Category: 1. Introduction

Although equipment for analyzing noise and vibration signals with constant frequency bandwidth filters and constant percentage bandwidth (CPB) filters are still available, these instruments have largely been replaced by Fast Fourier Transform (FFT) Digital Fourier analyzers. These types of analyzers give similar results in a fraction of the time and at a lower cost. These Fourier analyzers are manufactured…

Sound and vibration signals can be combined, but they can also be broken down into frequency components as shown by Fourier over 200 years ago. The ear seems to work as a frequency analyzer. We also can make instruments to analyze sound signals into frequency components. In order to determine experimentally the contribution of the overall…

In the case of nonperiodic signals (see Section 1.3.2), a quantity called the energy density function or equivalently the energy spectral density, S(f), is defined: (1.12) The energy spectral density S(f) is the “energy” of the sound or vibration signal in a bandwidth of 1 Hz. Note that S(ω) = 2πS(f) where S(ω) is the “energy” in a 1 rad/s bandwidth. We use the…

In the case of the pure tone a useful quantity to determine is the mean square value, i.e. the time average of the signal squared 〈x2(t)〉t [8] (1.7) where 〈〉t denotes a time average. For the pure tone in Figure 1.2a then we obtain (1.8) where A is the signal amplitude. The root mean square value is given by the…

So far we have discussed periodic and nonperiodic signals. In many practical cases the sound or vibration signal is not deterministic (i.e. it cannot be predicted) and it is random in time (see Figure 1.5). For a random signal, x(t), mathematical descriptions become difficult since we have to use statistical theory [1, 7, 9]. Theoretically, for random signals the…

Equation (1.1) is known as a Fourier series and can only be applied to periodic signals. Very often a sound signal is not a pure or a complex tone but is impulsive in time. Such a signal might be caused in practice by an impact, explosion, sonic boom, or the damped vibration of a mass‐spring system…

Sometimes in acoustics and vibration we encounter signals which are pure tones (or very nearly so), e.g. the 120 Hz hum from an electric motor. In the case of a pure tone, the time history of the signal is simple harmonic and could be represented by the waveform x(t) = A sin (2πf1 t) in Figure 1.2a. The pure tone can…

In noise and vibration control, signal analysis means determining from a measurement or a set of measurements certain descriptive characteristics of the environment that will help in identifying the sources of the noise and vibration. Frequency analysis is probably the most widely used method for studying noise and vibration problems. The frequency content of a…

Nonstationary signals are divided into transient and continuous signals. Transient signals are signals which start and end at zero level and last a finite and relatively short amount of time. They are characterized by a certain amount of “energy” they contain in the same way that continuous signals are characterized by a “power” value. Examples of transient signals are…

Stationary signals can be divided into deterministic and random signals. Stationary deterministic signals can be described by a mathematical function. They are made of a combination of sinusoidal signals (pure tones) with different amplitudes and frequencies. The spectrum of a stationary deterministic signal is characterized by content (power) at discrete frequencies (a line spectrum). The measured displacement signal of…