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This paper analyzes the energy detector that is commonly used to detect the presence of unknown information-bearing signals. The algorithm simply compares the energy (or power) in a sliding window to a threshold. The analysis allows for arbitrary spectra of information-bearing signal and noise processes. It yields two equations that relate five variables/parameters: the probability of false detection, the probability of missing a detection, window length, detection threshold, and signal-to-noise ratio (SNR). The probability density function of the detection variable is shown to be approximately Gamma distributed. All of the theoretical expressions and approximations are substantiated with simulation results.