Essentials of Geophysical Data Processing

This chapter is concerned with the relationship between frequency domain operations (using the DFT from ) and time domain operations (using discrete transient convolution from ). Frequency and time domain operations are connected by a convolution theorem, showing that multiplication in one domain corresponds to convolution in the other. This provides guidance to avoid unwanted wrap-around effects when performing DFT linear filtering. It also motivates the use of window functions as multipliers in both the time and frequency domains to improve linear filtering performance and DFT spectral estimates, as described in .