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 , an interval bounded by sparse data sampling and a large glitch .
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 568 \pm 10 days and a 1 / f ^ { 3 } power-law noise component in pulse phase with a noise strength S _ { \phi } = ( 1.24 \pm 0.067 ) \times 10 ^ { -16 } cycles ^ { 2 } / sec ^ { 2 } 
over the analysis frequency range f = 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 mass function f ( M ) = ( 6.8 \pm 2.4 ) \times 10 ^ { -16 } { M } _ { \odot } and a companion mass , M _ { c } \geq 3.2 { M } _ { \oplus } assuming a Crab pulsar mass of 1.4 { M } _ { \odot } .