We investigate the energy sources of the infrared (IR) emission and their relation to the radio continuum emission at various spatial scales within the Scd galaxy M33. We use the wavelet transform to analyze IR data at the Spitzer wavelengths of 24, 70, and 160$\mu$m, as well as recent radio continuum data at 3.6cm and 20cm. An H$\alpha$ map serves as a tracer of the star forming regions and as an indicator of the thermal radio emission. We find that the dominant scale of the 70$\mu$m emission is larger than that of the 24$\mu$m emission, while the 160$\mu$m emission shows a smooth wavelet spectrum. The radio and H$\alpha$ maps are well correlated with all 3 MIPS maps, although their correlations with the 160$\mu$m map are weaker. After subtracting the bright HII regions, the 24 and 70$\mu$m maps show weaker correlations with the 20cm map than with the 3.6cm map at most scales. We also find a strong correlation between the 3.6cm and H$\alpha$ emission at all scales. Comparing the results with and without the bright HII regions, we conclude that the IR emission is influenced by young, massive stars increasingly with decreasing wavelength from 160 to 24$\mu$m. The radio-IR correlations indicate that the warm dust-thermal radio correlation is stronger than the cold dust-nonthermal radio correlation at scales smaller than 4kpc. A perfect 3.6cm-H$\alpha$ correlation implies that extinction has no significant effect on H$\alpha$ emitting structures.

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