Vibrations Signatures Standards
Measurement system and Digital Signal: A measurement system is shown in Figure 1(a).
Necessary data are detected from the vibrating structure by sensors. In a rotating machine, rotor displacements in two directions form a right angle and a rotating speed are detected as voltage variations.
The output signal x ( t ) from the sensor is an analog signal that is continuous with time. But the signal is discretised when it is acquired by computer through an interface. This digital signal is a series of discrete data {xn} obtained by measuring (called sampling) an analog signal instantly at every time interval Δ t and is given as xn = x(n Δt) where n is an integer. This interval Δt is called a sampling interval. A digital signal is descretised in both time and magnitude. Discretization in magnitude is called quantization, and the magnitude is represented by binary numbers (unit: bits). Digital data in a personal computer are processed into various forms using software programs. In this operation, two representative processing are performed. One is signal extraction , where unnecessary signal components are abandoned in the acquired data, and the other is data transformation , where the data are converted to a convenient form.
Problems in Signal Processing : When an analog signal x(t) is changed into a sequence of digital data {xn} ( n = 0, 1, 2, …, N ) a virtual (or imaginary) wave is obtained if a fast signal is sampled slowly. For example, when a signal illustrated by the full line is sampled as shown in Figure 2, a virtual signal wave illustrated by the dashed line appears, although it is not contained in the original signal.
This phenomenon is called aliasing. It is obvious that we must sample with a smaller sampling interval as the signal frequency increases. We can determine whether or not we have this aliasing by following the sampling theorem. It says: when a signal is composed of the components whose frequencies are all smaller than ƒc we must sample it with a frequencies higher than 2ƒc or the sake of not losing the original signal's information.
The frequency 2ƒc is called Nyquist frequency. For example, if a sine wave with period T is sampled whenever x(t) = 0, that is, with sampling interval T/2, we have xn = 0. Therefore, two samplings in a period are clearly insufficient. However, this theorem teaches us that digital data with more than two points during one period can express the original signal correctly.
For example, if we sample the signal having components of 1, 2 and 6 kHz with a sampling frequency of 10 kHz, we have an imaginary spectrum of 4 kHz, which does not exist practically. But, if we sample it with a frequency of more than 12 kHz (2 × 6 kHz) , such an alising problem does not occur. In practical measurements, we do not commonly determine the sampling frequency by trial measurement. Instead, we use a low-pass filter to eliminate the unnecessary high-frequency components in the signal and sample with the frequency higher than twice the cut-off frequency. By such a procedure, we can prevent aliasing.
Services: - Vibrations Signatures Standards Homework | Vibrations Signatures Standards Homework Help | Vibrations Signatures Standards Homework Help Services | Live Vibrations Signatures Standards Homework Help | Vibrations Signatures Standards Homework Tutors | Online Vibrations Signatures Standards Homework Help | Vibrations Signatures Standards Tutors | Online Vibrations Signatures Standards Tutors | Vibrations Signatures Standards Homework Services | Vibrations Signatures Standards