Category: (((—Acoustics Engineering—))))
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Stationary Signals
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…
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Types of Noise and Vibration Signals
Depending on their time histories, noise and vibration signals can basically be divided into stationary and nonstationary. Examples of the various types of signals in the time and frequency domains are shown in Figure 1.1 [10].
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Introduction
Real‐world problems in the control of noise and vibration in aircraft, appliances, buildings, industry, and vehicles require the measurement of particular environmental parameters such as sound pressure, force, acceleration, velocity, displacement, etc. This process is often performed by using acoustical and vibration transducers. Vibration and acoustical sensors are transducers which convert a measured physical property…
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Fast Fourier Transform Analysis
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bandwidth filters and constant percentage bandwidth (CPB) filters are still available, these instruments have largely been replaced by Fast Fourier Transform (FFT) Digital Fourier analyzers.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…
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Frequency Analysis Using Filters
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…
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Energy and Power Spectral Densities
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…
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Mean Square Values
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…
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Random Noise
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…
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Nonperiodic Functions and the Fourier Spectrum
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…
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Fourier Series
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…