Let there be a signal f and its low pass filtered signal be fL. Then what can we say about the spectrum of f/fL ?
To be specific I am obtaining fL simply using gaussian blurring in the spatial domain.
If it helps in giving some intuitive explanation, f can be assumed to have large low frequency components and small high frequency components.
Although for me f is a 2D natural image but for simplicity we can take f to be a 1D signal.
From some MATLAB demos it appears that f/fL boosts the high frequency components and dampens the lower frequencies. But cannot find any mathematical or intuitive explanation for this.