A Time-Series Data Analyzing System Using a New Time-Frequency Transform

A new time-frequency transform, whose resulting spectrogram has the best frequency resolution among that of existing transforms, is employed to construct a simple system of data acquisition and analysis. The transform employs an iterative and diffusive filter to remove the non-sinusoidal part. The spectrum of the sinusoidal part is evaluated by a strategy involving a Fast Fourier Transform (FFT). By imposing a Gaussian window centered at a given frequency on the spectrum, a band-passed data is obtained which is just the corresponding mode or real part of the transform. Finally, the corresponding amplitude is obtained via the Hilbert transform. A commercial microphone plugged into a notebook computer properly equipped with necessary software and the transform form a complete portable system. Two tests show that the system is a new tool to look into detailed information of a complicated data string formed from a single or multiple sources.