In this paper, we present the superposition of chirp waveforms for simultaneous wireless information and power transfer (SWIPT) applications. Exploiting the chirp waveform characteristics enables us to superimpose multiple chirps, thereby allowing transmission of the same number of waveforms over less bandwidth. This enables us to perform subband selection when operating over set of orthogonal subbands. Furthermore, we consider a user equipped with a diplexer-based integrated receiver (DIR), which enables to extract radio frequency power and decode information from the same signal without splitting. Thereby, incorporating chirp superposition and subband selection, a transmission scheme is proposed to exploit both the diode's nonlinearity and frequency diversity. We derive novel closed-form analytical expressions of the average harvested energy (HE) via transmission of superimposed chirp over selected subbands based on tools from order statistics. We also analyze the downlink information rate achieved at the user. Through our analytical and numerical results, for the considered system setup, we show that superimposed chirp-based SWIPT provides an improvement of 30$\%$ in average HE performance as compared to multisine waveforms consisting of a set of fixed-frequency cosine signals, improves the minimum level of HE in a multiuser network, and extends the operating range of energy transfer as compared to fixed-frequency waveforms. Furthermore, we illustrate that the inclusion of DIR at the receiver for SWIPT enlarges the energy-information transfer region when compared to the widely considered power splitting receiver.