Digital Signal Processing: A Practitioner's Approach

6

Case Studies

Digital signal processing is all-pervading, so we have mostly selected the areas that interest engineers. Often the solutions look very similar, indicating many commonalities between them. These case studies also demonstrate that it is very difficult to categorise a given problem as exclusively DSP or non-DSP. Frequently we need to stretch our engineering hand a little and remove our blinkers to get an overall view of the solution.

In addition, problems are non-linear and we need a good systems background as well as DSP. Inverse problems are more difficult than forward problems or synthesis. For instance, the design of a filter for a given specification is trivial. It is the combinations of many disciplines put together that makes a problem very interesting. Perhaps you feel that problems are centred around some common solutions. But this chapter aims to demonstrate that the essence of any solution is a good problem formulation.

6.1 Difference Equation to Program

The following C code is for a digital filter implementation that includes testing by exciting it with a white Gaussian noise (WGN); the output is captured in the file fiiter.dat. The spectral characteristic of the output time series is the same as that of the filter, since the input is a WGN. This code demonstrates only that converting a given difference equation to a code is relatively trivial. Here we designate xk1 = x_k, xk2 = x_k−1, xk3 = x_k−2 and the filter is x_k = 0.5871 x_k−1 − 0.9025* x_k−2 + 0.0488 ...