  We describe an algorithm for the extraction of the angular power spectrum of
an intensity field, such as the cosmic microwave background (CMB), from
interferometer data. This new method, based on the gridding of interferometer
visibilities in the aperture plane followed by a maximum likelihood solution
for bandpowers, is much faster than direct likelihood analysis of the
visibilities, and deals with foreground radio sources, multiple pointings, and
differencing. The gridded aperture-plane estimators are also used to construct
Wiener-filtered images using the signal and noise covariance matrices used in
the likelihood analysis. Results are shown for simulated data. The method has
been used to determine the power spectrum of the cosmic microwave background
from observations with the Cosmic Background Imager, and the results are given
in companion papers.
