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Similar to other
technical domains, numerical signal processing comprises two main
operations: analysis and synthesis. Analysis is the process of
decomposing a function (or other object) into components which are
simple and easy to understand and interpret.
Sinus wave
In
nature and in most industrial processes, we find conditions similar to the
harmonic oscillator: a moving mass under the action of an elastic force.
According to Hooke’s
law, the elastic force is proportional to displacement and elasticity
constant:
Meanwhile, according
to the reaction principle, the elastic force is equal in module and of
contrary direction with the inertial force:
The second Newton’s
law defines the inertial force as the product between mass and
acceleration:
Therefore, the
displacement and acceleration of the oscillating movement have the same
shape while they are proportional to each other:
Knowing that speed
is the simple integrate of acceleration and displacement is the double
integrate of acceleration, we got the following differential movement
equation:
The solution of this
equation looks like:
where
is the resonance
frequency
We find that the
oscillating movement has a sinus shape, which is the only one that
observes the initial condition:
One may notice that the
resonance frequency does not depend on the movement amplitude, as it is a
physical characteristic of the mass-material assembly. That allows using
the resonance frequency as a main parameter in the identification of the
operating status of the machines components.
In the electronic and
power generation industries, the sinus waveform is used both as a useful
signal and for the definition of the electric characteristics and
operation regimes.
Thus, in the power
generation industry, the sinus regime is the ideal operating regime, which
is characterized by minimum loss and stress.
The following main
parameters have been defined for that regime:
Various operational
conditions make the stationary regime be only a theoretical one, while we
have a non-sinus regime in practice.
The calculation of the
electrical parameters for the non-sinus regime is based on the
decomposition of voltage and current into sinus (harmonic) components, and
the further application of the definitions specific to the sinus regime:
The harmonics
frequency is in direct relationship with the constructive components of
the generator or load and represents the main parameter for the
identification of the cause of the unwanted behavior.
FFT analysis
The Fourier analysis of
signals is based on the processing called Fourier Transform (FT) for the
analysis, and the Inverse Fourier Transform (IFT) for the synthesis.
FFT (Fast Fourier
Transform) is a fast FT calculation algorithm which is used by most signal
analyzers.
FT decomposes the
analyzed signals into sinus functions, each one having its amplitude,
frequency and phase. The contents in sinus components of the input signal
is called frequency spectrum and is usually represented as an
amplitude-frequency graph.
The results are being
used for diagnosis or calculation in the frequency domain.
Spectrum analyzers
The current industry
context, based on increased quality, competitiveness and efficiency for
products and processes, the spectrum analyzers are supposed to play a more
and more important role in the research, design, testing and diagnosis
activity.
The main features of
the spectrum analyzers are:
The increase of the
processing capacity, constructive and operating performance of the
computing systems has resulted in their integration in the structure of
the signal analyzers and therefore a new technical and business stage in
this field.
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