Simplified Welch Algorithm for Spectrum Monitoring

Abstract

Power Spectral Density (PSD) is an essential representation of the signal spectrum that depicts the power measurement content versus frequency. PSD is typically used to characterize broadband random signals and has a variety of usages in many fields like physics, engineering, biomedical, etc. This paper proposes a simple and practical method to estimate the PSD based on the Welch algorithm for spectrum monitoring. The proposed method can be easily implemented in most of software-based systems or low-level Field-Programmable Gate Arrays (FPGAs) and yields a smooth overview of the spectrum. The original Welch method utilizes the average of the amplitude squared of the previous Fast Fourier Transform (FFT) samples for better estimation of frequency components and noise reduction. Replacing the simple moving average with a weighted moving average can significantly reduce the complexity of the Welch’s method. In this way, the amount of required Random Access Memory (RAM) is reduced from K (where K is the number of FFT packets in averaging) to one. This new method allows users to adjust the dependency of the PSD on the previous observed FFTs and its smoothness by setting only one feedback parameter without any hardware change. The obtained results show that the algorithm gives a clear spectrum, even in the noisy situation because of the significant Signal to Noise Ratio (SNR) enhancement. The trade-off between spectrum accuracy and time convergence of the modified algorithm is also fully analysed. In addition, a simple solution based on Xilinx Intellectual Property (IP), which converts the proposed method to a practical spectrum analyzer device, is presented. This modified algorithm is validated by comparing it with two standard and reliable spectrum analyzers, Rohde & Schwarz (R&S) and Tektronix RSA600. The modified design can track any signal type as the other spectrum analyzers, and it has better performance in situations where the power of the desired signal is weak or where the signal is mixed with the background noise. It can display the spectrum when the input signal power is 5 dB lower than the visible threshold level of R&S and Tektronix. In both narrowband and wideband scenarios, the new implemented design can still display frequency components 5 dB higher than the noise, while the output spectrum of other analyzers is completely covered by noise.

Keywords

• Welch method
• spectrum monitoring
• power spectral density
• fast Fourier transform
• low complexity
• embedded design