  We present a multimode theory of non-Gaussian operation induced by an
imperfect on/off-type photon detector on a splitted beam from a wideband
squeezed light. The events are defined for finite time duration $T$ in the time
domain. The non-Gaussian output state is measured by the homodyne detector with
finite bandwidh $B$. Under this time- and band-limitation to the quantm states,
we develop a formalism to evaluate the frequency mode matching between the
on/off trigger channel and the conditional signal beam in the homodyne channel.
Our formalism is applied to the CW and pulsed schemes. We explicitly calculate
the Wigner function of the conditional non-Gaussian output state in a realistic
situation. Good mode matching is achieved for $BT\alt1$, where the discreteness
of modes becomes prominant, and only a few modes become dominant both in the
on/off and the homodyne channels. If the trigger beam is projected nearly onto
the single photon state in the most dominant mode in this regime, the most
striking non-classical effect will be observed in the homodyne statistics. The
increase of $BT$ and the dark counts degrades the non-classical effect.
