This paper deals with discrete Fourier transform (DFT)-based modulation and demodulation techniques for affine frequency division multiplexing (AFDM), as opposed to using the discrete affine Fourier transform (DAFT). This allows for a simple (de)modulation process based on the usual DFT, enabling the interpretation of AFDM as a precoded orthogonal frequency division multiplexing (OFDM) waveform. This makes the AFDM modulation scheme backward compatible with existing OFDM systems. Furthermore, the sampling frequency of the modulated AFDM signal can be finely tuned using the suggested methods, whereas the usual DAFT leads to signals sampled at the Nyquist rate. To achieve this, a DFT-based AFDM modulation technique is introduced, along with a corresponding demodulation method. The introduction considers necessary conditions on the AFDM signal parameters, albeit at the cost of reduced flexibility in parameter settings, as only a limited set of parameters can be considered. The validity of the presented method is supported by mathematical developments and proofs, and validated through simulations. Furthermore, a complexity analysis is conducted.