How It Works: Resolution

The value of each sampled point will be stored on a fixed-length variable. If this variable uses eight bits, this means it can hold values from 0 to 255 (2^8 = 256). If this variable uses 16 bits, this means it can hold values from 0 to 65,535 (2^16 = 65,536). And so on.

So, if you are using an 8-bit analog-to-digital converter, the lowest value will be zero and the highest value will be 255. If a 16-bit analog-to-digital converter is used, the lowest value will be zero and the highest value will be 65,535. See Figure 4.

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Figure 4: 8- and 16-bit resolutions comparison.

What the ADC does is to divide the “y” axis in “n” possible parts between the maximum and the minimum values of the original analog signal, and this “n” is given by the variable size. If the variable size is too small, what will happen is that two sampling points close to each other will have the same digital representation, thus not corresponding exactly to the original value found on the original analog signal, making the analog waveform available at the DAC output to not have the best quality.

Once again, the highest the variable size, the better the quality will be, but more storage space will be needed. Using a 16-bit variable will required twice the storage space if an 8-bit variable was used, but the quality will be far better.

One of the ways to know the necessary number of bits for an ADC is by calculating the desired noise level. Since the values sampled from the original analog signal will several times need to be “rounded” to the nearest possible digital equivalent, this provides what is called quantization noise. The tolerable noise level depends on the application. The phone system can have a higher noise level than an audio CD, for example, since we want to hear our CDs with the best possible quality.

The signal-to-noise ratio (SNR), which measures the noise level, can be easily calculated thru this formula, where n is the number of bits used on the ADC:

SNR = 6.02 x n + 1.76 dB

The higher the SNR, the better. An 8-bit ADC provides a SNR of 49.9 dB, while a 16-bit SNR provides a SNR of 98 dB (which is, by the way, a virtually no-noise value).

Audio CDs use 16-bit resolution, while the phone system uses 8-bit resolution. High-end and professional audio applications use 20- or even 24-bit resolution.

In summary, while the sampling rate give us the analog-to-digital “x” axis resolution, the variable size gives us the “y” axis resolution.

Knowing the sampling rate and the variable size (a.k.a. resolution) you can easily calculate the storage space (or the bandwidth, in the case of audio transmission) that will be necessary to store the data generated by the ADC.

The phone system, for example, uses an 8,000 Hz sampling rate and each sample is stored on an eight-bit variable. So the transmission rate of the analog-to-digital conversion is of 64,000 bits per second (8,000 x 8) or 64 Kbps (this is rounded, since 1 K = 1,024; thus 64 Kbps would be 65,536 bps and not 64,000 bps). If you whish to record a phone conversation, the space that it would require would be 8,000 bytes per second (64,000 / 8) or 480,000 bytes per minute (8,000 x 60), i.e. 468.75 KB per minute.

The CD uses a 44,100 Hz sampling rate and each sample is stored on a 16-bit variable. Also, the CD has two independent channels (left and right, what is played at one channel can be completely different from what is played at the other). So the transmission rate of the analog-to-digital conversion of the CD system is of 1,411,200 bps (44,100 x 16 x 2) or 1.41 Mbps (once again this is rounded, since 1 M = 1,048,576). The storage space that is necessary is of 176,400 bytes per second (1,411,200 / 8) or 10,584,000 bytes per minute (176,400 x 60), i.e. 10 MB per minute.

Since each CD can hold up to 74 minutes of music, this means that a CD can store 740 MB of music information (74 minutes x 10 MB per minute). On CD-ROM mode a CD can store less, 650 MB, because part of its storage space is used for error-correction code (ECC).

The “pure” data obtained from the analog-to-digital conversion is better known as PCM, Pulse Code Modulation. PCM is also referred as “uncompressed digital audio”. CDs use PCM audio, as we have been explained so far. DVDs, however, can use PCM audio as an option, but they can also use compressed audio – which is our next subject.