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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 |
#5 in #clipper
Used in surge-synthesizer
155KB
2.5K
SLoC
surgefx-shaper-clip crate description
Clipper
The Clipper
module is a non-linear processing
stage that can be used to introduce distortion and
non-linearities into an audio signal. The clipper
works by setting a threshold value, and any signal
above that threshold is clipped or "hard-limited"
to the threshold value. This creates a flattened,
"squared off" waveform, which can introduce new
harmonic content and other distortions into the
signal.
Shape
The shape
parameter in the Clipper
module
controls the shape of the clipper's threshold. The
threshold can be a hard clip, a soft clip, or
somewhere in between. A hard clip creates a sharp,
rectangular waveform, while a soft clip creates
a smoother, more rounded waveform. The shape
parameter can be used to adjust the amount of
distortion introduced by the clipper, as well as
the tonal characteristics of the resulting
waveform.
Smoke
The smoke
module is a simple smoke test for the
Clipper
module. It generates a test signal,
applies the Clipper
module with default
parameters, and outputs the resulting signal. This
can be used to quickly test the functionality of
the Clipper
module, as well as to explore the
different tonal characteristics that can be
achieved with different shape
parameters.
Overall, the Clipper
module is a non-linear
processing stage that can introduce distortion and
non-linearities into an audio signal. Its
mathematical properties can be described using
tools such as Fourier analysis and signal
processing theory, which allow us to understand
and analyze its behavior in different
contexts. The shape
parameter can be used to
adjust the amount and character of the distortion
introduced by the clipper, while the smoke
module provides a simple way to test and explore
the module's functionality.
59> what distinguishes this from AsymShaper?
The Clipper
module and the AsymShaper
module
are both non-linear processing stages that can
introduce distortion and non-linearities into an
audio signal. However, the main difference between
them is in how they apply the distortion.
The Clipper
module applies a hard clip to the
signal, which means that any signal above the
threshold value is clipped or "hard-limited" to
the threshold value. This creates a flattened,
"squared off" waveform.
The AsymShaper
module, on the other hand,
applies a more gradual shaping to the signal,
which can create a more natural-sounding
distortion. The AsymShaper
uses a soft-clipping
function that has a gradual transition into and
out of the clipping region, which can produce more
harmonically-rich distortion than a hard clip.
So, while both modules can be used for distortion,
the Clipper
module is more suited for
hard-clipping and creating a "squared off"
waveform, while the AsymShaper
module is more
suited for creating a more gradual and
natural-sounding distortion.
60> how can we improve the Clipper?
There are several ways to improve the performance and sound quality of a clipper module:
-
Implement higher-order clipping: Instead of simply clipping the signal at a fixed threshold, higher-order clipping applies a more complex distortion that can create more interesting harmonics and a richer sound. One example of higher-order clipping is the diode clipper, which uses a non-linear diode to create a more complex distortion.
-
Implement variable threshold: Instead of using a fixed threshold, a variable threshold can be used that adapts to the amplitude of the input signal. This can help to preserve the dynamic range of the input signal and avoid excessive distortion.
-
Implement oversampling: Oversampling involves increasing the sample rate of the input signal before applying the clipper and then downsampling the signal back to the original sample rate. This can reduce the distortion and improve the sound quality, especially at high levels of clipping.
-
Implement anti-aliasing filtering: When downsampling the signal back to the original sample rate, anti-aliasing filtering can be applied to remove any high-frequency artifacts that may have been introduced during the oversampling process. This can further improve the sound quality of the clipped signal.
-
Implement a soft-knee option: A soft-knee option can be added to the clipper, which creates a more gradual transition into and out of the clipping region. This can help to create a more natural-sounding distortion.
By incorporating these techniques, the performance and sound quality of a clipper module can be greatly improved, resulting in a more versatile and useful tool for audio processing.
61> could you show me a block diagram?
Sure! Here's a block diagram for a simple clipper:
+-------------------+
| |
| Input signal |
| |
+-------------------+
|
|
v
+------------------------+
| |
| Clipper function |
| (threshold = shape) |
| |
+------------------------+
|
|
v
+-------------------+
| |
| Output signal |
| |
+-------------------+
The input signal is fed into the clipper function, which applies a distortion that clips the signal at a fixed threshold (determined by the "shape" parameter). The resulting output signal is the clipped version of the input signal.
62> could you show me some python code to visualize its behavior across a spectrum of parameter values?
Sure! Here's an example of how you can implement a simple clipper function in Python and plot its output for different threshold values (i.e., the "shape" parameter):
import numpy as np
import matplotlib.pyplot as plt
def clipper(x, shape):
return np.clip(x, -shape, shape)
# Generate a test signal (sine wave)
fs = 44100 # Sample rate (Hz)
dur = 1.0 # Duration (seconds)
f0 = 1000 # Frequency (Hz)
t = np.linspace(0, dur, int(fs*dur))
x = np.sin(2*np.pi*f0*t)
# Plot the input signal
plt.figure(figsize=(10,4))
plt.plot(t, x)
plt.title('Input signal')
plt.xlabel('Time (seconds)')
plt.ylabel('Amplitude')
# Plot the output signals for different threshold values
shapes = [0.1, 0.3, 0.5, 0.7, 0.9] # Threshold values
plt.figure(figsize=(10,4))
plt.plot(t, x, label='Input signal')
for shape in shapes:
y = clipper(x, shape)
plt.plot(t, y, label=f'shape={shape}')
plt.title('Output signals for different threshold values')
plt.xlabel('Time (seconds)')
plt.ylabel('Amplitude')
plt.legend()
plt.show()
This code generates a test signal (a sine wave), applies the clipper function to it for different threshold values (specified by the "shapes" list), and plots the input and output signals for visualization. You can modify the code to use your own input signal and adjust the threshold values to see how the clipper affects the signal.
63> how do we compensate for the power loss which occurs as a result of this clipping?
One way to compensate for the power loss that occurs as a result of clipping is to apply a gain boost after the clipping operation. This is because clipping can effectively reduce the overall level of the signal, which can make it appear quieter or less present in a mix. By applying a gain boost after the clipping, we can bring the overall level of the signal back up to a desired level.
However, it's important to note that applying too much gain can also result in additional distortion or saturation, especially if the signal is already close to or at full scale. So it's important to use careful judgement when applying gain boosts after clipping, and to always monitor the signal for unwanted distortion or artifacts.
64> can this gain boost be adaptive, based on the measured amount of clipping? does matching the power result in an increase in overall signal amplitude of the clipped signal?
Yes, the gain boost can be adaptive and based on the amount of clipping that occurs. One way to implement this is to use a feedback loop that measures the amount of clipping in the output signal and adjusts the gain accordingly. For example, if the output signal is clipping too much, the gain can be reduced, and if the output signal is not clipping enough, the gain can be increased.
Matching the power after clipping does not necessarily result in an increase in overall signal amplitude of the clipped signal. Rather, it ensures that the clipped signal has the same average power as the original unclipped signal. This can be useful for ensuring that the clipped signal has a similar perceived loudness as the unclipped signal, even though the clipped signal may have a reduced peak level.
65> could you show me an example of the updated circuit, using the feedback loop?
Certainly! Here is an example of an updated clipping circuit that includes a feedback loop to adjust the gain based on the amount of clipping:
+---[ R1 ]---+
| |
V_in +---[ D1 ]---+---> V_out
| |
+---[ R2 ]---+
|
R3
|
+-------[ Op Amp ]--------> V_out_gained
In this circuit, V_in
is the input signal and
V_out
is the clipped outputd signal. The
clipping is performed by diode D1
, which limits
the voltage swing of the signal to a predetermined
threshold. R1
and R2
are resistors that set
the threshold for the clipping. R3
is a feedback
resistor that sends a portion of the clipped
signal back to an operational amplifier (op amp),
which is used to apply a gain boost.
The op amp has a feedback loop that measures the amount of clipping in the output signal and adjusts the gain accordingly. This can be done using a sidechain circuit that measures the amplitude of the clipped signal and sends a control voltage to the op amp to adjust the gain. Alternatively, the feedback loop can be implemented using an automatic gain control (AGC) circuit that measures the peak level of the clipped signal and adjusts the gain accordingly.
The output of the op amp is V_out_gained
, which
is the clipped output signal with a gain boost
applied. The gain can be adjusted based on the
amount of clipping that occurs, so that the
overall level of the signal is maintained even if
clipping occurs. This helps to ensure that the
clipped signal has a similar perceived loudness as
the unclipped signal.
66> could you show me how to implement higher order clipping?
Sure! Higher order clipping can be implemented by cascading multiple clipping stages in series. Each stage can be a simple clipper with a different clipping threshold. The output of each stage is then fed into the next stage as input.
Here's an example Python code snippet that implements a 3-stage clipper:
import numpy as np
def clip(x, shape, thresholds):
"""Applies multiple stages of clipping to input signal x.
Args:
x (np.ndarray): Input signal to clip.
shape (float): Amount of shaping to apply to signal.
thresholds (list): List of clipping thresholds for each stage.
Returns:
np.ndarray: Clipped output signal.
"""
y = x.copy()
for threshold in thresholds:
y = np.clip(y * (1 / threshold), -1, 1) * threshold
y = np.tanh(y * shape)
return y
This clip
function takes in an input signal x
,
a shaping amount shape
, and a list of clipping
thresholds thresholds
for each stage. It applies
the first stage of clipping to the input signal
using the first threshold, and then applies
shaping to the clipped output. The resulting
signal is then passed into the second stage of
clipping using the second threshold, and the
process is repeated for the third stage.
Here's an example usage of the function with three stages of clipping and different thresholds:
import matplotlib.pyplot as plt
# Create a test signal
t = np.linspace(0, 1, 44100, endpoint=False)
x = np.sin(2 * np.pi * 440 * t)
# Apply clipping
thresholds = [0.2, 0.4, 0.6]
y = clip(x, 2.0, thresholds)
# Plot the input and output signals
plt.plot(td, x, label='Input')
plt.plot(t, y, label='Output')
plt.legend()
plt.show()
In this example, we apply three stages of clipping with thresholds of 0.2, 0.4, and 0.6. We also set the shaping amount to 2.0. The resulting clipped output signal is plotted alongside the input signal.
67> could you show me how to implement variable threshold?
Sure, here's an example implementation of a clipper with a variable threshold in Python:
import numpy as np
def clipper(x, threshold):
return np.clip(x, -threshold, threshold)
In this implementation, the threshold
parameter
controls the maximum value that the input signal
x
can take before it is clipped. By varying the
value of threshold
, we can adjust the amount of
clipping that occurs.
For example, to apply variable threshold clipping
to an input signal signal
with a range of -1 to
1 and a default threshold of 0.5, we could use the
following code:
import numpy as np
def clipper(x, threshold):
return np.clip(x, -threshold, threshold)
signal = np.random.uniform(-1, 1, size=44100) # Generate a random signal
threshold = 0.5 # Set the default threshold
# Apply variable threshold clipping to the signal
output_signal = clipper(signal, threshold)
# Plot the input and output signals
import matplotlib.pyplot as plt
plt.plot(signal)
plt.plot(output_signal)
plt.show()
In this example, the input signal signal
is
generated using NumPy's random.uniform
function,
which creates an array of random numbers between
-1 and 1. The clipper
function is then used to
apply variable threshold clipping to the signal,
with the default threshold set to 0.5. The
resulting clipped signal is stored in
output_signal
.
Finally, the input and output signals are plotted using the Matplotlib library, allowing us to visualize the effect of the variable threshold clipping.
68> could you show me how to implement oversampling?
Sure, oversampling is a technique used to reduce the impact of aliasing distortion in digital signal processing by sampling the signal at a higher rate than the original signal. Here's an example implementation of oversampling in Python using linear interpolation:
import numpy as np
from scipy.interpolate import interp1d
def oversample(x, factor):
# Upsample by factor
upsampled = np.zeros(len(x) * factor)
upsampled[::factor] = x
# Create linear interpolator
interp = interp1d(np.arange(0, len(upsampled)), upsampled, kind='linear')
# Resample at original rate
resampled = interp(np.linspace(0, len(upsampled) - 1, len(x)))
return resampled
This function takes in an input signal x
and
a factor factor
, which specifies the degree of
oversampling. The signal is upsampled by factor
,
and then a linear interpolator is created to
resample the signal back to its original
rate. This process helps to reduce aliasing
distortion by effectively increasing the
resolution of the digital signal.
Note that oversampling can increase the computational load of a DSP algorithm, so it's important to consider the tradeoff between reducing distortion and increasing processing requirements.
69> could you show me how to implement anti-aliasing filtering?
Sure! Anti-aliasing filtering is a crucial step in
digital signal processing to remove high frequency
content from a signal before downsampling it. This
is important to prevent aliasing, which can cause
unwanted artifacts in the downsampled
signal. Here's an example of how you can implement
anti-aliasing filtering in Python using the
scipy
library:
import numpy as np
from scipy.signal import butter, filtfilt
def anti_aliasing_filter(x, fs, cutoff_freq):
# Design a Butterworth low-pass filter with the given cutoff frequency
nyquist_freq = fs / 2
normalized_cutoff_freq = cutoff_freq / nyquist_freq
b, a = butter(4, normalized_cutoff_freq, 'lowpass')
# Apply the filter to the input signal using forward-backward filtering
y = filtfilt(b, a, x)
return y
Here, x
is the input signal, fs
is the
sampling rate of the signal, and cutoff_freq
is
the frequency at which you want to cut off the
high frequencies. The butter
function is used to
design a fourth-order Butterworth low-pass filter
with the given cutoff frequency. The filtfilt
function is used to apply the filter to the input
signal using forward-backward filtering, which
ensures zero phase distortion.
You can use this function to filter the output of the clipper or any other signal that you want to downsample without introducing aliasing artifacts.
70> could you show me how to implement a soft-knee option?
Sure! Here's an example implementation of a soft-knee option in the clipper function:
import numpy as np
def clipper(x, shape, softness=0.1):
abs_x = np.abs(x)
sign_x = np.sign(x)
if softness == 0:
threshold = shape
else:
threshold = np.log(1 + np.exp(shape)) / np.log(1 + np.exp(shape * softness))
y = np.zeros_like(x)
indices = abs_x > threshold
y[indices] = sign_x[indices] * (threshold + (abs_x[indices] - threshold) / (1 + np.exp(-shape * softness)))
y[~indices] = x[~indices]
return y
The softness
parameter controls the steepness of
the transition between the linear and nonlinear
regions of the clipper. A value of 0 results in
a hard clipper, while larger values result in
a more gradual transition.
The calculation of the threshold value uses the logarithmic function and the sigmoid function to achieve a smooth transition between the linear and nonlinear regions.
Note that this implementation assumes that the input signal is normalized to the range [-1, 1]. If the signal is not normalized, the threshold and gain parameters should be adjusted accordingly.
71> what else can you teach about the clipping operation? how does it work mathematically? what does clipping do to the frequency spectrum?
Sure, I can explain more about clipping and its mathematical properties.
Clipping is a nonlinear distortion effect that limits the amplitude of a signal to a certain level. It is often used to add warmth and character to audio signals, particularly in guitar and bass amplifiers. When a signal exceeds the threshold of the clipping function, the waveform is "clipped" or "flattened," resulting in a distortion of the original signal.
Mathematically, clipping can be represented as a function that applies a limit or threshold to the input signal. The output of the function is the input signal if it is below the threshold, and the threshold value if the input signal is above it. The simplest form of a clipping function is a hard clipper, which is a function that sets all input values below a certain threshold to that threshold value, and all input values above the threshold to the threshold value with the opposite sign.
In the frequency domain, clipping causes harmonic distortion of the input signal. As the input signal is clipped, higher order harmonics are created, which can lead to an increase in overall harmonic content. The frequency spectrum of the clipped signal is essentially a sum of the original signal's harmonics and the harmonics created by the clipping process.
In addition to the hard clipper, there are other types of clipping functions that produce different effects, such as soft clipping, asymmetrical clipping, and variable threshold clipping. Soft clipping functions, for example, apply a gradual limiting to the input signal, which results in a smoother distortion effect than a hard clipper. Asymmetrical clipping functions, on the other hand, apply different thresholds to positive and negative portions of the input signal, resulting in a more complex waveform. Variable threshold clipping functions allow for adaptive clipping, where the threshold is adjusted based on the input signal's level.
Overall, clipping is a powerful and versatile distortion effect that can be used to add character and warmth to audio signals. Its mathematical properties can be analyzed to understand its effects on the frequency spectrum, and its implementation can be improved with techniques such as oversampling, anti-aliasing filtering, and soft-knee options.
72> is it typically implemented on analog hardware?
Clipping can be implemented on both analog and digital hardware. In the early days of audio recording and processing, clipping was often performed unintentionally due to the limited headroom of analog equipment. As digital audio technology has advanced, clipping can now be intentionally introduced through digital processing. In fact, many software plugins and digital audio workstations (DAWs) include various forms of clipping algorithms as a standard feature. However, there are still many analog hardware devices that use clipping for various purposes, such as guitar overdrive pedals, tube guitar amplifiers, and analog tape distortion.
73> can you show an example of a clipper in verilog-a?
Certainly! Here's an example of a simple clipper implemented in Verilog-A:
`include "disciplines.vams"
module clipper_va (vin, vout, vth);
// Define electrical terminals
electrical vin, vout;
electrical vth;
// Define parameters
parameter real Vcl = 1.0;
parameter real Vch = -1.0;
// Define internal variables
real v;
// Calculate the output voltage
analog begin
v = vin.v;
if (v > Vcl) begin
vout.v = Vcl;
end else if (v < Vch) begin
vout.v = Vch;
end else begin
vout.v = v;
end
end
endmodule
This clipper takes an input voltage vin
,
compares it to two threshold voltages Vcl
and
Vch
, and outputs the clipped voltage vout
. The
vth
parameter can be used to adjust the
threshold voltages dynamically.
Note that this example uses Verilog-A, a hardware description language used for analog and mixed-signal simulations. It is typically used in the design of integrated circuits, but can also be used to simulate and model analog circuits.
Dependencies
~12–20MB
~304K SLoC