RIAA EQ improves audio

Audio result using spline differentiation:
The music sample without RIAA EQ reproduction filter:
http://kakyoism.webhop.net/~kakyo/0.report/43.RIAA_EQ/audio_mitac_stereo_v2_algo7_music.wav

The music sample processed with RIAA EQ reproduction filter:
http://kakyoism.webhop.net/~kakyo/0.report/43.RIAA_EQ/audio_mitac_stereo_v2_algo14_RIAA.wav

Audio result using wavelet differentiation
The music sample generated with wavelet differentiation after resampling, without RIAA EQ:
http://kakyoism.webhop.net/~kakyo/0.report/43.RIAA_EQ/audio_mitac_stereo_v2_algo15.wav

The signal generated with RIAA EQ
http://kakyoism.webhop.net/~kakyo/0.report/43.RIAA_EQ/audio_mitac_stereo_v2_algo15_RIAA.wav

Signals above are all resampled to 48kHz.

As we can notice, the crackle noise is not reduced using spline differentiation, but the musical signal's spectral balance is restored after applying RIAA reproduction EQ. Using wavelet differentiation is somehow similar to apply a low-pass filtering (the non-EQ'ed version), after applying the RIAA reproduction filter, the output signal's spectral balance can be heard as not restored, still sounds like low-passed.

Summary
Wavelet differentiation offers better crackle-noise reduction, but it is unknown yet how to counteract its strong low-pass effect.

Other differentiation methods are more susceptible to crackle noise (local signal noise) but maintain the spectral balance.

Question

1. Which way do we go: wavelet or regular differentiation?
2. Can we derive the equivalent filter spec that the wavelet differentiation introduces?