  Conventional Glauber coherent states (CS) can be defined in several
equivalent ways, e.g., by displacing the vacuum or, explicitly, by their
infinite Poissonian expansion in Fock states. It is well known that these
definitions become inequivalent if applied to finite $d$-level systems
(qudits). We present a comparative Wigner-function description of the qudit CS
defined (i) by the action of the truncated displacement operator on the vacuum
and (ii) by the Poissonian expansion in Fock states of the Glauber CS truncated
at $(d-1)$-photon Fock state. These states can be generated from a classical
light by its optical truncation using nonlinear and linear quantum scissors
devices, respectively. We show a surprising effect that a macroscopically
distinguishable superposition of two qudit CS (according to both definitions)
can be generated with high fidelity by displacing the vacuum in the qudit
Hilbert space. If the qudit dimension $d$ is even (odd) then the superposition
state contains Fock states with only odd (even) photon numbers, which can be
referred to as the odd (even) qudit CS or the female (male) Schr\"odinger cat
state. This phenomenon can be interpreted as an interference of a single CS
with its reflection from the highest-energy Fock state of the Hilbert space, as
clearly seen via phase-space interference of the Wigner function. We also
analyze nonclassical properties of the qudit CS including their photon-number
statistics and nonclassical volume of the Wigner function, which is a
quantitative parameter of nonclassicality (quantumness) of states. Finally, we
study optical tomograms, which can be directly measured in the homodyne
detection of the analyzed qudit cat states and enable the complete
reconstructions of their Wigner functions.
