Bounded uncorrelated signal impairment deconvolution for total signal impairment extrapolation

Methods and systems are described for analyzing signal impairments using a test and measurement instrument. A method may include decomposing aggregate signal impairments into signal impairments that are correlated and uncorrelated to an acquired data pattern. The uncorrelated signal impairments may be further decomposed into periodic signal impairments (e.g., PJ) and non-periodic uncorrelated signal impairments. A PDF of the non-periodic uncorrelated signal impairments may be mathematically integrated, thereby producing an estimated cumulative distribution function (CDF) curve. Random signal impairments may be estimated as an unbound Gaussian distribution. The CDF curve of the non-periodic uncorrelated signal impairments and the unbound Gaussian distribution may be plotted in Q-space on a display device. Non-periodic bounded uncorrelated signal impairments (e.g., NP-BUJ) PDF may then be isolated. Bounded uncorrelated signal impairments PDF may then be synthesized. Complete uncorrelated signal impairments PDF may be synthesized. A synthesis of the decomposed components can be performed at a user-defined bit error rate to generate the total estimated jitter (e.g., TJ@BER or TN@BER).