  The signal of continuous gravitational waves has a longer duration than the
observation period. Even if the waveform in the source frame is monochromatic,
we will observe the waveform with modulated frequencies due to the motion of
the detector. If the source location is unknown, a lot of templates having
different sky positions are required to demodulate the frequency, and the
required huge computational cost restricts the applicable parameter region of
coherent search. In this work, we propose and examine a new method to select
candidates, which reduces the cost of coherent search by following-up only the
selected candidates. As a first step, we consider an idealized situation in
which only a single-detector having 100\% duty cycle is available and its
detector noise is approximated by the stationary Gaussian noise. Also, we
assume the signal has no spindown and the polarization angle, the inclination
angle, and the initial phase are fixed to be $\psi=0$, $\cos\iota=1$, and
$\phi_0=0$, and they are treated as known parameters. We combine several
methods: 1) the short-time Fourier transform with the re-sampled data such that
the Earth motion for the source is canceled in some reference direction, 2) the
excess power search in the Fourier transform of the time series obtained by
picking up the amplitude in a particular frequency bin from the short-time
Fourier transform data, and 3) the deep learning method to further constrain
the source sky position. The computational cost and the detection probability
are estimated. The injection test is carried out to check the validity of the
detection probability. We find that our method is worthy of further study for
analyzing $O(10^7)$sec strain data.
