  We present timing and spectral analysis of RXTE-PCA observations of SMC X-1
between January 1996 and December 2003. From observations around 30 August 1996
with a time span of $\sim 6$ days, we obtain a precise timing solution for the
source and resolve the eccentricity as 0.00089(6). We find an orbital decay
rate of $\dot P_{orb}/P_{orb} =-3.402(7) \times 10^{-6}$ yr$^{-1}$ which is
close to the previous results. Using our timing analysis and the previous
studies, we construct a $\sim 30$ year long pulse period history of the source.
We show that frequency derivative shows long (i.e. more than a few years) and
short (i.e. order of days) term fluctuations. From the spectral analysis, we
found that all spectral parameters except Hydrogen column density showed no
significant variation with time and X-ray flux. Hydrogen column density is
found to be higher as X-ray flux gets lower. This may be due to the increase in
soft absorption when the pulsar is partially obscured as in Her X-1 or may just
be an artifact of the tail of a soft excess in energy spectrum.
