In this paper, algorithms of power spectral density (PSD) approaches applied to the detection of pileup problem associated with gamma ray signal analysis. These techniques namely are: periodogram, Welch, Multiwindow, Yule-walker, Burg, covariance, and multiple signal classification (MUSIC) algorithm. Transform domain based methods are also studied, such as Fast Fourier Transform (FFT), Walsh-Hadamard, Hilbert, and Hankel transform. In both cases, the resultant extracted features are fed to train an artificial neural network (ANN) expert system using the Error BackPropagation Training (EBPT) algorithm. A comparison between studied algorithms is performed in terms of percentage recognition rate of original signal and execution time using the matlab environment. Studies showed that MUSIC and Welch in PSD methods have the highest recognition rate. Also, Hankel and walshhadamard in transform domain based methods have been given the highest recognition rate, under the application of different types of noise to the original signal, and FFT algorithm has the least execution time in all methods.1. Introduction