Design of a digital down-converter based on the CORDIC algorithm
2026-04-06 06:02:36··#1
Abstract : The basic function of digital downconversion technology is to convert broadband high-speed data stream signals into narrowband low-speed data stream signals for real-time processing by DSPs. This paper studies the design of a digital downconversion system based on the Coordinated Rotating Digital Computer (CORDIC) algorithm. This method can effectively improve signal processing efficiency and reduce hardware design costs. Simulations demonstrate the high efficiency of this method. Keywords : Digital downconversion; CORDIC algorithm; numerically controlled oscillator 0 Introduction Traditional digital downconverters achieve downconversion by multiplying the signal generated by the local NCO (numerically controlled oscillator) with the input signal. Figure 1 shows the functional block diagram of the specific implementation of the digital downconverter. When a digital downconverter (DDC) is working, for each signal sample input to the DDC, the NCO adds a phase increment of 2π×f[sub]Lo[/sub]/f[sub]s[/sub]. Then, using the accumulated phase angle of ∑2π×/f[sub]Lo[/sub]/f[sub]s[/sub] as the address, the sine and cosine values at that address are checked and output to the digital mixer. Multiplying these values by the signal sample completes the digital downconversion. Typically, a digital downconverter multiplies the input signal by the sample values in the corresponding sine and cosine tables. To obtain a high-resolution output signal, the sine and cosine tables become very large, increasing hardware overhead and significantly reducing processing speed. However, calculating sine and cosine values using a Coordinated Rotating Digital Computer (CORDIC) method effectively overcomes this problem, requiring only simple addition, subtraction, and shift operations. 1. CORDIC Algorithm Volther proposed the original CORDIC algorithm, which calculates the multiplication of free coordinate transformations between Cartesian and polar coordinate systems. Walther generalized the CORDIC algorithm to include circular, linear, and hyperbolic transformations. In the circular rotation mode (as shown in Figure 2, formulas (1) and (2) can be derived within the unit circle), for vectorization, a vector with the origin (X<sub>1</sub>, Y<sub>1</sub>) is rotated as follows: by iteratively converging y<sub>k</sub> to 0, the vector finally falls on the x-coordinate. The rotation is to rotate the vector with the origin (X, Y) by 1 angle, and the final value of the angle register called Z converges to 0. The angle is closed, so each iteration only requires 1 addition and 1 binary conversion. [b][align=center]For more details, please click: Design of Digital Down-Converter Based on CORDIC Algorithm[/align][/b]