Signal Downsampling Using Polynomial LSA and OpenCL

This is a class project for EE590 Applied High-Performance GPU Computing at the University of Washington. The goal is to provide downsampling of a complex IQ data from 4 gigasamples per second (GSPS) to 3.5 GSPS.

The project has two stages:

• Complete Sequential Code
• Add OpenCL Code

Sequential Code

The sequential code performs a Least Squared Approximation using QR Decomposition and Back Substitution to solve for coefficients. The sequential code is run through its paces in the function Test_Resample() within sequential.cpp. The general breakdown follows:

• Read Sample Data
• Create Time Step Vector
• Generate A Matrix using Time Step Vector and Polynomial Order (for QR Decomposition)
• Do QR Decomposition, returning Q and R matrices
• Multiply Q by Sample Data column vector
• Use Back Substitution to solve for LSA Coefficients
• Create Output Time Step Vector
• Evaluate Polynomial with LSA Coefficients on Output Time Step Vector

It is important to note that we assume a constant input sample rate and sample size. This means that all calculations up through the QR Decomposition only need to happen once before sampling data begins.

Parallel Code

The parallel code can help in a couple situations. Since startup through QR Decomposition can happen before we get going on downsampling, there is no need to do any of that via parallel.

• Matrix Multiplication
• Polynomial Evaluation