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This paper presents a novel completely scaling-free CORDIC algorithm in rotation mode for hyperbolic trajectory. We use most-significant-1 bit detection technique for micro-rotation sequence generation to reduce the number of iterations. By storing the sinh/cosh hyperbolic values at octant boundaries in a ROM, we can extend the range of convergence to the entire coordinate space. Based on this, we propose a pipeline hyperbolic CORDIC processor to implement a direct digital synthesizer (DDS). The DDS is further used to derive an efficient arbitrary waveform generator (AWG), where a pseudo-random number generator modulates the linear increments of phase to produce random phase-modulated waveform. The proposed waveform generator requires only one DDS for generating variety of modulated waveforms, while existing designs require separate DDS units for different type of waveforms, and multiple DDS units are required to generate composite waveforms. Therefore, area complexity of existing designs gets multiplied with the number of different types waveforms they generate, while in case of proposed design that remains unchanged. The proposed AWG when mapped on Xilinx Spartan 2E device, consumes 1076 slices and 2016 4-input LUTs. The proposed AWG involves significantly less area and lower latency, with nearly the same throughput compared to the existing CORDIC-based designs.