Frequency response Function (FRF)

A common application of dynamic signal analyzers is the measurement of the Frequency Response Function (FRF) of mechanical systems. This is also known as Network Analysis, where both system inputs and outputs are measured simultaneously. With these multi-channel measurements, the analyzer can measure how the system “changes” the inputs. If the system is linear, which is a common assumption, then this “change” is fully described by the Frequency Response Function (FRF). In fact, for a linear and stable system, the response of the system to any input can be predicted just by knowing the Frequency Response Function. The relationship between the input and output is known as the transfer function or frequency response function and represented by H(y,x). In general, a transfer function is a complex function that describes how the system modifies the input signal magnitude and phase as a function of the excitation frequency. With various excitations, the characteristics of the UUT system are measured experimentally. These characteristics include:

  • Frequency Response Function (FRF), which is described by:
    • Gain as a function of frequency
    • Phase as a function of frequency
    • Resonant Frequencies
    • Damping factors
    • Total Harmonic Distortion
    • Non-linearity

Single Response              Two responses

Frequency response is measured using the FFT, cross power spectral method with broadband random excitation. Broadband excitation can be a true random noise signal with Gaussian distribution, or a pseudo-random signal of which the amplitude distribution can be defined by the user. The term broadband may be misleading, as a well implemented random excitation signal should be frequency band-limited and controlled by the upper limit of the analysis frequency range. That is, the excitation should not excite frequencies above that which can be measured by the instrument. The random generator will only generate random signals up to the analysis frequency range. This will also concentrate the excitation energy on the useful frequency range.

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