CORDIC Algorithm for Computing Transcendental Functions

The CORDIC (Coordinate Rotation Digital Computer) algorithm is an efficient method for computing transcendental functions such as trigonometric, exponential, and logarithmic functions, making it particularly suitable for hardware implementation. This algorithm avoids complex multiplication operations by using predefined rotation angles and iterative approximation, accomplishing calculations with only shift and addition operations.

When implementing the CORDIC algorithm in MATLAB, the following steps are typically required: Parameter Initialization: Set the number of iterations, rotation angle lookup table, and input values (such as angles or coordinates). Iterative Computation: Gradually adjust coordinate values based on rotation direction and current angle. Each iteration updates intermediate results using bit-shifts and additions. Result Correction: Due to the scaling factor introduced during iterations, final results require normalization. In MATLAB, this can be implemented using predefined rotation sequences and vectorized operations for efficiency.

The advantage of the CORDIC algorithm lies in its hardware-friendly nature, making it suitable for FPGA or embedded system implementations. After successful MATLAB simulation, the algorithm's correctness can be verified, providing a reference for subsequent hardware migration. This algorithm finds widespread applications in digital signal processing, communication systems, and computer graphics. MATLAB implementation typically involves creating modular functions for rotation modes (circular, linear, hyperbolic) and using fixed-point arithmetic simulations for hardware accuracy validation.