Cover: Analytic evaluation of the Fourier coefficients of a clipped periodic function.

Analytic evaluation of the Fourier coefficients of a clipped periodic function.

Published 1965

Purchase Print Copy

 Format Price
Add to Cart Paperback45 pages $23.00

For periodic input u(t), a time representation c(t) for the clipper is obtained such that the output y(t) = c(t) u(t). The Fourier coefficients of y(t) are obtained in terms of the Fourier coefficients of both c(t) and u(t). For light clipping, the Fourier coefficients of y(t) equal the Fourier coefficients of u(t) plus a small correction factor of the order of the percentage of time the signal exceeds clipping limits. An exact expression for the correction factor is obtained which may require numerical solutions. Some algorithms for obtaining numerical solutions are discussed. 40 pp.

This report is part of the RAND paper series. The paper was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.