Characterization of polynomial functions and application to time-frequency analysis

We propose necessary and sufficient conditions for a function /spl phi/(t) to be a polynomial and establish a formula that allows us to compute the value of the derivative /spl phi/'(t) of a polynomial at any point in terms of the values of this polynomial. For this purpose, we establish that any polynomial /spl phi/(t) of degree /spl les/Q can be represented as a linear combination of /spl phi/(t-t/sub 1/), ..., Q(t-t/sub Q/), where t/sub 1/, ..., t/sub Q/ denote arbitrary parameters. A similar property is established for the derivative /spl phi/'(t). Some signal processing applications of these results are discussed,.