Meta.Numerics is a Mono-compatible .NET library for scientific and numerical programming. It includes functionality for matrix algebra (including SVD, non-symmetric eigensystems, and sparse matrices), special functions of real and complex numbers (including Bessel functions and the complex error function), statistics and data analysis (including PCA, logistic and nonlinear regression, statistical tests, and nonuniform random deviates), and signal processing (including arbitrary-length FFTs).
PFFFT is a very small 1D Fast Fourier Transform library based on the venerable FFTPACK v4. It handles single precision real and complex transforms. Computations take advantage of SSE1 instructions on x86, Altivec on PowerPC, and NEON on ARM, allowing it to achieve a performance level that is not too far from the very best FFTs (FFTW, Intel MKL, Apple vDSP).
The 2DECOMP&FFT library is a software framework in Fortran to build large-scale parallel applications. It is designed for applications using three-dimensional structured mesh and spatially implicit numerical algorithms. At the foundation, it implements a general-purpose 2D pencil decomposition for data distribution on distributed-memory platforms. On top, it provides a highly scalable and efficient interface to perform three-dimensional distributed FFTs.
Impulse is a bit of eye candy for your desktop. It is a widget that displays a graphical spectrum analyzer on your GNOME desktop. It is written in C and Python, and uses GTK and Cairo graphics to generate the animation. The impulse library creates a pulse audio connection context that reads the output stream from pulseaudio in a thread natively, which can then be read from Python. You can instruct impulse to either output the raw stream or output the FFT of the raw stream.