Time varying filter for doppler synthesis

Time companding of broad band signals or doppler shifts of sinusoidal signals can be interpreted as linearly time varying delay. For any stationary signal, a linear time invariant filter can always be designed to generate a prescribed delay using minimum mean square error criteria . A FIR filter of order 2m is sufficient to generate any delay with zero mean square error for signal consisting of m sinusoidals. The coefficients of such a filter are derived by solving normal equations. By using time varying delay parameter for estimation the solution of normal equation generates time varying filter coefficients. This fiIter produces appropriate doppler shifts. Here an expression is derived for the filter coefficients. The performance of the filter is evaluated by comparing the correlation of the signal with the doppler shifted signal.