Would I get same results with STFT method (short-time Fourier transform) if I try this?
With all due caution, no in both cases (title and body question). I'll start with the second one.
- Continuous wavelets use all dilations of the mother wavelet, which are not accessed with the STFT
- The STFT is complex in general, and the windowed sine is not.
For the first one: I never tried it, and do not remember having seen it in use, and one should check first whether it satisfies the admissibility condition (first thought: seems OK on 0 in Fourier, and decays at infinity, I'd expect families of synthesis wavelets). You can compute the effects in Fourier using SE.Math: Fourier transform of 1 cycle of sine wave.
However, the sine falls abruptly at its edges, without differentiability, in other words it is not smooth enough. So I would not expect a more interesting interpretation of the scalogram than with other continuous wavelet.
But it could be used as an exploratory tool (analysis) for some specific signals. You can think about hybrid methods as well: try to fit (in more or less robust ways) a parametric sine model, at different scales.
No, since the STFT gives you complex values by not only correlating to sines of different periods, but also cosines.
Depends on what kind of “sense” you want.
A 1 cycle sine wavelet might give you good time resolution for locating a mostly positive to negative zero-crossing waveform slice, but almost no frequency resolution, as the nearest orthogonal sinewave is a whole octave higher.
Add more cycles and you get more frequency resolution, but less time resolution.
A longer windowed DFT provides more information, as most of the basis vectors have more than one cycle, and the complex, or sine & cosine format also adds some phase information to each slice.