Educational Material

Technical Review, No. 1 - 1984
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An introduction to basic dual channel FFT measurements. Including:

Auto Spectrum
Cross Spectrum
Frequency Response Function (FRF)
Coherence Function

Various excitation techniques for system analysis are described and their advantages and disadvantages for specific application outlined.

Technical Review, No. 2 - 1984
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An introduction to basic dual channel FFT measurements and their physical interpretation is dealt with in some detail. Including:

Impulse Response Function
Autocorrelation
Cross Correlation

Implementation of Hilbert Transforms on these time domain functions, is introduced to compute the corresponding complex analytical signals, and the advantages of using the magnitude in the presentation of these functions are illustrated in some practical situations.

Technical Review, No. 3 - 1987
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This article demonstrates how the analogy between DFT/FFT (Discrete Fourier Transform/Fast Fourier Transform) analysis and filter analysis (analogue or digital) can be used to better understand the applications of different weighting function used in DFT/FFT. The filter characteristics of the most commonly used weighting functions (also called windows) are illustrated and discussed with respect to their use various practical applications of system and signal analysis. Covers the following windows:

Rectangular (also called Boxcar, uniform or no window)
Hanning
Flat Top

Technical Review, No. 4 - 1987
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The mathematical formulation of the analogy as well as rigorous details of weighting functions. The shape of the window function and the frequency span of the analyzer, determine the noise bandwidth of the filters and the analysis time for the signal. Consequently, it is important that the correct units are used to scale the frequency spectra.

Technical Review, No. 1 - 1994
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In this article several methods for measurement of damping are summarised with respect to their advantages and disadvantages. Especially the use of Digital Filter (DF) and Fast Fourier Transform (FFT) are compared. In general FFT analysis is best suited for heavily damped structures although with proper memory and post-processing facilities, lightly damped structures can also be covered, while it is advantageous to use DF analysis when dealing with lightly damped structures only. The use of Time-frequency analysis techniques such as the Wavelet Transform and the Short-time Fourier Transform are also demonstrated.

Technical Review, No. 2 - 1994
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This article discusses the errors that are introduced when calculating the impulse response function from the frequency response function using DFT/FFT analysis technique. The impulse response function is used in many applications of system analysis where a description of the system characteristics is preferred in the time domain rather than in the frequency domain.

Primer: Measurement Microphones
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This booklet gives an introduction to the design features and operating principles of measuring microphones. Some knowledge about the measurement of sound would be an advantage, so you might wish to consult our companion booklet 'Measuring Sound'.

Primer: Measurements in Building Acoustics
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This booklet answers some of the basic questions asked by the newcomer to building acoustic measurements. It gives a brief explanation of the following:

Behaviour of Sound in a Room
Sabine's Formula for Reverberation Time
Measuring the Sound Absorption
Speech Intelligibility
Rapid Speech Transmission Index (RASTI)
Acoustics of Buildings.
Sound Reduction Index of a Wall
Survey of Building Acoustic Measurements (ISO)

Primer: Measuring Sound
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This booklet gives answers to some of the basic questions asked by the newcomer to a noise measuring programme. It gives a brief explanation to questions like:

What is sound?
Why do we measure sound?
What units do we use?
How do we hear?
What instruments do we use for measurement?
What is a weighting network?
What is frequency analysis?
What is noise dose?
How does sound propagate?
Where should we make our measurements?
How does the environment influence measurements?
How should the microphone be positioned in the sound field?

Primer: Measuring Vibration
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This booklet answers some of the basic questions asked by the newcomer to vibration measurement. It gives a brief explanation to the following:

What is vibration?
The vibration parameters, Acceleration, Velocity and Displacement
Accelerometer types
How to mount the accelerometer
Force and impedance measurements
Logarithmic scales and decibels
What is frequency analysis?
Using vibration measurements
Vibration as a machine condition indicator
Vibration troubleshooting charts
Vibration and the human body

Primer: Structural Testing, Part I
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An overview of structural testing covering:

Noise and Vibration: Cause and Effect
Signal vs. System Analysis
Modal Analysis
Application of Modal Data
Frequency Response Measurements
Random Excitation
Pseudo-Random Excitation
Impact Excitation
Impact Testing and the Coherence Function
Window Techniques for Impact Testing
Comparison between Excitation Forms
Calibration

Primer: Structural Testing, Part II
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An overview of modal analysis covering:

Experimental Modal Analysis
Single-degree-of-freedom (SDOF) Models
The DOF and MDOF models
What is a Mode Shape?
Normal Modes and Complex Modes
Scaling the Mode Shapes
Modal Coupling
What Does the Modal Description Assume?
Mode Shapes from Quadrature Picking
Parameter Estimation by Curve-fitting
What is Curve-fitting?
Curve-fitters for Modal Analysis
Local and Global Curve-fitters

Application Note: Determining Modal Parameters of Simple Structures
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The modal parameters of simple structures can be easily established by the use of PULSE. This application note describes how to:

Measure the modal frequencies by inspection of frequency response functions
Determine the modal damping
Establish the mode shapes Quadrature Picking

Application Note: Time Windows
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FFT analyzers process finite blocks of digital information. The analyzer extracts, or “cuts out”, these blocks from the complete time record using time weighting functions, or “time windows”. Unless we can understand the basic concepts of time limited data, we can’t be sure that our interpretation of FFT analysis is correct. Neither can we be sure of the accuracy of our results. Covers the following windows:

Rectangular (also called Boxcar, uniform or no window)
Hanning
Flat Top

Application Note: Choose Your Units!
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Brüel & Kjær Signal Analyzers allow you to choose the appropriate units to suit your measurement signal, be it deterministic, random or transient.

The frequency spectrum amplitude can be scaled in terms of:

Root mean square (RMS) for deterministic signals
Mean square, Power (PWR) for deterministic signals
Power spectral density (PSD) for random signals
Energy spectral density (ESD) for transients