  We present a model for one-dimensional (1D) matter power spectra in redshift
space as estimated from data provided along individual lines of sight. We
derive analytic expressions for these power spectra in the linear and nonlinear
regimes, focusing on redshift distortions arising from peculiar velocities. In
the linear regime, redshift distortions enhance the 1D power spectra only on
small scales, and do not affect the power on large scales. This is in contrast
to the effect of distortions on three-dimensional (3D) power spectra estimated
from data in 3D space, where the enhancement is independent of scale. For CDM
cosmologies, the 1D power spectra in redshift and real space are similar for
wavenumbers $q<0.1h/Mpc$ where both have a spectral index close to unity,
independent of the details of the 3D power spectrum. Nonlinear corrections
drive the 1D power spectrum in redshift space into a nearly universal shape
over scale $q<10h/Mpc$, and suppress the power on small scales as a result of
the strong velocity shear and random motions. The redshift space, 1D power
spectrum is mostly sensitive to the amplitude of the initial density
perturbations. Our results are useful in particular for power spectra computed
from the SDSS quasars sample.
