7 Active Noise and Vibration Control Algorithms

This chapter documents the functions used to create, initialize, and update the coefficients of active noise and vibration control filters. Table 7.1 summarizes the ANVC functions and gives a short description and a pointer to the reference page of each function.

Table 7.1: Functions for creating, initializing, and updating active noise and vibration control filters.

Function Name	Reference	Short Description
asptadjlms	7.1	Adjoint-LMS algorithm.
asptfdadjlms	7.2	Frequency Domain Adjoint LMS algorithm.
asptfdfxlms	7.3	Frequency Domain Filtered-x LMS algorithm.
asptfxlms	7.4	Filtered-x LMS algorithm.
asptmcadjlms	7.5	Multichannel Adjoint-LMS algorithms.
asptmcfdadjlms	7.6	Multichannel Frequency Domain Adjoint LMS algorithm.
asptmcfdfxlms	7.7	Multichannel Frequency Domain Filtered-x LMS algorithm.
asptmcfxlms	7.8	Multichannel Filtered-x LMS algorithm.
init_ adjlms	7.9	Initialize Adjoint LMS.
init_ fdadjlms	7.10	Initialize Frequency Domain Adjoint LMS.
init_ fdfxlms	7.11	Initialize Frequency Domain Filtered-x LMS.
init_ fxlms	7.12	Initialize Filtered-x LMS.
init_ mcadjlms	7.13	Initialize Multichannel Adjoint LMS.
init_ mcfdadjlms	7.14	Initialize Multichannel Frequency Domain Adjoint LMS.
init_ mcfdfxlms	7.15	Initialize Multichannel Frequency Domain Filtered-x LMS.
init_ mcfxlms	7.16	Initialize Multichannel Filtered-x LMS.

Each function is documented in a separate section including the following information related to the function:

• Purpose: Short description of the algorithm implemented by this function.
• Syntax: Shows the function calling syntax. If the function has optional parameters, this section will have two calling syntaxes. One with only the required formal parameters and one with all the formal parameters.
• Description: Detailed description of the function usage with explanation of its input and output parameters.
• Example: A short example showing typical use of the function. The examples listed can be found in the ASPT/test directory of the ASPT distribution. The user is encouraged to copy from those examples and paste in her own applications.
• Algorithm: A short description of the operations internally performed by the function.
• Remarks: Gives more theoretical and practical remarks related to the usage, performance, limitations, and applications of the function.
• Resources: Gives a summary of the memory requirements and number of multiplications, addition/subtractions, and division operations required to implement the function in real time. This can be used to roughly calculate the MIPS (Million Instruction Per Second) required for a specific platform knowing the number of instructions the processor needs to perform each operation.
• See Also: Lists other functions that are related to this function.
• Reference: Lists literature for more information on the function.

Active noise and vibration control systems usually operate in two phases. The first phase is an identification phase in which models of the system secondary paths are obtained and stored in memory. The second phase is the control phase in which the coefficients of an adaptive controller are adjusted to reduce the noise or vibration at the error sensors. When the secondary paths are continuously changing, it is also necessary to continuously update the models of the secondary paths during the control phase. The functions documented here assume that the models of the secondary paths are obtained using an external identification process and perform the control task only. The identification process can be performed using any of the transversal or recursive adaptive algorithms in a system identification setup. The functions, therefore, distinguish between the physical secondary paths (usually named $s$) and the estimated secondary paths $se$. The physical model is used to calculate the response of the secondary actuators at the error sensors, while the estimated secondary paths are used to adapt the coefficients of the controller.