I'm trying to detect the presence of a sinusoid in 1/f noise conditions using the STFT and the DWT with Haar wavelets. I find this interesting phenomenon that I'm not able to explain (see plot at 1)
My sampling rate is 1200 Hz and the graphs show the one sided response (0-600 Hz). I am using 2 scales for the Wavelet Transform.
My question is, why in the FFT method can I clearly see the blips in about the correct frequency as my simulated data (180 Hz), while in the WT method, the increase in energy is spread visible across all three bands. Shouldn't I see a bright line only in the highpass segment of the second scale?