Bit Depth

In digital samples amplitude is represented as “bit depth.” Bit depth determines both the number of steps, or levels, that are possible in a sample and how loud a signal the system can tolerate. CD-quality sound uses 16 bits. We can calculate the number of steps by raising the number two to the 16th power. 2 ^ 16 = 65,536 steps. The number of steps is divided into 32,767 positive (plus 0) and 32,768 negative steps, representing the crests and troughs in a sample of music. Each time we take a sample of a piece of sound the actual amplitude must be rounded to the nearest available level, introducing something called a “quantization error.” Simply put, this means that a small amount of noise is produced each time a digital recording is sampled.

The next section will cover the signal-to-noise ratio, which is the amount of inherent noise versus the system’s capacity for the desired signal. In theory the overall capacity of a digital system is approximately six decibels per bit. For a 16-bit CD-quality a system can tolerate 96 dB. (Source: Cornell University Music Department. http://digital.music.cornell.edu/cemc/book/export/html/1594).

Illustration of bit depth

Sampling Rate

Sampling rates are measured in hertz (Hz) or cycles per second. This value represents the number of samples captured in order to represent the waveform. The more samples you take per second, the higher the sound quality. The human ear can hear sounds that fall approximately between 20 Hz and 20,000 Hz.

Capturing a sound at a particular frequency requires a sampling rate of at least twice that frequency. This frequency is known as the Nyquist frequency. If you want to capture sound within the range of human hearing, the sampling rate has to be at least 40,000 Hz. Capturing sound at higher rates than this is known as over-sampling. Aliasing occurs when a signal is sampled at sampled at less than twice the highest frequency present in the A sampling rate of 44,100 Hz is used for audio CDs. The most common sampling rates for audio are: 8 kHz, 16 kHz, 22.05 kHz, 22.25 kHz, 44.1 kHz, 48 kHz, 96 kHz, and 192 kHz. (Audacity manual and Wake Forest University).

Aliasing

Waveform with high and low sample rates