In this second paper in a series we present measurements of spectral features of 432 low-redshift (z < 0.1) optical spectra of 261 Type Ia supernovae (SNe Ia) within 20 d of maximum brightness. The data were obtained from 1989 through the end of 2008 as part of the Berkeley SN Ia Program (BSNIP) and are presented in BSNIP I (Silverman et al. 2012). We describe in detail our method of automated, robust spectral feature definition and measurement which expands upon similar previous studies. Using this procedure, we attempt to measure expansion velocities, pseudo-equivalent widths (pEW), spectral feature depths, and fluxes at the centre and endpoints of each of nine major spectral feature complexes. We investigate how velocity and pEW evolve with time and how they correlate with each other. Various spectral classification schemes are employed and quantitative spectral differences among the subclasses are investigated. Several ratios of pEW values are calculated and studied. The so-called Si II ratio, often used as a luminosity indicator (Nugent et al. 1995), is found to be well correlated with the so-called SiFe ratio and anticorrelated with the analogous SSi ratio, confirming the results of previous studies. Furthermore, SNe Ia that show strong evidence for interaction with circumstellar material or an aspherical explosion are found to have the largest near-maximum expansion velocities and pEWs, possibly linking extreme values of spectral observables with specific progenitor or explosion scenarios. [Abridged]
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