  The LISA time-delay-interferometry responses to a gravitational-wave signal
are rewritten in a form that accounts for the motion of the LISA constellation
around the Sun; the responses are given in closed analytic forms valid for any
frequency in the band accessible to LISA. We then present a complete procedure,
based on the principle of maximum likelihood, to search for stellar-mass binary
systems in the LISA data. We define the required optimal filters, the
amplitude-maximized detection statistic (analogous to the F statistic used in
pulsar searches with ground-based interferometers), and discuss the false-alarm
and detection probabilities. We test the procedure in numerical simulations of
gravitational-wave detection.
