1. A Doppler shift compensation apparatus, comprising: an analog to digital converter which transforms an analog input signal including Doppler frequency shifts to a series of digital data; a memory which stores said serial digital data from said analog to digital converter; a window function weighting part for multiplying and weighting a specified window function to a part of input data read out from said memory; a fast Fourier transformer (FFT) for transforming said input data to frequency spectrum data; an interpolation judgment part which distinguishes line spectrum from dispersed spectrum in said frequency spectrum data from said fast Fourier transformer and judges that an interpolation be possible when said line spectrum is found; a spectrum interpolator which measures the true frequency, amplitude and phase of the line spectrum based on the judgement of said interpolation judgement part; an accumulator for accumulating the frequency domain data interpolated by said spectrum interpolator; a summation part for vector-summing the frequency domain data accumulated by said accumulator to a Fourier transform output of said fast Fourier transformer; a regression computation part for performing a predetermined regression computation for the frequency data from said summation part based on the output data from said interpolation judgment part; and a first subtractor for subtracting the output data of said regression computation part from said frequency data of said summation part, wherein the subtracted result is compensated in terms of said Doppler frequency shift.