Window Function Shape Independent Short Time Fourier Transform and Efficient Signal Reconstruction from Time Frequency Distribution
摘要
Time–frequency transform is very important in terms of obtaining the change of frequency content over time in non-stationary signals. To achieve this, window functions are widely used in existing methods. The type of window function used affects the time and frequency resolutions achieved. In this study, window function shape independent Short Time Fourier Transform is presented to obtain time–frequency distribution. Short Time Fourier Transform is implemented using a unit amplitude rectangular window function whose length is defined according to frequency. The unit amplitude rectangular window function allows analysis independently of the shape of the window function and obtaining the time–frequency distribution with pure sinusoidal frequencies without affecting the time energy concentration of analyzed signal. Additionally, the edge effects of windowing are eliminated by determining the length of the window function according to frequency. Obtaining time–frequency analysis with the proposed method is simpler than existing methods, the original signal is effectively reconstructed by the inverse transform for the entire signal duration and for custom interval of interest. The effectiveness of the proposed method is tested by synthetic and real-world signals and compared with existing methods.