10.3 Signal Types

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Signals can be classified into different types

depending on their characteristics. Note that the

signal itself is a time function, but its frequencydomain

representation can bring up some of its

salient features. Signals particularly important to us

here are the excitations and responses of vibrating

systems. These can be divided into two broad

classes: deterministic signals and random signals

depending on whether we are dealing with

deterministic vibrations or random vibrations.

Consider a damped cantilever beam that is

subjected to a sinusoidal base excitation of

frequency v and amplitude u0 in the lateral

direction (Figure 10.8). In the steady state, the tip

of the beam will also oscillate at the same frequency,

but with a different amplitude y0 and, furthermore, there will be a phase shift by an angle f: For a given

frequency and known beam properties, the quantities y0 and f can be completely determined. Under these

conditions the tip response of the cantilever is a deterministic signal in the sense that when the experiment

is repeated, the same response is obtained. Furthermore, the response can be expressed as a mathematical

relationship in terms of parameters whose values are determined with 100% certainty, and probabilities are

not associated with these parameters (such parameters are termed deterministic parameters). Random

signals are nondeterministic (or stochastic) signals. Their mathematical representation requires probability

considerations. Furthermore, if the process were to be repeated there would always be some uncertainty as

to whether an identical response signal could be obtained again.

Deterministic signals can be classified as periodic, quasi-periodic, and transient. Periodic signals repeat

exactly at equal time periods. The frequency (Fourier) spectrum of a periodic signal constitutes a series of

equally spaced impulses. Furthermore, a periodic signal will have a Fourier series representation. This

implies that a periodic signal can be expressed as the sum of sinusoidal components whose frequency

ratios are rational numbers (not necessarily integers). Quasi-periodic (or almost periodic) signals also

have discrete Fourier spectra, but the spectral lines are not equally spaced. Typically, a quasi-periodic

signal can be generated by combining two or more sinusoidal components, provided that at least two of

the components have as their frequency ratio an irrational number. Transient signals have continuous

Fourier spectra. These types of signals cannot be expressed as a sum of sinusoidal components (or a

Fourier series). All signals that are not periodic or quasi-periodic can be classified as transient. Most

often, highly damped (overdamped) signals with exponentially decaying characteristics are termed

transient, even though various other forms of signals such as exponentially increasing (unstable)

responses, sinusoidal decays (underdamped responses), and sinesweeps (sinewaves with variable

frequency) also fall into this category. Table 10.1 gives examples for these three types of deterministic

signals. The corresponding amplitude spectra are sketched in Figure 10.9. A general classification of

signals, with some examples is given in Box 10.1.

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