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Identifying periodically expressed genes and their subsequent transcriptional circuitry can shed new lights in studying the molecular basis of many diseases including cancer; and subsequently provide potential drug targets to treat them. Classical approaches for detecting periodically expressed transcripts in paradigms such as cell-cycle implicitly assume the given data to be stationary. However, it has been experimentally shown that modulation in the magnitude of gene expression is ubiquitous and defy stationary assumptions. In this paper, we formulate the problem of estimating the frequencies of multicomponent amplitude modulated (AM) signals as a hypothesis testing problem based on a time-dependent extension of the MUSIC algorithm. We subsequently propose a test statistic to detect periodic components in AM time-series. The power of the proposed algorithm is assessed in synthetic test signals and in real cell-cycle gene profiles extracted from microarray data.