High-Performance Code Generation for FIR Filters and the Discrete Wavelet Transform Using SPIRAL

The discrete wavelet transform (DWT) and filtering algorithms, together with certain classes of trigonometric transforms, are among the most frequently used methods in digital signal processing (DSP) applications. For example, the DWT is used in detection, identification, denoising, prediction, channel coding, and compression such as in the JPEG2000 standard. In many of these applications, filters and the DWT are the computationally most intensive components, and their performance is crucial for the overall efficiency of the application. Creating high-performance software implementations of fast DSP algorithms is a difficult problem. For example, in many cases the data access and data flow patterns of the implementation play a more important role than the computational cost of the algorithm. As a consequence, the best implementation is platformdependent, and, when the platform is changed, the application has to be reimplemented to retain optimal performance. In many cases, the best implementation on one platform is far suboptimal on another. Because of these problems, there is a need for a systematic and automated way to create, modify and adapt implementations across different platforms. The SPIRAL system [1] offers a solution to this problem for the class of linear DSP transforms by automatically generating implementations that are highly optimized and adapted to the given software platform. SPIRAL’s current version generates code for the discrete Fourier transform (DFT), the discrete cosine and sine transforms (DCTs and DSTs), and several other transforms. This paper extends SPIRAL to generate high performance code for FIR filters and the DWT.