8 Nonlinear Adaptive Algorithms

This chapter documents the functions used to create, initialize, and update the coefficients of nonlinear adaptive filters (Section 2.2.5). Table 8.1 summarizes the nonlinear adaptive functions currently supported and gives a short description and a pointer to the reference page of each function.

Table 8.1: Functions for creating, initializing, and updating nonlinear adaptive filters.

Function Name	Reference	Short Description
asptsovlms	8.1	Second Order Volterra LMS and several of its variants.
asptsovnlms	8.2	Second Order Volterra Normalized LMS algorithm.
asptsovrls	8.3	Second Order Volterra RLS algorithm.
asptsovtdlms	8.4	Second Order Volterra Transform domain LMS algorithm.
asptsovvsslms	8.5	Second Order Volterra Variable Step Size LMS algorithm.
init_ sovlms	8.6	Initialize Second Order Volterra LMS.
init_ sovnlms	8.7	Initialize Second Order Volterra NLMS.
init_ sovrls	8.8	Initialize Second Order Volterra RLS.
init_ sovtdlms	8.9	Initialize Second Order Volterra Transform domain LMS.
init_ sovvsslms	8.10	Initialize Second Order Volterra Variable Step Size 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.