Consistent estimates for hidden frequencies in a linear process

Traditional methods for detecting the hidden frequencies in white or coloured noise is based on the distribution of periodogram ordinates I(2;j/N) and hypothesis testing. The power is low when a hidden frequency falls midway between two 2;j/N and it is difficult to discuss the consistency of the procedures. Using theorems on almost sure convergence of the periodogram, this paper offers a procedure for detecting and estimating the hidden frequencies, and discusses the consistency and the rates of convergence. Simulation shows very good results, when the spectrum of the noise is not too steep.