De-noising the CN Tower lightning current signal using short term Fourier transform-based spectral substraction

Abstract

The CN Tower is a transmission tower and it is not unexpected that recorded lightning current signals be corrupted by noise. The existence of noise may affect the calculation of current waveform parameters (current peak, 10-90% risetime to current peak, maximum steepness, and pulse width at half value of current peak). But accurate statistics of current waveform parameters are required to design systems for the protection of structures and devices, especially those with electrical and electronic components, exposed to hazards of lightning. Since more electrical devices are used nowadays, lightning protection becomes more important. So to determine accurate statistics of current waveform parameters, the interfering noise must be removed. In this thesis we describe a technique for de-noising the CN Tower lightning current by modifying its Fourier Transform (FT) where a simulated current waveform (Heidler function) is used to represent the lightning current signal.The limitations of Discrete Fourier Transform (DFT) for removal of non-stationary noise signals, including the noise connected with CN Tower lightning current signals and its properties are discussed. The Short Term Fourier Transform (STFT) is explored to analyze non-stationary signals and to deal with the limitations of DFT. Last of all, an STFT-based Spectral Subtraction method is developed to denoise the CN Tower lightning current signal. In order to evaluate the Spectral Subtraction method, a simulated current derivative waveform ( obtained by differentiating Heidler function) is artificially distorted by a noise signal measured at the CN Tower in the absence of lightning. The Spectral Subtraction method is then used to de-noise the distorted waveform. The de-noised waveform proved to be very close to the original simulated waveform. A signal-peak to noise-peak ratio (SPNPR) of the CN Tower lightning current signal is defined and calculated before and after the de-noising process. For example, for a typical measured current derivative signal, the SPNPR before de-noising is 7.27, and after de-noising it becomes 151.30. Similarly for its current waveform (obtained by numerical integration) the SPNPR before de-noising is 20,16 and it becomes 361.39 after de-noising. Statistics of current waveform parameters are obtained from the de-noised waveforms. The Spectral Subtraction method is also applied for de-noising the electric and magnetic field waveforms generated by lightning to the CN Tower which enables the calculation of their waveform parameters.