# What is a MIMO (Multi-Input Multi-Output) Model?

NOTE:  The commands in this tutorial are only available if the VES-3600 Advanced Signal Processing option is authorized by your ME'scope license. Check Help | About to verify authorization of this option.

Calculation of Transfer Functions, Outputs, and Inputs are all based upon use of a MIMO (Multi-Input Multi-Output) model of the dynamics of a structure. A MIMO model is a frequency domain model where Fourier spectra of multiple Inputs are multiplied by elements of a Transfer Function matrix to yield the Fourier Spectra of multiple Outputs.

The MIMO model is expressed with the equation:

{X(w)} = [H(w)] {F(w)}

where:

{F(w)} = Input Fourier spectra (m - vector).

[H(w)] = Transfer Function matrix (n by m).

{X(w)} = Output Fourier spectra (n - vector).

m = number of Inputs.

n = number of Outputs.

w = frequency variable (radians per second).

NOTE:  Rows of the Transfer Function matrix correspond to Outputs, and columns correspond to Inputs.  Each Input and Output corresponds to a measurement DOF (point & direction).  Each Transfer Function is a Cross-channel function between two DOFs, an Input DOF and an Output DOF.

## Definitions

### Transfer Function

• A Transfer Function is defined as the Fourier spectrum of an Output divided by the Fourier spectrum of an Input.

### Frequency Response Function (FRF)

• An FRF is defined as the Fourier spectrum of a displacement, velocity, or acceleration response (Output) divided by the Fourier spectrum of the excitation force (Input) that caused the response.

### Transmissibility

• A Transmissibility is defined as the Fourier spectrum of an Output divided by the Fourier spectrum of an Input with the same units.

NOTE:  An FRF and Transmissibility are special cases of a Transfer Function.

## MIMO Calculations

Any one of the components of the MIMO model, (Inputs, Outputs, or Transfer Functions) can be calculated from the other two components using commands in the Transform | MIMO menu.

• Inputs and Outputs can be either time or frequency domain M#s

• Transfer Functions can be either experimentally derived or synthesized from modal parameters

The MIMO model is also used to calculate and display in animation a sinusoidal ODS due to multiple sinusoidal excitation forces at the same frequency.  (See the Transform | MIMO | Sinusoidal ODS command description for details.)