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An analytical tool is presented in order to analyze and elucidate the impact of the optical filter position and steepness on eye opening in an optical vestigial sideband system with direct detection. It is shown that bit sequences containing solitarities (i.e., bit sequences containing single bits surrounded by several bits of opposite kind) are the major bit sequences to cause eye closure. In comparison with double-sideband modulation format, an eye opening penalty of 3-6 dB can be achieved with vestigial sideband format. The analytical tool helps to understand the interrelation between the bit sequence properties and the optical filter parameters.