The data I chose for this analysis were the maximum daily temperatures for Chapel Hill, North Carolina, in 2010. There are 365 days along the X axis, and various wavelengths ranging from 4 to 64 days along the Y axis. Colors indicate "power" at a given wavelength, for a given time of the year. Significant areas within the hemicurve are circled with a black line.
This analysis shows that there were some 6-day cycles in springtime (near DOY 150) that were statistically significant. Beyond that, not much jumps out: the signal does now have high periodicity. Now I'm looking for better-behaving data.