Frequency response function H(f) in the frequency domain and impulse response function h(t) in the time domain are used to describe input-output (force-response) relationships of any system, where signal a(t) and b(t) represent input and output of the physical system. The system is assumed to be linear and time-invariant. Frequency response function and impulse response function are so-called system descriptors. They are independent of the signals involved.
In the table below you can see typical frequency response function formulations:
|Force / Displacement
|Displacement / Force
|Force / Velocity
|Velocity / Force
|Force / Acceleration
|Acceleration / Force
The estimation of the frequency response function depends upon the transformation of data from time to the frequency domain. For this computation, we use the Fast Fourier transform (FFT) algorithm which is based on a limited time history. The frequency response functions satisfy the following single and multiple input relationships:
Single Input Relationship
Xp is a spectrum of the output, Fp is a spectrum of the input, and Hpq is frequency response function.
Multiple Input Relationship
In the image below we can see an example of two inputs - two outputs case.