Move NCO delay inline

This allows the first phase offset to always be `offset`. If a frequency was passed in `__call__()`, the initial phase offset was advanced by the phase increment. This is also more consistent with textbooks and MATLAB.

src/sdr/__init__.py

@@ -23,6 +23,7 @@
 from ._link_budget import *
 from ._measurement import *
 from ._modulation import *
+from ._nco import *
 from ._probability import *
 from ._sequence import *
 from ._signal import *

src/sdr/_synchronization/_nco.py → src/sdr/_nco.py

@@ -9,7 +9,7 @@
 import numpy.typing as npt
 from typing_extensions import Literal
 
-from .._helper import export
+from ._helper import export
 
 
 @export
@@ -24,19 +24,19 @@ class NCO:
                           constant           constant
                          increment            offset    p[n]
                              |                  |         |
-                    +----+   v                  v         v   +--------+
-            f[n] -->| K0 |-->@--------------+-->@-------->@-->| e^(j.) |--> y[n]
-                    +----+   ^              |                 +--------+
-                             |   +------+   |
-                             +---| z^-1 |<--+
-                                 +------+
+                    +----+   v   +------+       v         v   +-----------+
+            f[n] -->| K0 |-->@-->| z^-1 |---+-->@-------->@-->| output(.) |--> y[n]
+                    +----+   ^   +------+   |                 +-----------+
+                             |              |
+                             +--------------+
 
             f[n] = Input frequency signal (radians/sample)
             p[n] = Input phase signal (radians)
             y[n] = Output complex signal
             K0 = NCO gain
             increment = Constant phase accumulation (radians/sample)
             offset = Absolute phase offset (radians)
+            output(.) = Phase-to-output mapping function, either: ., sin(.), cos(.), exp(j .)
             z^-1 = Unit delay
             @ = Adder
 
@@ -115,13 +115,10 @@ def reset(self):
         r"""
         Resets the NCO.
 
-        The internal accumulator is set to $-\omega$ radians such that the phase of the first output sample
-        is $\theta$ radians.
-
         Examples:
             See the :ref:`phase-locked-loop` example.
         """
-        self._z_prev = -self.increment
+        self._z_prev = 0.0
 
     @overload
     def __call__(
@@ -179,10 +176,10 @@ def __call__(
         z = freq * self.gain + self.increment
         z = np.atleast_1d(z)
 
-        # Increment the first sample by the previous output. Then run a cumulative sum over all samples.
-        z[0] += self._z_prev
+        # Insert the previous output in front of the current input. Then run a cumulative sum over all samples.
+        z = np.insert(z, 0, self._z_prev)
         z = np.cumsum(z)
-        self._z_prev = z[-1]
+        z, self._z_prev = z[0:-1], z[-1]
 
         # Add the absolute offset to every sample
         y = z + self.offset + phase

src/sdr/_synchronization/__init__.py

@@ -3,6 +3,5 @@
 """
 from ._agc import *
 from ._loop_filter import *
-from ._nco import *
 from ._phase_error import *
 from ._pll import *