The digital recorder deals with the electrical signal it is presented in an entirely different manner. The digital recording process involves the conversion of the signal to a string of discrete numbers, and then the storage and retrieval of those numbers.
The conversion to numbers happens in an analog-to-digital converter (ADC). There are other separate components that perform other tasks prior to the ADC in a digital system (such as a dither generator, anti-aliasing filter, sample and hold circuits, etc.), but for the sake and intended scope of this discussion we will include them all in the ADC process (Wilkinson 18-20).
The rate at which the ADC takes measurements of the instantaneous voltage or amplitude of the signal is the sampling rate. The sampling rate of CD sound is 44.1 kilohertz, meaning 44,100 samples are taken every second. As shown below, increasing the sampling rate increases our horizontal grid resolution, allowing for the plotting of more dots along that axis. More dots on the grid allow for a smoother, more accurate storage and reproduction of the sound. When the digital-to-analog converter (DAC) fills in the lines between the points on playback, the resultant wave gets closer to the original wave as the sampling rate increases (Wilkinson 20-22). Refer to Figures 3-6.
Figure 3: A Low Sampling Rate, With Each Sample Represented by a Black Splotch - Movement to the Right on the Horizontal Axis Represents the Passage of Time
Figure 4: When the Playback Converters Connect Lines Between These Dots, the Wave is Very Rough and Inaccurate
Figure 5: A Higher Sampling Rate, Represented by More Lines Crossing the Horizontal Axis
Figure 6: Connecting the Dots Here Results in a Truer RepresentationThe detail of each sample is represented by resolution, bit depth, or word length. The CD uses 16 bits to represent each sample. The binary arithmetic details are boring and unnecessary, so suffice to say 16 bits allow for 65,536 steps between the lowest and highest amplitudes. This is significant in understanding digital systems. The incoming voltage is not tied to the grid that will be used for digital representation, it has an infinite number of places it could be between any two consecutive vertical steps. Thus the chance that the instantaneous voltage of any sample will exactly match one of our necessary steps is almost zero. The actual measurement value is rounded to the nearest binary number (a sting of zeroes and ones that represent a vertical step, stopping point, or gridline) in a process called quantization. The difference between the actual amplitude and the quantization value is called quantization error, which can lead to audible noise, especially in low-level signals. As bit depth increases, the vertical resolution of our grid increases. As when increasing the sampling rate, this produces a smoother and truer representation, which will benefit the quality of playback. It also decreases quantization error - the distances that need to be rounded to are closer to the actual measurement (Wilkinson 22-25). Refer to Figures 7-10.
Figure 7: A Low Bit Depth, Represented by the Vertical Axis, Results in Quantization Values in Red to Vary Greatly From the Actual Values in Black
Figure 8: The Resultant Wave in Playback is Drawn From the Red Quantization Values - Very Inaccurate
Figure 9: A Higher Bit Depth, Represented by More Stopping Points Along the Vertical Axis, Results in Quantization Values in Red to be Very Close to the Actual Values in Black
Figure 10: When Looking at Just the Dots, the Difference is MarginalSampling frequency and bit depth do correspond to the theoretical limits of frequency response and dynamic range, respectively, but represent much more. The Nyquist frequency is the highest audio frequency that a digital system can represent, and is exactly half the sampling frequency. This explains the initial choosing of 44.1 kHz for a sampling rate - its Nyquist frequency sits at 22.05 kHz, above the upper limits of human hearing. Some people will argue that sampling rates above 44.1 kHz are therefore unnecessary. They might also use the same logic to brand resolutions above 24 bits unnecessary also, as the dynamic ranges they represent are beyond those of any microphone / mixer / etc. But increasing either is always a good thing, as it allows for the plotting of a more detailed, accurate wave representation. Many engineers have weighed in on the superiority of audio quality in high sampling, high resolution systems, and that is the crux of the matter: the final sound quality.
The most common compensation for digital sound is called dithering. This is a process of adding a small amount of noise to the input signal before it is sampled. This noise randomizes the quantization error, reducing its audible effect. Dithering is also used when reducing the resolution of a recording, as when a 24-bit recording must be prepared for a 16-bit CD. In this case it is often called 'dithering down' (Wilkinson 25).
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