TABLE OF CONTENTS The terrain has many randomly distributed scatterers. The Doppler return is the sum of the reflections from these scatterers as they pass through the antenna beam. In consequence, the Doppler radar echo will be modeled as a random waveform whose exact analysis requires the use of generalized harmonic analysis. In order to establish a common notation and viewpoint, the following is a pr cis of the elements of harmonic and system analysis we ll require.
The study of systems that interact with complex waveforms is often simplified by expressing the complex waveform as a linear combination of other waveforms from a set with certain specified characteristics. One of the most useful sets for use in the study of linear time-invariant (LTI) systems is the set of sinusoids. The reason is that the response of an LTI system to an input sinusoid is a sinusoid with the same frequency. The representation of a waveform as the sum of sinusoids is called Fourier analysis. If the waveform is periodic, the representation is called a Fourier series; if the waveform is aperiodic, the representation is called a Fourier transform.
A periodic waveform p( t) is one that is equal to a shift of itself. That is, there is a number T such that p( t + T) = p( t). Observe that a periodic waveform p( t) must be nonzero for ? ? < t <
