A simple procedure to eliminate known poles from a time series

An extremely simple procedure is presented for eliminating known or previously computed poles from a time series and for obtaining a `deflated' time series which contains only the remaining poles. Time-series deflation can be used in combination with any numerical algorithm used to compute poles. As an important example, it is demonstrated how the time-series deflation technique combined with Prony's method can produce more accurate results than the use of Prony's method alone