I have a predicted mel log spectrogram $S$ and I want to add a noise signal $\eta$ to it.
S = log(mel-filterbank(abs/real part of(stft(signal)))
The naive way would be to approximate the linear spectrogram, add the noise signal and then apply the log mel transform again. However, it seems to me that this approximation adds unwanted artifacts which would not show up in a natural signal.
Is there a way to combine the signal without doing the approximation, given that I want the combined signal to be a mel log spectrogram too?