  We present a power spectral analysis of the Crab pulsar's timing noise,
mainly using radio measurements from Jodrell Bank taken over the period
1982-1989. The power spectral analysis is complicated by nonuniform data
sampling and the presence of a steep red power spectrum that can distort power
spectra measurement by causing severe power ``leakage''. We develop a simple
windowing method for computing red noise power spectra of uniformly sampled
data sets and test it on Monte Carlo generated sample realizations of red
power-law noise. We generalize time-domain methods of generating power-law red
noise with even integer spectral indices to the case of noninteger spectral
indices. The Jodrell Bank pulse phase residuals are dense and smooth enough
that an interpolation onto a uniform time series is possible. A windowed power
spectrum is computed revealing a periodic or nearly periodic component with a
period of about 568 days and a 1/f^3 power-law noise component with a noise
strength of 1.24 +/- 0.067 10^{-16} cycles^2/sec^2 over the analysis frequency
range 0.003 - 0.1 cycles/day. This result deviates from past analyses which
characterized the pulse phase timing residuals as either 1/f^4 power-law noise
or a quasiperiodic process. The analysis was checked using the Deeter
polynomial method of power spectrum estimation that was developed for the case
of nonuniform sampling, but has lower spectral resolution. The timing noise is
consistent with a torque noise spectrum rising with analysis frequency as f
implying blue torque noise, a result not predicted by current models of pulsar
timing noise. If the periodic or nearly periodic component is due to a binary
companion, we find a companion mass > 3.2 Earth masses.
