The effects of computational complexity on the characteristics of a physical signal that is reconstructed from its representation of sampled data are analyzed. It is found that a more complex algorithm does not only require longer time to implement, but also yields an erroneous reconstruction. The reconstruction suffers from contrast degradation, phase shifts, and attenuation of details relative to the true signal. These unwanted effects are caused by the existence of spurious frequencies in the computed spectrum due to rounding‐off errors. The amplitude distribution of the spurious frequencies across the spectral bandwidth strongly depends on the number of data points handled and on the complexity of the particular reconstruction algorithm employed. Since the floating point representation of numbers in a computer is always finite, an upper limit exists in the maximum number of additions or multiplications required to compute a quantity reliably without errors.