The d i s c r e t e prolate spheriodal (DPS) f i l t e r i s one of the class of nonrecursive f i n i t e impulse response (FIR) f i l t e r s . The DPS f i l t e r , f i r s t introduced by TUFTS and FRANCIS (19701, i s superior t o other f i l t e r s i n t h i s c l a s s i n that i t has maximum energy concentration i n the frequency passband and minimum ringing i n the t i m e domain. DPS f i l t e r properties, provide information required t o construct the f i l t e r , and compare the properties of t h i s f i l t e r with those of the more commonly used f i l t e r s of the same class. W e note that use of the DPS f i l t e r allows f o r p a r t i c u l a r l y useful statements of data time/frequency resolution "cell" values and t h a t overall it forms an especially useful t o o l for d i g i t a l signal processing.

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Scattering by a uniformly translating sphere of a pulse that modulates the amplitude of a linearly polarized plane wave was formulated using the frame-hopping method involving a laboratory inertial reference frame and the sphere's comoving inertial reference frame. The incident signal was defined in the laboratory frame and transformed to the comoving frame with the Lorentz transformation, thereby altering the incident signal's spectrum, direction of propagation of the carrier plane wave, and the direction of the incident electric field, depending on the sphere's velocity. In the comoving frame, the incident signal was Fourier-transformed to the frequency domain, and the scattered field phasors were computed in all directions using the constitutive parameters of the material of the sphere at rest. The scattered signal in the comoving frame was obtained using the inverse Fourier transform. Finally, the scattered signal in the laboratory frame was obtained by inverting the original Lorentz transformation. The backscattered signal was found to depend strongly on the sphere's velocity, when the sphere's speed is an appreciable fraction of the speed of light in free space. The change in the backscattered signal compared with the backscattered signal from a stationary sphere is the greatest when the sphere's velocity is either parallel or antiparallel to the direction of propagation of the incident signal. The backscattered signal is also affected by motion transverse to the incident signal's direction of propagation; then, the backscattered signal depends on whether or not the motion is aligned with the direction of the incident electric field.