Add Equal Loudness Filter

audio_filters/equal_loudness_filter.py

@@ -0,0 +1,61 @@
+from json import loads
+from pathlib import Path
+
+import numpy as np
+from yulewalker import yulewalk
+
+from audio_filters.butterworth_filter import make_highpass
+from audio_filters.iir_filter import IIRFilter
+
+data = loads((Path(__file__).resolve().parent / "loudness_curve.json").read_text())
+
+
+class EqualLoudnessFilter:
+    r"""
+    An equal-loudness filter which compensates for the human ear's non-linear response
+     to sound.
+    This filter corrects this by cascading a yulewalk filter and a butterworth filter.
+
+    Designed for use with samplerate of 44.1kHz and above. If you're using a lower
+     samplerate, use with caution.
+
+    Code based on matlab implementation at https://bit.ly/3eqh2HU
+    (url shortened for flake8)
+
+    Target curve: https://i.imgur.com/3g2VfaM.png
+    Yulewalk response: https://i.imgur.com/J9LnJ4C.png
+    Butterworth and overall response: https://i.imgur.com/3g2VfaM.png
+
+    Images and original matlab implementation by David Robinson, 2001
+    """
+
+    def __init__(self, samplerate: int = 44100) -> None:
+        self.yulewalk_filter = IIRFilter(10)
+        self.butterworth_filter = make_highpass(150, samplerate)
+
+        # pad the data to nyquist
+        curve_freqs = np.array(data["frequencies"] + [max(20000.0, samplerate / 2)])
+        curve_gains = np.array(data["gains"] + [140])
+
+        # Convert to angular frequency
+        freqs_normalized = curve_freqs / samplerate * 2
+        # Invert the curve and normalize to 0dB
+        gains_normalized = np.power(10, (np.min(curve_gains) - curve_gains) / 20)
+
+        # Scipy's `yulewalk` function is a stub, so we're using the
+        #  `yulewalker` library instead.
+        # This function computes the coefficients using a least-squares
+        #  fit to the specified curve.
+        ya, yb = yulewalk(10, freqs_normalized, gains_normalized)
+        self.yulewalk_filter.set_coefficients(ya, yb)
+
+    def process(self, sample: float) -> float:
+        """
+        Process a single sample through both filters
+
+        >>> filt = EqualLoudnessFilter()
+        >>> filt.process(0.0)
+        0.0
+        """
+        tmp = self.yulewalk_filter.process(sample)
+        return self.butterworth_filter.process(tmp)

audio_filters/loudness_curve.json

@@ -0,0 +1,76 @@
+{
+  "_comment": "The following is a representative average of the Equal Loudness Contours as measured by Robinson and Dadson, 1956",
+  "_doi": "10.1088/0508-3443/7/5/302",
+  "frequencies": [
+    0,
+    20,
+    30,
+    40,
+    50,
+    60,
+    70,
+    80,
+    90,
+    100,
+    200,
+    300,
+    400,
+    500,
+    600,
+    700,
+    800,
+    900,
+    1000,
+    1500,
+    2000,
+    2500,
+    3000,
+    3700,
+    4000,
+    5000,
+    6000,
+    7000,
+    8000,
+    9000,
+    10000,
+    12000,
+    15000,
+    20000
+  ],
+  "gains": [
+    120,
+    113,
+    103,
+    97,
+    93,
+    91,
+    89,
+    87,
+    86,
+    85,
+    78,
+    76,
+    76,
+    76,
+    76,
+    77,
+    78,
+    79.5,
+    80,
+    79,
+    77,
+    74,
+    71.5,
+    70,
+    70.5,
+    74,
+    79,
+    84,
+    86,
+    86,
+    85,
+    95,
+    110,
+    125
+  ]
+}

requirements.txt

@@ -17,3 +17,4 @@ tensorflow
 texttable
 tweepy
 xgboost
+yulewalker