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## Signals and systems

A physical process that shows the same state after certain time epochs is called an oscillation. We can distinguish oscillations with identical and different sections, called periodic and aperiodic oscillations, respectively.

Both kinds of vibration are signals that may be observed in linear as well as in non-linear systems. A linear system is understood as a system with only linear electrical and mechanical components. In such a system the ratio between the input and output amplitude is always constant, in contrast to non-linear systems. The superposition principle that holds for linear systems says that an oscillation occuring in a linear system is not influenced by cooccurring oscillations. Most important, this includes also the frequency  concerned. This principle is especially important for a speech recording chain, where many oscillations with different frequencies always exist at the same instant.

A simple but more mathematical interpretation of superposition may be formulated as follows. The superposition principle requires that the response of a system to a weighted sum of signals is equal to the corresponding weighted sum of outputs of the system to each of the individual input signals. This includes the additive and multiplicative (scaling) properties of linear systems. In other words, a relaxed, linear system with zero input produces a zero output. If a system produces a non-zero output with a zero input, the system may be either non-relaxed or non-linear. If a relaxed system does not satisfy the superposition principle, it is called non-linear.

Systems can also be classified into the two broad categories of time-variant and time-invariant systems. A system is called time-invariant if its input-output characteristics do not change with time. On the other hand, if the outputs to the same input differ for the same system at different times, the system is called time-variant. A common class of systems is that of Linear and Time-Invariant (LTI) systems.

An important property that must be considered in any practical application of a system is stability . A system is defined to be bounded-input-bounded output-stable, if and only if every bounded input produces a bounded output. An LTI-system  is stable, if the output response to an input impulse is absolutely summable. Unstable systems usually exhibit erratic and extreme behaviour and cause ``overflow'' in any practical implementation.

The devices of a recording chain are not LTI-systems  in the ideal sense, and consequently we have to reckon with non-linearities. The oscillations at certain frequencies come under mutual influence, and new frequencies are produced. If this process was intended, it is called modulation or demodulation. Otherwise, we call it a distortion.

In the following subsections we consider signal behaviour during transmission through linear and non-linear systems. We start with simple sinusoidal oscillations.

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