  The short-time Fourier transform (STFT) usually computes the same number of
frequency components as the frame length while overlapping adjacent time frames
by more than half. As a result, the number of components of a spectrogram
matrix becomes more than twice the signal length, and hence STFT is hardly used
for signal compression. In addition, even if we modify the spectrogram into a
desired one by spectrogram-based signal processing, it is re-changed during the
inversion as long as it is outside the range of STFT. In this paper, to reduce
the number of components of a spectrogram while maintaining the analytical
ability, we propose the frequency-undersampled STFT (FUSTFT), which computes
only half the frequency components. We also present the inversions with and
without the periodic condition, including their different properties. In simple
numerical examples of audio signals, we confirm the validity of FUSTFT and the
inversions.
