This paper provides a time-frequency approach to modeling and estimating the communication channel, and to symbol transmission in multi-carrier wireless systems. The method is based on the evolutionary spectral theory of signals and systems. Multi-carrier systems, such as orthogonal frequency division multiplexing (OFMD) and multi-carrier spread spectrum (MCSS), are very efficient in fast fading channels. However, the basic pulse used in the modulation causes dispersion in time-frequency, complicating inter-symbol and inter-channel interferences. Our time-frequency approach deals separately with the channel modeling and estimation, and with the symbol transmission. Using the properties of the response of the channel to a linear chirp signal it is shown that the typical linear time-variant channel model, needed to characterize multi-path and Doppler, is simplified into a linear time-invariant model of minimal order. Time and Doppler shifts are represented by equivalent time-shifts, and are estimated in a blind fashion from the evolutionary kernel of the received signal. Thus, the linear chirp signal is used as a pilot sequence to characterize the channel. A coherent receiver uses such information to detect the sent symbols. A multi-user OFDM system is obtained using a linear chirp as the modulating signal for basic pulses shifted in time, and by choosing the instantaneous frequency of the linear chirp to be of unity slope for an optimal time-frequency lattice. This optimal lattice increases the transmission rate, diminishes the inter-symbol and inter-channel interference, and provides a new way of looking at OFDM. This approach is extended to MCSS. To illustrate the concepts, simulations, with different signal to noise ratios, are performed. The results are encouraging and worth of further investigation.