An existing Fast Fourier Transform (FFT) algorithm with small spectrum error is modified to construct the two-dimensional spectrogram of a new Short Time Fourier Transform (SFTF). Before the data string is treated by the FFT algorithm, an iterative filter via Gaussian smoothing is applied to remove the undesired non-sinusoidal part and wave components whose frequencies are not in the band of interest. The proposed short time
Fourier spectrum is evaluated in a rectangular window whose end points are
defined by zero crossing positions of the high frequency data. After
sweeping all the designed windows and designating the corresponding
spectrums to the center of the window, a two-dimensional time-frequency
data set is constructed. This two-dimensional spectrogram is an approach
more direct than that of the Gabor transform and is somewhat more
complicated than that of the existing STFT. As compared with these
transforms, the proposed transform does not modify the data as the former
one does and every window has zero ends unlike the latter. A test case
examines the beat wave formed by 3 known sine waves and shows that the
zero crossing point can not be put at the region where the approximate
amplitude of the beat attains local minimum value. Two additional test cases are employed to show the capability of capturing local properties of this new time-frequency analysis. It seems that, because of the uncertainty of the time-frequency analysis via the Fourier series expansion and the non-uniform window width, the resulting time-spectrum plot evaluated via a relatively short window width arrangement shows a faded characteristic in spite of the capability of capturing temporary properties. For a sufficiently large window size, the plot shows a steady and clear quality but loses the capability of capturing temporary properties.