filtering harmonics: preserving overall spectrum without simple notch filtering

I'm trying to remve the (mains power) harmonics from the signal shown below. A notch filter would reduce the signal to zero in these bands of peaks, which is too strong as I would like to preserve ('interpolate') the noisy overall shape of the spectrum, across the entire frequency axis. Is there a tool/method/'intelligent' way of doing this?

Answer 1

[Frantz Bouchereau]

Please take a look at the following example:

Wavelet packet harmonic interference removal

The example guides you to use wavelet packets to remove harmonics from a signal. It compares the results with notch filters and shows that the signal spectral shape is better preserved with the wavelet packet technique.