Scale and Gridded Data: Fourier and Wavelet Transforms
Christopher D Lloyd · 2014
This chapter is concerned with the idea of decomposing spatial variation in gridded data. In other words, a key concern is with characterising spatial scales of variation. The methods and concepts outlined have been used widely in decomposing signals. The Fourier transform (FT) entails the translation of a function which depends on space to another function which depends on frequency. The chapter describes continuous Fourier transform, discrete Fourier transform (DFT), and fast Fourier transform (FFT) and spectral analysis. Another, more recently developed, class of approaches to decomposing signals is the wavelet transform (WT). A key advantage of the WT over the FT is the capacity of the former to deal with local discontinuities. The chapter discusses continuous wavelet transforms (CWTs), discrete wavelet transforms (DWTs) and fast wavelet transforms (FWTs), besides other types.