# Transform | MIMO Transfer Functions

This command is used to calculate Transfer Functions from time or frequency measurements in a Data Block.  Transfer functions can be calculated from,

• Input & Output time waveforms.

• Input Auto spectra and Cross spectra between Inputs & Outputs.

Before executing this command,

1. All Input measurements functions must be designated as Input (or Both) in the Input Output column of the in the M#s spreadsheet.

2. All Output measurement functions must be designated as an Output (or Both) in the Input Output column of the M#s spreadsheet.

3. All measurements must have a DOF that designates the Point & direction of the measurement

4. All measurements should have engineering units.

When this command is executed, the MIMO dialog box will open for selecting Data Blocks with Input & Output measurements in them. • If Data Blocks containing time waveforms are open in the Work Area, Time Waveforms will be enabled in the Data Source section.

• If Data Blocks containing Auto & Cross spectra are open in the Work Area, Auto & Cross spectra will be enabled in the Data Source section.

## Using Auto & Cross Spectra

Transfer Functions are calculated from Auto & Cross spectra using the following formula;

[H1(w)] = [{X(w)} {F(w)}t] [{F(w)} {F(w)}t]-1

where:

[{X(w)} {F(w)}t] = Cross spectrum matrix between Outputs & Inputs (n by m)

[{F(w)} {F(w)}t] = Input Auto spectrum matrix (m by m)

[H1(w)] - H1 Transfer Function matrix (n by m)

{F(w)} - Fourier spectra of Inputs (m-vector)

{X(w)} - Fourier spectra of Outputs (n-vector)

m - number of Inputs

n - number of Outputs

w - frequency variable

t - denotes conjugate transposed

-1 - denotes the matrix inverse

## Using Time Waveforms

If time waveforms are used to calculate Transfer Functions, time domain windowing, overlap processing,and spectrum averaging can be used to calculate Auto & Cross spectra, which are then used to calculate the Transfer Functions.

• (See Transform | Calculate | Spectra for details on spectrum averaging.)

• Auto & Cross Spectra can also be saved with the Transfer Functions by checking them in the Include section of the dialog box.

• Coherences can also be saved by checking them in the Include section of the dialog box.

## Time Domain Windowing

Time waveforms can have different windows applied to them before the FFT is applied.  Each window is most effective when used on a specific type of data, as described below.

• Rectangular (for periodic-in-the-window signals)

• Hanning (for broad band signals)

• Flat Top (for narrow band signals)

• See the Time Domain Windows section in the Signal Processing commands chapter for details.)