Comonotone approximation of periodic functions

Suppose that a continuous 2 pi-periodic function f on the real axis R changes its monotonicity at different ordered fixed points yi epsilon(-pi,pi), i = 1,..., 2s, s E epsilon N. In other words, there is a set Y := {yi}(i epsilon z) of points yi = y(i+2s) + 2 pi on R such that, on [y(i,)y(i-1)], f is nondecreasing if i is odd and nonincreasing if i is even. For each n >= N(Y), we construct a trigonometric polynomial P-eta of order <= n changing its monotonicity at the same points y(i) epsilon Y as f and such.