diff --git a/src/scgenerator/noise.py b/src/scgenerator/noise.py
index 8da2eba..0382502 100644
--- a/src/scgenerator/noise.py
+++ b/src/scgenerator/noise.py
@@ -19,9 +19,10 @@ class NoiseMeasurement:
 
     @classmethod
     def window_function(cls, name: str):
+        if name in cls._window_functions:
+            raise ValueError(f"a function labeled {name!r} has already been registered")
+
         def wrapper(func: Callable[[int], np.ndarray]):
-            if name in cls._window_functions:
-                raise ValueError(f"a function labeled {name!r} has already been registered")
             cls._window_functions[name] = func
             return func
 
@@ -45,7 +46,7 @@ class NoiseMeasurement:
         cls,
         signal: Sequence[float],
         dt: float,
-        window: str = "Hann",
+        window: str | None = "Hann",
         num_segments: int = 1,
         force_no_dc: bool = True,
     ) -> NoiseMeasurement:
@@ -60,9 +61,10 @@ class NoiseMeasurement:
             the 0 frequency bin of the PSD
         window : str | None, optional
             window to use on the input data to avoid leakage. Possible values are
-            'Square' (default), 'Bartlett', 'Welch' and 'Hann'. You may register your own window
+            'Square', 'Bartlett', 'Welch' and 'Hann' (default). You may register your own window
             function by using `NoiseMeasurement.window_function` decorator, and use the name
             you gave it as this argument.
+            `None` is an alias for square, since in that case, no windowing is performed.
         num_segments : int, optional
             number of segments to cut the signal into. This will trade lower frequency information
             for better variance of the estimated PSD. The default 1 means no cutting.
@@ -83,14 +85,14 @@ class NoiseMeasurement:
                 f"window function {window!r} not found. "
                 f"Possible values are {set(cls._window_functions)}"
             ) from None
-        window_correction = np.sum(window_arr**2) / n
+        window_correction = np.sum(window_arr**2)
         signal_segments = signal_segments * window_arr
 
         if force_no_dc:
             signal_segments = (signal_segments.T - signal_segments.mean(axis=1)).T
 
         freq = np.fft.rfftfreq(n, dt)
-        psd = np.fft.rfft(signal_segments) * np.sqrt(dt / n)
+        psd = np.fft.rfft(signal_segments) * np.sqrt(dt)
         phase = math.mean_angle(psd)
         psd = psd.real**2 + psd.imag**2
         psd[..., 1:-1] *= 2
@@ -220,7 +222,7 @@ class NoiseMeasurement:
 
         # DC is assumed to be always positive
         # Nyquist frequency has an unknowable phase
-        amp[-1] *= self.rng.choice((1, -1))
+        # amp[-1] *= self.rng.choice((1, -1))
         amp[1:-1] *= np.exp(1j * phase)
 
         signal = np.fft.irfft(amp) * np.sqrt(nt / dt)
@@ -248,6 +250,9 @@ def square_window(n: int):
     return np.ones(n)
 
 
+NoiseMeasurement._window_functions[None] = square_window
+
+
 @NoiseMeasurement.window_function("Bartlett")
 def bartlett_window(n: int):
     hn = 0.5 * n