Simple audio filters

audio_filters/butterworth_filter.py

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+from math import sqrt, sin, tau, cos
+
+from audio_filters.iir_filter import IIRFilter
+
+
+class ButterworthFilter:
+    """
+    Create 2nd-order IIR filters with Butterworth design.
+
+    Code based on https://webaudio.github.io/Audio-EQ-Cookbook/audio-eq-cookbook.html
+    Alternatively you can use scipy.signal.butter, which should yield the same results.
+    """
+
+    @staticmethod
+    def make_lowpass(frequency: int, samplerate: int, q_factor: float = 1 / sqrt(2)) -> IIRFilter:
+        """
+        Creates a low-pass filter
+
+        >>> ButterworthFilter.make_lowpass(1000, 48000)
+        <audio_filters.iir_filter.IIRFilter object at 0x7f3dbb93d040>
+        """
+        w0 = tau * frequency / samplerate
+        _sin = sin(w0)
+        _cos = cos(w0)
+        alpha = _sin / (2 * q_factor)
+
+        b0 = (1 - _cos) / 2
+        b1 = 1 - _cos
+
+        a0 = 1 + alpha
+        a1 = -2 * _cos
+        a2 = 1 - alpha
+
+        filt = IIRFilter(2)
+        filt.set_coefficients([a0, a1, a2], [b0, b1, b0])
+        return filt
+
+    @staticmethod
+    def make_highpass(frequency: int, samplerate: int, q_factor: float = 1 / sqrt(2)) -> IIRFilter:
+        """
+        Creates a high-pass filter
+
+        >>> ButterworthFilter.make_highpass(1000, 48000)
+        <audio_filters.iir_filter.IIRFilter object at 0x7f3dbb93d040>
+        """
+        w0 = tau * frequency / samplerate
+        _sin = sin(w0)
+        _cos = cos(w0)
+        alpha = _sin / (2 * q_factor)
+
+        b0 = (1 + _cos) / 2
+        b1 = - 1 - _cos
+
+        a0 = 1 + alpha
+        a1 = -2 * _cos
+        a2 = 1 - alpha
+
+        filt = IIRFilter(2)
+        filt.set_coefficients([a0, a1, a2], [b0, b1, b0])
+        return filt
+
+    @staticmethod
+    def make_bandpass(frequency: int, samplerate: int, q_factor: float = 1 / sqrt(2)) -> IIRFilter:
+        """
+        Creates a band-pass filter
+
+        >>> ButterworthFilter.make_bandpass(1000, 48000)
+        <audio_filters.iir_filter.IIRFilter object at 0x7f3dbb93d040>
+        """
+        w0 = tau * frequency / samplerate
+        _sin = sin(w0)
+        _cos = cos(w0)
+        alpha = _sin / (2 * q_factor)
+
+        b0 = _sin / 2
+        b1 = 0
+        b2 = - b0
+
+        a0 = 1 + alpha
+        a1 = -2 * _cos
+        a2 = 1 - alpha
+
+        filt = IIRFilter(2)
+        filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
+        return filt
+
+    @staticmethod
+    def make_allpass(frequency: int, samplerate: int, q_factor: float = 1 / sqrt(2)) -> IIRFilter:
+        """
+        Creates an all-pass filter
+
+        >>> ButterworthFilter.make_allpass(1000, 48000)
+        <audio_filters.iir_filter.IIRFilter object at 0x7f3dbb93d040>
+        """
+        w0 = tau * frequency / samplerate
+        _sin = sin(w0)
+        _cos = cos(w0)
+        alpha = _sin / (2 * q_factor)
+
+        b0 = 1 - alpha
+        b1 = -2 * _cos
+        b2 = 1 + alpha
+
+        filt = IIRFilter(2)
+        filt.set_coefficients([b2, b1, b0], [b0, b1, b2])
+        return filt
+
+    @staticmethod
+    def make_peak(frequency: int, samplerate: int, gain_db: float, q_factor: float = 1 / sqrt(2)) -> IIRFilter:
+        """
+        Creates a peak filter
+
+        >>> ButterworthFilter.make_peak(1000, 48000, 6)
+        <audio_filters.iir_filter.IIRFilter object at 0x7f3dbb93d040>
+        """
+        w0 = tau * frequency / samplerate
+        _sin = sin(w0)
+        _cos = cos(w0)
+        alpha = _sin / (2 * q_factor)
+        big_a = 10 ** (gain_db / 40)
+
+        b0 = 1 + alpha * big_a
+        b1 = -2 * _cos
+        b2 = 1 - alpha * big_a
+        a0 = 1 + alpha / big_a
+        a1 = -2 * _cos
+        a2 = 1 - alpha / big_a
+
+        filt = IIRFilter(2)
+        filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
+        return filt
+
+    @staticmethod
+    def make_lowshelf(frequency: int, samplerate: int, gain_db: float, q_factor: float = 1 / sqrt(2)) -> IIRFilter:
+        """
+        Creates a low-shelf filter
+
+        >>> ButterworthFilter.make_lowshelf(1000, 48000, 6)
+        <audio_filters.iir_filter.IIRFilter object at 0x7f3dbb93d040>
+        """
+        w0 = tau * frequency / samplerate
+        _sin = sin(w0)
+        _cos = cos(w0)
+        alpha = _sin / (2 * q_factor)
+        big_a = 10 ** (gain_db / 40)
+        pmc = (big_a+1) - (big_a-1)*_cos
+        ppmc = (big_a+1) + (big_a-1)*_cos
+        mpc = (big_a-1) - (big_a+1)*_cos
+        pmpc = (big_a-1) + (big_a+1)*_cos
+        aa2 = 2*sqrt(big_a)*alpha
+
+        b0 = big_a * (pmc + aa2)
+        b1 = 2 * big_a * mpc
+        b2 = big_a * (pmc - aa2)
+        a0 = ppmc + aa2
+        a1 = -2 * pmpc
+        a2 = ppmc - aa2
+
+        filt = IIRFilter(2)
+        filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
+        return filt
+
+    @staticmethod
+    def make_highshelf(frequency: int, samplerate: int, gain_db: float, q_factor: float = 1 / sqrt(2)) -> IIRFilter:
+        """
+        Creates a high-shelf filter
+
+        >>> ButterworthFilter.make_highshelf(1000, 48000, 6)
+        <audio_filters.iir_filter.IIRFilter object at 0x7f3dbb93d040>
+        """
+        w0 = tau * frequency / samplerate
+        _sin = sin(w0)
+        _cos = cos(w0)
+        alpha = _sin / (2 * q_factor)
+        big_a = 10 ** (gain_db / 40)
+        pmc = (big_a+1) - (big_a-1)*_cos
+        ppmc = (big_a+1) + (big_a-1)*_cos
+        mpc = (big_a-1) - (big_a+1)*_cos
+        pmpc = (big_a-1) + (big_a+1)*_cos
+        aa2 = 2*sqrt(big_a)*alpha
+
+        b0 = big_a * (ppmc + aa2)
+        b1 = -2 * big_a * pmpc
+        b2 = big_a * (ppmc - aa2)
+        a0 = pmc + aa2
+        a1 = 2 * mpc
+        a2 = pmc - aa2
+
+        filt = IIRFilter(2)
+        filt.set_coefficients([a0, a1, a2], [b0, b1, b2])
+        return filt

audio_filters/iir_filter.py

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+from typing import List
+
+
+class IIRFilter:
+    """
+    N-Order IIR filter
+    Assumes working with float samples normalized on [-1, 1]
+
+    ---
+
+    Implementation details:
+    Based on the 2nd-order function from https://en.wikipedia.org/wiki/Digital_biquad_filter,
+    this generalized N-order function was made.
+
+    Using the following transfer function
+    H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+...+b_{k}z^{-k}}{a_{0}+a_{1}z^{-1}+a_{2}z^{-2}+...+a_{k}z^{-k}}
+    we can rewrite this to
+    y[n]={\frac{1}{a_{0}}}\left(\left(b_{0}x[n]+b_{1}x[n-1]+b_{2}x[n-2]+...+b_{k}x[n-k]\right)-\left(a_{1}y[n-1]+a_{2}y[n-2]+...+a_{k}y[n-k]\right)\right)
+    """
+    def __init__(self, order: int) -> None:
+        self.order = order
+
+        # a_{0} ... a_{k}
+        self.a_coeffs = [1.0] + [0.0] * order
+        # b_{0} ... b_{k}
+        self.b_coeffs = [1.0] + [0.0] * order
+
+        # x[n-1] ... x[n-k]
+        self.input_history = [0.0] * self.order
+        # y[n-1] ... y[n-k]
+        self.output_history = [0.0] * self.order
+
+    def set_coefficients(self, a_coeffs: List[float], b_coeffs: List[float]) -> None:
+        """
+        Set the coefficients for the IIR filter. These should both be of size order + 1.
+        a_0 may be left out, and it will use 1.0 as default value.
+
+        This method works well with scipy's filter design functions
+            >>> # Make a 2nd-order 1000Hz butterworth lowpass filter
+            >>> b_coeffs, a_coeffs = scipy.signal.butter(2, 1000, btype='lowpass', fs=samplerate)
+            >>> filt = IIRFilter(2)
+            >>> filt.set_coefficients(a_coeffs, b_coeffs)
+        """
+        if len(a_coeffs) < self.order:
+            a_coeffs = [1.0] + a_coeffs
+
+        if len(a_coeffs) != self.order + 1:
+            raise ValueError(f"Expected a_coeffs to have {self.order + 1} elements for {self.order}-order filter, got {len(a_coeffs)}")
+
+        if len(b_coeffs) != self.order + 1:
+            raise ValueError(f"Expected b_coeffs to have {self.order + 1} elements for {self.order}-order filter, got {len(a_coeffs)}")
+
+        self.a_coeffs = a_coeffs
+        self.b_coeffs = b_coeffs
+
+    def process(self, sample: float) -> float:
+        """
+        Calculate y[n]
+
+        >>> filt = IIRFilter(2)
+        >>> filt.process(0)
+        0
+        """
+        result = 0.0
+
+        # Start at index 1 and do index 0 at the end.
+        for i in range(1, self.order+1):
+            result += (
+                self.b_coeffs[i] * self.input_history[i-1] - self.a_coeffs[i] * self.output_history[i-1]
+            )
+
+        result = (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]
+
+        self.input_history[1:] = self.input_history[:-1]
+        self.output_history[1:] = self.output_history[:-1]
+
+        self.input_history[0] = sample
+        self.output_history[0] = result
+
+        return result

audio_filters/show_response.py

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+from math import pi
+from typing import Protocol
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+class FilterType(Protocol):
+    def process(self, sample: float) -> float:
+        pass
+
+
+def show_frequency_response(filter: FilterType, samplerate: int) -> None:
+    """
+    Show frequency response of a filter
+    """
+
+    size = 512
+    inputs = [1] + [0] * (size - 1)
+    outputs = [0] * size
+    for i in range(size):
+        outputs[i] = filter.process(inputs[i])
+
+    filler = [0] * (samplerate - size)  # zero-padding
+    outputs += filler
+    fft_out = np.abs(np.fft.fft(outputs))
+    fft_db = 20 * np.log10(fft_out)
+
+    # Frequencies on log scale from 24 to nyquist frequency
+    plt.xlim(24, samplerate/2-1)
+    plt.xlabel("Frequency (Hz)")
+    plt.xscale('log')
+
+    # Display within reasonable bounds
+    lowest = min([-20, np.min(fft_db[1:samplerate//2-1])])
+    highest = max([20, np.max(fft_db[1:samplerate//2-1])])
+    plt.ylim(max([-80, lowest]), min([80, highest]))
+    plt.ylabel("Gain (dB)")
+
+    plt.plot(fft_db)
+    plt.show()
+
+
+def show_phase_response(filter: FilterType, samplerate: int) -> None:
+    """
+    Show phase response of a filter
+    """
+
+    size = 512
+    inputs = [1] + [0] * (size - 1)
+    outputs = [0] * size
+    for i in range(size):
+        outputs[i] = filter.process(inputs[i])
+
+    filler = [0] * (samplerate - size)  # zero-padding
+    outputs += filler
+    fft_out = np.angle(np.fft.fft(outputs))
+
+    # Frequencies on log scale from 24 to nyquist frequency
+    plt.xlim(24, samplerate / 2 - 1)
+    plt.xlabel("Frequency (Hz)")
+    plt.xscale('log')
+
+    plt.ylim(-2*pi, 2*pi)
+    plt.ylabel("Phase shift (Radians)")
+    plt.plot(np.unwrap(fft_out, -2*pi))
+    plt.show()