A former IBM researcher, he is best known for his work with Welch's method to reduce signal noise.

[4][5] At IBM Research he worked in the areas of speech recognition, spectral estimation, queueing theory, seismic signal processing, fast Fourier methodology, pattern recognition, computer and communication system performance modeling, simulation output analysis, and graphics system design.

Welch's paper on the "use of fast Fourier transform for the estimation of power spectra" or Welch's method, has been cited over 5,000 times and remains widely used to reduce noise caused by imperfect and finite data.

[12] The INFORMS Lifetime Professional Achievement Award cites Welch's 62-year career marked by "contributions of fundamental importance not only in the field of computer simulation but also in the broader fields of applied mathematics, applied statistics, computer science."

Since the mid-1970s, states INFORMS, "Peter has made groundbreaking contributions to the theory and practice of computer simulation, to the dissemination of knowledge in that field, and to the development of simulation-related software systems.