#non-linear #x #plot #signal #duration #signals #tanh #real-number #plt

surgeshaper-tanh

surge synthesizer -- tanh waveshaper

8 releases

0.2.12-alpha.0 Apr 7, 2023
0.2.11-alpha.0 Dec 19, 2022
0.2.5-alpha.0 Jun 21, 2022
0.2.4-alpha.0 Mar 14, 2022
0.1.42-alpha.0 Oct 27, 2021

#37 in Visualization

45 downloads per month
Used in surge-synthesizer

GPL-3.0 license

155KB
2.5K SLoC

TanhShaper

The TanhShaper is an implementation of a soft clipping algorithm using the hyperbolic tangent function. This shaper can be used to add saturation and warmth to an audio signal, similar to a tube amplifier. The amount of shaping can be controlled by adjusting the shape parameter.

Mathematical analysis

The hyperbolic tangent function is defined as:

tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))

When x is small, tanh(x) is approximately equal to x, and as x becomes larger, tanh(x) approaches 1. This non-linear response curve makes it suitable for use as a shaper function.

The TanhShaper takes an input signal and applies the hyperbolic tangent function to it, which has the effect of softly clipping the signal. The degree of soft clipping is controlled by the shape parameter, which scales the input signal.

Usage

The TanhShaper can be used in any application where saturation or warmth is desired, such as in guitar amplifiers, synthesizers, or mixing consoles. It can be used in conjunction with other shaping algorithms to create complex and unique sounds.

Caveats

One potential issue with using a soft clipping algorithm like TanhShaper is that it can introduce additional harmonic distortion to the signal. This can result in a loss of clarity or fidelity, depending on the application. Additionally, care must be taken when adjusting the shape parameter to avoid introducing unwanted artifacts or distortion.

Overall, the TanhShaper is a powerful tool for shaping audio signals and can be a valuable addition to any audio processing toolbox.

94> could you teach me about the hyperbolic tangent function?

Sure! The hyperbolic tangent function, usually denoted as tanh(x), is a mathematical function that maps any real number x to a value between -1 and 1. The function is defined as:

tanh(x) = (e^x - e^-x) / (e^x + e^-x)

where e is the mathematical constant approximately equal to 2.71828.

The graph of the hyperbolic tangent function is similar to the graph of the standard tangent function, but with a vertical scaling of 1 and a horizontal scaling of 2. The function is symmetric about the origin, meaning that tanh(-x) = -tanh(x) for all x.

The hyperbolic tangent function is often used as an activation function in artificial neural networks because it is differentiable and has a range between -1 and 1. It is also commonly used in signal processing, particularly in audio and image processing, for its ability to compress and expand dynamic range.

95> could you show me some python code illustrating the effect on the input signal?

Certainly, here is an example of using the tanh function to shape an input signal:

import numpy as np
import matplotlib.pyplot as plt

# Create a sine wave input signal
sample_rate = 44100
duration = 1.0
freq = 440.0
t = np.linspace(0, duration, int(sample_rate * duration), endpoint=False)
signal = np.sin(2 * np.pi * freq * t)

# Apply tanh shaping with a shape factor of 0.5
shape_factor = 0.5
shaped_signal = np.tanh(signal * shape_factor)

# Plot the input and output signals
fig, ax = plt.subplots(2, 1)
ax[0].plot(t, signal)
ax[0].set_title('Input Signal')
ax[0].set_xlabel('Time (s)')
ax[0].set_ylabel('Amplitude')
ax[1].plot(t, shaped_signal)
ax[1].set_title('Output Signal')
ax[1].set_xlabel('Time (s)')
ax[1].set_ylabel('Amplitude')
plt.show()

In this example, we create a 1 second sine wave input signal with a frequency of 440 Hz sampled at a rate of 44100 Hz. We then apply the tanh function with a shape factor of 0.5 to the input signal to create the shaped output signal. The resulting input and output signals are then plotted for visualization.

Dependencies

~12–21MB
~304K SLoC