<!– SPDX-FileCopyrightText: 2026 Ahmed Imamović SPDX-FileCopyrightText: 2026 Tarik Hamedović SPDX-License-Identifier: CC-BY-SA-4.0 –>

Polar Conversion

The to_polar/ directory contains logic for converting Cartesian (I/Q) signals into polar form. This typically involves computing the magnitude and phase of a complex input signal.

to_polar/to_polar.v

This module converts signed Cartesian input samples into a polar representation consisting of magnitude and phase.

Overview

The module accepts I/Q-style inputs:

  • I (in-phase component),

  • Q (quadrature component),

and produces:

  • magnitude (signal amplitude),

  • phase (signal angle).

Responsibilities

The block performs:

  • conversion from Cartesian coordinates to polar coordinates,

  • magnitude estimation,

  • phase computation,

  • alignment of outputs with the input data stream.

Interface summary

Typical signals:

  • i_clk – system clock,

  • i_reset – synchronous reset,

  • i_ce – clock enable,

  • i_x – in-phase (I) input component,

  • i_y – quadrature (Q) input component,

  • o_mag – output magnitude,

  • o_phase – output phase.

Implementation notes

The conversion from Cartesian to polar form follows:

magnitude = sqrt(I^2 + Q^2)
phase     = atan2(Q, I)

In hardware, this is typically implemented using a CORDIC-based vectoring algorithm rather than direct multiplication and square-root operations.

Depending on the implementation, the module may:

  • reuse an existing CORDIC pipeline in vectoring mode,

  • operate as a pipelined block with fixed latency,

  • propagate a valid/auxiliary signal alongside the data.

Latency and alignment

As with other DSP blocks, the conversion is typically pipelined. Any auxiliary or valid signals should be delayed to match the latency of the magnitude and phase outputs.

Role in the datapath

The polar conversion block is typically used:

  • after downconversion (I/Q generation),

  • before magnitude/phase analysis,

  • in feedback or tracking loops.

It provides a bridge between:

  • Cartesian-domain DSP processing, and

  • magnitude/phase-domain processing.

Structure summary

Conceptually, the processing flow is:

I/Q input
   ↓
vectoring (CORDIC or equivalent)
   ↓
magnitude + phase
   ↓
downstream processing