An efficient procedure for broadband Doppler compensation

Frequently, it is necessary to compress or expand a function by scaling independent variables relating to time and/or distance. For example, the Doppler phenomena, caused by a change in the position of the source of a waveform measured radially from the position where the waveform is received, affects the time scale of the received waveform. For applications that do not satisfy the narrowband criterion, a procedure other than frequency translation is needed to produce a scaling of the independent variable of time to compensate for the Doppler effect. An approach, intended for discrete time applications, involves the two-step process of interpolation and decimation. The proper scaling factor is obtained by interpolation by an integer factor L and decimating, i.e., decreasing the sampling rate, by an integer factor K. The computationally efficient procedure which uses FIR filters is described: the corresponding expressions are derived for the interpolation errors associated with this procedure. Also, modifications to this procedure are described. One such modification is used to accommodate time varying scale factors; another incorporates frequency translations to accommodate uncertainties in the scale factor.