Tao, R., Li, Y.L., Wang, Y.: Short-time fractional fourier transform and its applications. Wei, D., Li, Y.M.: Generalized sampling expansions with multiple sampling rates for lowpass and bandpass signals in the fractional Fourier transform domain. Miao, H., Zhang, F., Tao, R.: Fractional Fourier analysis using the Möbius inversion formula. Juillerat, N., Müller Arisona, S., Schubiger-banz, S.: Enhancing the quality of audio transformations using the multi-scale short time Fourier transform. pp 56–73 (2009)īonada, J.: Automatic technique in frequency domain for near-lossless time-scale modification of audio. Pihlajamäki, T.: Multi-resolution short-time Fourier transform implementation of directional audio coding. In: 45th International Conference: Applications of Time-Frequency Processing in Audio. Gnann, V., Becker, J.: Signal reconstruction from multiresolution STFT magnitudes with mutual initialization. Pei, S.C., Huang, S.G.: STFT with adaptive window width based on the chirp rate. Xie, H., Lin, J., Lei, Y., Liao, Y.: Fast-varying AM–FM components extraction based on an adaptive STFT. Kara, S., Içer, S., Erdogan, N.: Spectral broadening of lower extremity venous Doppler signals using STFT and AR modeling. Zhang, W.Y., Hao, T., Chang, Y., Zhao, Y.H.: Time-frequency analysis of enhanced GPR detection of RF tagged buried plastic pipes. Liu, H., Li, L., Ma, J.: Rolling Bearing Fault Diagnosis Based on STFT-Deep Learning and Sound Signals. Zhang, H., Hua, G., Yu, L., Cai, Y., Bi, G.: Underdetermined blind separation of overlapped speech mixtures in time-frequency domain with estimated number of sources. Xing, F., Chen, H., Xie, S., Yao, J.: Ultrafast three-dimensional surface imaging based on short-time Fourier transform. It could also be considered a variant of the CQT and a special case of multi-resolution STFT. The analysis in this paper shows that the proposed transform can be expressed as a variant of STFT, and as an alternative discretization of the CWT. Finally, the representations of a period chirp and an electrocardiogram signal in the time–frequency domain and the time-scale domain are obtained and used to compare the different techniques. Fourthly, the analogies with multi-resolution STFT are analyzed. Thirdly, the constant-Q transform (CQT) is analyzed showing the similarities in the equations of both transforms, and the differences in terms of how the sweep is carried out are discussed. Secondly, the continuous wavelet transform (CWT) equation is used to formulate the transform in the continuous time using wavelet theory and to discretize it. Firstly, the formulation is revisited from the point of view of the STFT and some improvements are proposed. In this paper, we revisit that formulation, showing its similarity to existing techniques. Recently, we proposed a variant of that transform which fixes the window size in the frequency domain (STFT-FD). However, the standard STFT has the drawback of having a fixed window size. The short-time Fourier transform (STFT) is extensively used to convert signals from the time-domain into the time–frequency domain.
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