Fourier series approximations and low pass filtering: facilitating learning of digital signal processing for biomechanics students

Filtering raw biomechanical data to remove noise is a key first step that must be performed prior to further biomechanical analysis. Raw biomechanical data are usually filtered to remove noise above a specified cutoff frequency, a process known as "low pass filtering". The concept of frequency content within a signal may be difficult for students to grasp, and authors of biomechanics textbooks often use Fourier series approximations to introduce this concept. To facilitate student learning, we have created an Excel spreadsheet that allows students to observe several orders of Fourier series approximations to a representative set of biomechanical data. In this paper, we provide a short tutorial on Fourier series approximations and instructions for using the Excel spreadsheet. The Fourier series coefficients are determined iteratively with a first-principles approach of minimizing the sum of squared error between the original data and the approximation using the Solver function in Excel. The user can reset these coefficients and run Solver to observe the iterative process. This first-principles approach may be helpful in a broad range of applications because it allows users to perform non-linear regression within an Excel spreadsheet. The Excel spreadsheet also includes a fourth-order zero-lag Butterworth low pass filter with adjustable cutoff frequency so that the effects of filtering can be observed and compared with the Fourier series approximations. We believe this tutorial and Excel spreadsheet will be helpful to those teaching and learning digital signal processing in biomechanics.