 The first successful implementation was achieved by Mecklenbrauker and Mersereau and was later revised by McClellan and Chan.For a zero phase filter the one phase impulse response is given by

formula_190

where formula_191 represents the complex conjugate of formula_192.Let formula_193 be the frequency response of formula_192.Assuming formula_192 is even,we can write

formula_196

where formula_197 is defined as formula_198 if n=0 and formula_199 if nformula_2000.Also formula_201 is a polynomial of degree n known as the Chebyshev polynomial.