Employ an advanced analysis of one or multiple waveforms with features such as resampling, filtering, and advanced graphing functions (PSD, transfer function, etc.).

### Frequency-domain Analysis

Analyze time-waveform data in the frequency domain with the following advanced graphing functions:

• Fast Fourier Transform (FFT): Transforms time-domain data into the frequency domain.
• Power Spectral Density (PSD): Displays the power in a frequency band.
• Transfer Function: Signifies a resonance or antiresonance in a system.
• Coherence: Indicates how closely a pair of signals (x and y) are statistically related.
• Cross Spectral Density: Displays the power in a frequency band for a pair of signals that have been multiplied in the frequency domain.
• Transmissibility: Like transfer function estimates, signifies a resonance or antiresonance in a system.

• Spectrogram: Displays the amplitude of multiple FFTs. What is a spectrogram?
• Nyquist: View transfer function data as a scatter plot. Used to assess the stability of a system with feedback during modal analysis.

### Understanding Waveform Relationships

#### Free VRU Course

Fast Fourier transform (FFT) and power spectral density (PSD) mathematics are powerful tools for analyzing the characteristics of a waveform. There are also several mathematic functions that help to explain the relationships between two or more waveforms.

The “Mathematics for Understanding Waveform Relationships” VRU course introduces three functions for comparing data: transfer function, correlation, and cross-spectral density.

### Resampling & Filtering

#### Resampling

Resampling changes the sample rate to user specifications on a time waveform.

• Comparing two data files with different sample rates.
• Downsampling data for quicker, more convenient handling if there is no high-frequency data.
• Increasing the smallest sample rate of the input files to increase the frequency resolution of an analysis algorithm like the fatigue damage spectrum (FDS).

#### Filtering

Filtering removes frequency components from a time waveform. They can filter out, accept, or boost frequency components. Filter options include high-pass, low-pass, and bandpass filters.

• Filtering out a DC offset or a frequency band contaminated by noise
• Removing frequencies outside a shaker’s specifications during file playback
• Filtering to the transducer’s specifications to remove data outside its rated operation
• Attenuating rapidly changing frequency components to smooth a noisy data sequence

General Purpose FIR Filters

If your tests require the following, then you may need an FIR filter:

• Notch out one or multiple single-frequency components
• Filter out one or multiple bands of frequency components
• Add dips and bumps in the filter response to equalize