Sinusoidal and pulse responses of morphological filters

The amplitude and phase responses of 1-D morphological filters to sinusoidal input signals are analyzed. The studied filters are dilation, erosion, opening, closing, and also open-closing and close-opening. The power spectral density of the filters is also analyzed for i.i.d. (independently identically distributed) Gaussian noise input. Rectangular pulse responses and root signals are discussed and responses to noisy edges are shown. It is shown that the opening filter has wider passband than the other morphological filters studied, and the open-closing filter behaves more consistently in the stopband than the corresponding median-based filters. The effect of the relative phase of the input signal is analyzed. The phase shift is found to change the amplitude response only at some discrete frequencies.<
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