A.W. Phillips’s discovery that inflation is negatively correlated with unemployment served as a heuristic model for conducting monetary policy; but the flattening of the Phillips curve post-1970 has divided debate on this empirical relation into two camps: “The Phillips curve is alive and well,” and “The Phillips curve is dead.” However, this dichotomy oversimplifies the issue. In this article, we apply spectral analysis to the U.S. inflation rate and unemployment rate to conduct a comprehensive analysis of the Phillips curve in the frequency domain. We find that in the very short run, there is no systemic relationship between inflation and unemployment; in the intermediate run, which includes the business cycle frequency, they are strongly negatively correlated; and in the very long run the Phillips curve is strongly positively sloped. Such an analysis of the frequency domain provides a natural demarcation of frequency bands that allows us to recover the Phillips curve in the time domain by applying band-pass filters. Most importantly, we show how spectral analysis can be used to identify a “supply” (permanent) and a “demand” (nonpermanent) shock in the context of a vector autoregression and that demand shocks drive the Phillips curve. Finally, the phase spectral analysis also shows that despite the existence of the Phillips curve at the business cycle frequency under a demand shock, the monetary policy implications are not obvious, due to the unclear lead-lag relationship between inflation and unemployment.