Linearly independent (rather than orthogonal) superpositions of harmonically related sine and cosine pulses of durationTform the basis of partial-response signals for parallel data transmission throughKoverlapping channels. The channels are equally spaced byb=1/T, each one carrying a signaling rate2b. With a large number of channels, such systems very closely approach the Nyquist rate. Duality relations are shown to exist between the frequencydomain partial-response (FDPR) signals which will be described and the time-domain partial-response (TDPR)-signals which were defined by Kretzmer. FDPR signals are characterized by: 1) a specific coherent envelope with a gradual roll-off, 2) precisely prescribed amounts of interchannel interference between adjacent channels, and 3) more than two received levels with binary input data, which requires transmitter precoding or receiver decoding. Three FDPR signal classes are defined, and system implementation and performance are discussed with respect to a system utilizing time-limited orthogonal signals. Band occupancies and Gaussian noise performance are given, and sensitivities to various receiver impairments are investigated by computer simulation.