SmallRotation

This module rotates an I/Q vector through an angle whose tangent is a negative power of two in the spirit of the Cordic algorithm,

x_n+1 = x_n - 2^−shift y_n
y_n+1 = y_n + 2^−shift x_n

requiring only additions and bit shifts. The module is intended for interpolation between waypoints where only a small rotation each time step is required. It does not preserve the vector's magnitude, but with these small angles magnitude may be preserved sufficiently well. Although it only implements a single power-of-two rotation, it may be cascaded to better approximate a given rotation, and in fact can be used in a pipelined Cordic implementation.

The module also implements I/Q up/down conversion via the IF parameter – 0 (no frequency translation), 90 (fs/4), 180 (inversion), and 270 (-fs/4).

Ports | Parameters | Notes | Example

Ports

clk	input	The clock input.
reset	input	The reset input.
selin	input	When high, loads the register; when low, performs the rotation of the time step.
sign	input	The rotation direction.
shift	input	The negative power-of-two exponent specifying the tangent of the rotation angle. It is 5 bits wide.
x1, y1	input	The signed I/Q vector input.
x2, y2	output	The signed I/Q vector output, simultaneously clocked.
x2N, y2N	output	The inverted signed I/Q vector output, simultaneously clocked.
selout	output	The `selin` input delayed one clock.

Parameters

wd	16	The bit width of the signed `x1`, `y1`, `x2`, `y2`, `x2N`, and `y2N` ports.
IF	0	The I/Q modulation/demodulation type: 0 – none; 90 – 90-degree CCW modulation; 180 – 180-degree rotation (fs/2); and 270 – 90-degree CW rotation.

Notes

This module does not check for overflow. It is up to the user to ensure that the vector magnitude does not ever exceed the range of the signed bit width.

Example instantiation:

wire	signed	[w-1:0]    Iin, Qin;	// baseband input
wire	signed	[w-1:0]    IFI, IFQ;	// IF output
wire	signed	[w-1:0]    IFIN, IFQN;	// IF output (inverted)
SmallRotation
    #(.wd(w), .IF(270))
    interpolate (
        .clk(clk),		.reset(reset),
        .selin(inputvalid),
        .sign(direction),	.shift(shift),
        .x1(Iin),		.y1(Qin),	// input vector
        .x2(IFI),		.y2(IFQ),	// output vector
        .x2N(IFIN),		.y2N(IFQN),	// output vector (inverted)
        .valid(valid)
    );