Muffler Appendix

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Mathematically, a signal can be represented as acoustic pressure as a function of time. This is illustrated in the following diagram.

Usually, when a sample is digitally synthesized, the continuous waveform is broken up into segments called samples. Each sample holds one piece of data, which is the amplitude of the signal at a specific time. As one can clearly see, a digitally synthesized signal is the result of a discrete concatenation of these samples.

A digitally synthesized signal has several characteristics: sampling rate, number of bits, and number of channels.

The sampling rate is the number of times that the amplitude level is recorded. This can be interpreted as the number of samples generated per second. When the sampling rate increases, the signal clarity increases, which means that the amount of data stored per second also increases. Most digital recording schemes use several standard sampling rates in order allow a tradeoff between data storage and signal detail. These schemes will be discussed later in this paper.

The number of bits determines how accurately the amplitude of a sample is recorded. A piano, for instance, uses a one-bit coding schema: it can only play sounds differentiated by approximately 45 Hertz. On the other hand a violin has the ability (due to its string interface) to generate sounds that are differentiated with a frequency below 45 hertz. Likewise, a signal digitization configuration that uses a sixteen-bit decoding schema (216 different levels of amplitude) will naturally have more precision than an eight-bit decoding schema (28 different levels of amplitude). Of course, the more bit precision is used, the memory needed per sample increases also.

The number of channels determines how many sound tracks are supported by the signal. For instance, a signal with one channel (known as mono / monoaural) contains only one sound track. A signal with two channels (known as stereo / stereo audio) has information for two sound tracks. Even though multiple channels can provide three-dimensional sound and is imperative in modeling life-like sound, there is a high memory / data cost in its implementation. For instance, a two channel signal requires twice the storage / memory of a one channel signal.