Objective:

The usual transformation in acoustics is the Fourier-Transformation. A fast and simple implementation is the windowed Fast Fourier Transformation. A disadvantage of the FFT is that all frequencies are equally spaced in the time frequency plane. A logarithmic spacing that allows keeps the relative resolution in the frequency plane constant is the Wavelet Transformation. This gives the possibility of a higher temporal resolution in the high frequency plane. Several types are implemented in STX and PAK.

Method:

A higher temporal resolution is possible, if quadratic transformations defined in the Cohen Class are used. The Windowed Pseudo Wigner Ville Distribution and a discrete version of the Choi-Williams Distribution are implemented in STX and PAK. Disadvantages of these transformations are the cross products that are reduced by smoothing in the different transformations of the Cohen class.

Application:

A handbook is written for or the practical use of the difficult transformations. The Handbook documents the possibilities and the limits of the transformations.

Objective:

The beam forming method focuses an arbitrary receiver coil using time delay and amplitude manipulation, and adds to the temporal signal of the microphones or the short time Fourier transform.

Method:

64 microphones are collected by a microphone array with arbitrary shape. For compatibility with acoustic holography, equal spacing and a grid with 8 x 8 microphones is used.

Application:

Localization of sound sources on high speed trains is a typical application. The method is used to separate locations along the train and especially the height of different sound sources. Typical sound sources on high speed trains are rail-wheel contact sites and aerodynamic areas. The aerodynamic conditions occur at all heights, especially at the pantograph.

Objective:

If measurements are possible only at the hull of a machine, a tool is needed to separate the dominating near-field components from the far-field components. This, in turn, allows the far-field levels to be estimated. The separation is often not possible using spectral methods, because both components have nearly the same frequency. Using a limited number of microphones, a modal separation is also impossible. Instead of a modal analysis, a principal component analysis is applied.

Method:

The narrow-band Fourier transform method is used, and a separate analysis is conducted for each frequency. The cross-power matrix spanning all microphone positions is used. The components are then calculated using the PCA. As long as the modes at the microphone positions have different relative values, PCA can be used to separate them. In an initial test, the far field is observed and the transfer function for every component from the near field to the far field is estimated. These transfer functions are assumed to be constant in time. They are used for the estimation of the overall far-field level.

Application:

Observation of the far-field level of machines.

Objective:

This project aims to develop an independent modulus for the wavelet analysis that contains a simple program interface and can be used flexibly.

Method:

The implementation was in C++ in the form of a wavelet analysis class and a signal queue. Features:

• The Input/Output data format can be chosen at run time. The Input and the Output are separately configurable.
• There are several possibilities for choosing the array and distribution of the frequency bin. The frequency bin vector can also be transferred.
• Seven wavelets are implemented.
• A down-sampling method can be used for the acceleration (factor: 1.2 convert frequency bins are chosen automatically).
• Because of the disjunction in signal queue and analysis, an asynchrony Input/Output is possible.
• Compiling an optimized numerical library can be achieved. Currently, the application of the "Intel® Signal Processing Library" (SPL) or of the "Intel® Integrated Performance Primitives" (IPP) is possible.
• The signal queue class can be used independently of the analysis class. It also implements the down-sampling function.

Application:

The developed classes are used as a modulus in the acoustic measurement and analysis system PAK. The analysis class was also integrated as a signal processing atom WLLIB in STx.