files generated using a 44.1 KHz sampling clock. Consequently, increasing the industry-standard sampling frequency of 44.1 KHz may render current audio players obsolete in favor of new audio players designed for the increased sampling frequency.