The linear frequency swept light source is a critical device for several sensing applications, including FMCW LiDAR, with which the maximum sensing distance is determined by the coherence length of the light source and the spatial resolution is limited by the frequency scan nonlinearity. Here, we report what we believe to be a novel approach to generate highly coherent optical linear frequency sweeps (LFS) with a Fourier domain mode-locked (FDML) opto-electronic oscillator (OEO) deploying carrier suppressed single sideband (CS-SSB) modulation enabled by a dual-parallel Mach-Zehnder modulator (DP-MZM), with the coherence length determined by the fixed frequency laser used in the OEO, without the need of an expensive high-speed arbitrary waveform generator (AWG). Concurrently, a radio frequency (RF) LFS synchronized with the optical LFS is also generated with the FDML OEO. We obtained a nearly ideal optical LFS around 1550 nm with a side-mode suppression ratio of 27.4 dB, by controlling the bias point and the RF power feeding back to the DP-MZM in the OEO loop. The resulting dual optical and RF LFS' achieved a chirp rate of 27.27 MHz/µs and a frequency tuning range of 0.6 GHz, which can be extended to 142 MHz/µs and 2.0 GHz, respectively by reducing the size of the tunable ring filter circuit inside the OEO loop. By using pre-distortion method, the residual nonlinearity is reduced to 1.9881 × 10-5, and the root mean square (RMS) value of the frequency swept nonlinearity is less than 0.764 MHz. Our dual optical and RF LFS generation with a CS-SSB FDML-OEO has the advantages of long coherence length, high tuning speed, excellent frequency tuning linearity and repeatability, and potentially low cost, which can be used to make a dual optical and RF FMCW ranging system (LiDAR and RADAR) and are attractive for many applications, such as 3D sensing and autonomous driving, as well as optical frequency domain reflectometer (OFDR), and other applications requiring fast and reliable linear frequency sweeps in either optical and RF domains.