Discretization accuracy of continuous signal peak values in limited bandwidth systems

In many real-processes or physically modelled, the signals' peak-values must be calculated. A work's real-scale receives an amplificated impact of the small-scale measurements performed in the laboratory. Therefore, computations the maximum and minimum of the signal values have greater relevance. Likewise, other signal digital processing applications have the same behaviour. The sampling rate contributes significantly to measurement accuracy, and their effects are significant. Often, the measurement error due to the sampling frequency is not quantified. So, there are incomplete measurement specifications. There are no understandable formulations to obtain the possible highest errors due to the continuous signals' discretization, especially when the system bandwidth is limited. This paper presents a comprehensive general analysis based on the relation between the sampling frequency and the highest measurement error for a sinusoidal signal. The relative maximum (highest) errors on the peak values are calculated, with understandable mathematical expressions. Computations of peakvalues' relative maximum errors for post-processing mode have more details by its increased use. Additionally, analyses for signals composited of several harmonics, such as biomechanical signals and waves in hydraulic research laboratories, have specific examples in this paper. Some case studies analyze cubic spline interpolation effects.