Aims. 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. Methods. We use the data at the Spitzer wavelengths of 24, 70, and 160 µm, as well as recent radio continuum maps at 3.6 cm and 20 cm observed with the 100–m Effelsberg telescope and VLA, respectively. We use the wavelet transform of these maps to a) separate the diffuse emission components from compact sources, b) compare the emission at different wavelengths, and c) study the radio–IR correlation at various spatial scales. An Hα map serves as a tracer of the star forming regions and as an indicator of the thermal radio emission. Results. The bright HII regions affect the wavelet spectra causing dominant small scales or decreasing trends towards the larger scales. The dominant scale of the 70 µm emission is larger than that of the 24 µm emission, while the 160 µm emission shows a smooth wavelet spectrum. The radio and Hα maps are well correlated with all 3 MIPS maps, although their correlations with the 160 µm map are weaker. After subtracting the bright HII regions, the 24 and 70 µm maps show weaker correlations with the 20 cm map than with the 3.6 cm map at most scales. We also find a strong correlation between the 3.6 cm and Hα emission at all scales. Conclusions. Comparing the results with and without the bright HII regions, we conclude that the IR emissio
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