When implementing signal processing algorithms, I've used off-the-shelf systems based on the Motorola DSP56303 and later the Texas Instruments TMS320C62xx/C671x . Octave has become my main matrix maths tool for DSP and AI work (and I keep an eye on julia). Octave works well on desktops including very small but powerful ARM64 systems such as the ROCK64 (running Armbian) through to multicore AMD64 systems running FreeBSD or pop-os.
Development with TI C6x DSPs
The original beagle board has an OMAP3530 device containing a superscalar ARM Cortex-A8 CPU (with NEON SIMD coprocessor) and TMS320C64x+ DSP components, running a linux port. Links: beagle board blog.
Subsequent developments included the BeagleBoard-xM, the BeagleBoneBlack series (ARM CPU with 2x PRU cores, options like built-in wifi, smaller form factors, etc.), and the BeagleBoard-X15 (includes TI AM5728 2×1.5-GHz ARM® Cortex-A15 ARM cores, 2x 700MHz C66 DSP cores, 4x PRU cores, and 2 ARM M4 cores) which later had the 32bit ARM general purpose cores replaced by 64bit cores. More recently there are RISC-V based boards and systems with specialist AI support - see https://www.beagleboard.org/boards
Matrix Mathematics Tools
julia is a scientific computation environment that is in very active development and runs on many platforms. It supports JIT compilation.
SciLAB is a comprehensive matrix mathematics package initially developed by France's INRIA and now produced by the SciLAB Consortium.
Octave is a very powerful matrix mathematics package initially developed by John W. Eaton (Uni of Texas). It supports JIT.
Fourier Transform:
FFTW is a fast platform-independent portable (!) FFT created by a team at MIT.
Kiss FFT is a BSD licenced FFT that tries to keep everything simple.
Project Nayuki provides clean DCT implementations in various languages (Java, python, C, C++, javascript, C#, Rust).