# 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 [PERSON]'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. W 2020 2  
results in an expensive device that can be difficult to replace and repair or needs heavy algorithms that may be unnecessary for smaller devices and complex to implement. While a reliable spectrum representation is necessary for research and development in the scientific community, some applications do not need the most accurate value if the amplitude ratio and the shape of the spectrum are properly reflected with a simpler method [5]. To obtain the Power Spectral Density (PSD) estimation, there are parametric and non-parametric methods [6]. The non-parametric methods, based on the Discrete Fourier Transform (DFT) [7], do not assume that the data have any structure. Some of the non-parametric methods are the periodogram method [8], which is the squared of the absolute value of the DFT and the [PERSON]'s method [9], which benefits from the average of multiple DFT scans. For the parametric methods, it is assumed that the data follows a certain model [10] and they require a certain amount of past information to calculate the PSD properly. Some examples of parametric methods are the autoregressive model (AR) [11], the moving-average model (MA), the autoregressive moving average (ARMA) [11], etc. To retrieve this specific data, the most commonly used system is the Fast Fourier Transform (FFT). FFT transforms a window of discrete samples into its frequency domain representation [12]. However, because of the noise, it is not ideal for locating low power interferences and cannot involve several time packets for better estimation of each frequency component.