App note: DSP library for LPC1700 and LPC1300 microcontrollers

Here is a reference guide from NXP for the DSP library made for LPC17xx, and LCP13xx microcontrollers. You can download the library here.

The DSP library has been developed as a commonly used set of DSP functions optimized for the NXP Cortex-M3 LPC1700 and LPC1300 family products. Most functions have been implemented in Thumb-2 assembler unless there was little or no performance benefit in doing so.
The library is supplied as a static library project with source code in LPCXpresso (Code Red), Keil and IAR versions, and can also be linked into any ARM-EABI tool chain as a binary library