Spider DSA User’s Manual
184
Real-Time FFT Analysis
FFT analysis is conducted in the DSA real-time operation mode. These
applications involve Digital Signal Processing calculations such as the Auto-Power
Spectrum, Cross Power Spectrum, and Fourier Transform etc. for input channel
signals.
Dynamic Signal Analyzer Basics
This section will give an overview of the theory behind the functions performed in
the FFT analysis mode of the Spider module. For more detailed information on
this topic please refer to “Dynamic Signal Analyzer Basics” published by Crystal
Instruments.
The Fourier Transform is one of the most fundamental and popular methods of
signal analysis. It transforms an infinite time waveform into its frequency
components. These frequencies may then be analyzed or further manipulated to
calculate phase or transfer functions. Because the Fourier Transform involves an
infinite sum the signal must be broken into finite blocks of N samples. Each block
is then transformed using the Discrete Fourier Transform (DFT)However,
computing DFT is computationally intensive and so a more efficient algorithm
called Fast Fourier Transform (FFT) was developed.
Some applications of the FFT are listed below:
Power Spectrum
The magnitude of the frequency components of signals are collectively called the
amplitude spectrum. In many applications, the quantity of interest is the power or
the rate of energy transfer that is proportional to the squared magnitude of the
frequency components. The average squared magnitudes of all of the DFT
frequency lines are collectively referred to as the Power Spectrum, G
xx
. The
averaging process is more properly termed an ensemble average, wherein the
squared amplitude from N signal blocks at a each measured frequency, f, are
averaged together. Letting an asterisk (*) denote conjugation of a complex
number, the “power” averaging process is defined by:
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