cordicangle

CORDIC-based phase angle

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Syntax

theta = cordicangle(c) theta = cordicangle(c,niters)

Description

theta = cordicangle(c) returns the phase angles, in radians, of matrix c, which contains complex elements.

theta = cordicangle(c,niters) performs niters iterations of the algorithm.

Input Arguments

c

Matrix of complex numbers

niters

niters is the number of iterations the CORDIC algorithm performs. This argument is optional. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters, or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is the word length of r or one less than the word length of theta, whichever is smaller. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results but also increases the expense of the computation and adds latency.

Output Arguments

theta

theta contains the polar coordinates angle values, which are in the range [–pi, pi] radians. If x and y are floating-point, then theta has the same data type as x and y. Otherwise, theta is a fixed-point data type with the same word length as x and y and with a best-precision fraction length for the [-pi, pi] range.

Examples

Phase angle for double-valued input and for fixed-point-valued input.

dblRandomVals = complex(rand(5,4), rand(5,4));
theta_dbl_ref = angle(dblRandomVals);
theta_dbl_cdc = cordicangle(dblRandomVals)
fxpRandomVals = fi(dblRandomVals);
theta_fxp_cdc = cordicangle(fxpRandomVals) 

theta_dbl_cdc =

    1.0422    1.0987    1.2536    0.6122
    0.5893    0.8874    0.3580    0.2020
    0.5840    0.2113    0.8933    0.6355
    0.7212    0.2074    0.9820    0.8110
    1.3640    0.3288    1.4434    1.1291

theta_fxp_cdc =
 
    1.0422    1.0989    1.2534    0.6123
    0.5894    0.8872    0.3579    0.2019
    0.5840    0.2112    0.8931    0.6357
    0.7212    0.2075    0.9819    0.8110
    1.3640    0.3289    1.4434    1.1289

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 16
        FractionLength: 13

More About

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CORDIC

CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see References). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions.

Increasing the number of CORDIC iterations can produce more accurate results, but doing so increases the expense of the computation and adds latency.