A high precision method for mapping phase to amplitude in direct digital synthesis and its hardware implementation

Area of Science:

• Digital Signal Processing
• Computer Engineering
• Algorithm Development

Background:

• Direct digital synthesis (DDS) requires algorithms to map phase to amplitude.
• The Coordinate Rotation Digital Computer (CORDIC) algorithm is a high-precision standard for DDS with over 14 output bits, simultaneously providing in-phase and quadrature components.

Purpose of the Study:

• To propose a novel Taylor expansion-based method for phase-to-amplitude mapping in DDS.
• To enable simultaneous calculation of in-phase and quadrature components.
• To compare the proposed method's performance against the CORDIC algorithm.

Main Methods:

• A Taylor expansion-based algorithm was developed for phase-to-amplitude conversion.
• Numerical simulations were performed using Matlab and Quartus with double and finite bit data formats.
• Hardware implementation was conducted on a Field Programmable Gate Array (FPGA).

Main Results:

• The Taylor expansion method demonstrated higher precision than the CORDIC algorithm.
• The proposed method utilized fewer logic elements in hardware implementation.
• Simulations confirmed performance across different data formats.

Conclusions:

• The Taylor expansion method is a superior alternative to CORDIC for DDS phase-to-amplitude mapping.
• This method offers improved precision and resource efficiency for DDS applications.
• The findings support the adoption of Taylor expansion for high-performance digital synthesis.