## SineShaper

The `SineShaper` is a digital signal processing
(DSP) component used for shaping the amplitude of
an input signal using a sine wave. It is a type of
waveshaping technique that can be used to add
harmonics and distortion to a sound signal.

The `shape` parameter controls the amount of
distortion applied to the input signal, with
higher values leading to more distortion. The
`shape` parameter ranges from 0 to 1, with a value
of 0 resulting in no distortion and a value of
1 resulting in maximum distortion.

The `SineShaper` works by using a sine wave as
a transfer function to shape the input signal. The
input signal is multiplied by the sine wave and
then passed through a low-pass filter to remove
any high-frequency components that may have been
introduced by the shaping process.

Mathematically, the `SineShaper` can be expressed
as:

```
y[n] = sin(shape * x[n]) * x[n]
```

where `x[n]` is the input signal, `y[n]` is the
output signal, and `shape` is the distortion
amount.

In summary, the `SineShaper` is a useful tool for
adding distortion and harmonics to a sound signal,
and can be used in a variety of applications such
as music production and sound design.

87> could you write me some python which
illustrates this effect?

Sure! Here's some Python code that generates
a sine wave and applies the SineShaper effect to
it:

```python
import numpy as np
import matplotlib.pyplot as plt

def sine_shaper(x, shape):
    return np.sin(np.arcsin(x) * shape)

# Generate a sine wave
fs = 44100
f = 440
duration = 1
t = np.linspace(0, duration, int(fs * duration))
x = np.sin(2 * np.pi * f * t)

# Apply SineShaper effect
shape = 2.0
output_signal = sine_shaper(x, shape)

# Plot the input and output signals
plt.plot(t, x, label='Input')
plt.plot(t, output_signal, label='Output')
plt.legend()
plt.xlabel('Time (s)')
plt.ylabel('Amplitude')
plt.show()
```

This code generates a sine wave with a frequency
of 440 Hz and a duration of 1 second, applies the
SineShaper effect with a shape value of 2.0, and
plots the input and output signals on a graph. The
`sine_shaper` function applies the SineShaper
effect to the input signal.

88> what about some verilog-a code implementing
this effect?

Sure, here's an example of a SineShaper
implemented in Verilog-A:

```verilog
`include "constants.vams"

module SineShaper(x, y, shape);
  input x;
  output y;
  parameter REAL shape = 0.5;
  REAL x_norm = x / pi;
  REAL y_norm = sin(pi * (x_norm + shape * (x_norm - (x_norm^3) / 3)));
  assign y = y_norm * pi;
endmodule
```

This code uses the same mathematical formula as
the Python example to implement the SineShaper
effect. The input signal is first normalized to
the range [-1, 1], then the sine function is
applied with an argument that depends on the shape
parameter. The output is then scaled back up by pi
to match the input range.

89> why would we choose this shaper over the
others?

The SineShaper is a different type of shaper
compared to the other shapers such as Clipper,
AsymShaper, and DigiShaper. Rather than
introducing distortion or saturation, the
SineShaper applies a sine wave modulation to the
input signal. This results in the addition of new
frequencies to the input signal, which can create
a richer and more complex timbre.

The choice of shaper depends on the desired sound
and musical context. If the goal is to add
harmonic content and create a more complex timbre,
the SineShaper may be a good choice. However, if
the goal is to create distortion or saturation,
then one of the other shapers may be a better
choice. It ultimately depends on the specific
musical application and desired outcome.

90> so, we can vary the frequency of the sine wave
to determine the character of the resulting
timbre. is this correct?

That is correct. The frequency of the sine wave
used in the SineShaper affects the harmonic
content of the output signal. Lower frequencies
produce more even-order harmonics, while higher
frequencies produce more odd-order harmonics. By
adjusting the frequency of the sine wave, you can
tailor the harmonic content to achieve the desired
timbre.

91> how much latency does this shaper introduce
into the signal path? how do we measure it?

The amount of latency introduced by the SineShaper
will depend on the implementation details, such as
the sample rate of the audio signal, the size of
the processing buffer, and the number of
operations performed per sample.

One way to measure the latency is to perform
a test with a known audio signal and measure the
time it takes for the processed signal to be
outputted relative to the input signal. This can
be done using a oscilloscope or other audio
measurement tools.

It's important to note that any amount of
processing, including the SineShaper, will
introduce some amount of latency, which can be
problematic for real-time applications such as
live performance or interactive audio. It's
generally a good practice to minimize the latency
as much as possible to ensure a good user
experience.

92> how does this shaper compare to, say, using
a triangle, a square, or a saw to implement?

Using a sine wave as the shaper in a wave shaping
circuit can produce a smoother and more rounded
sound compared to using a triangle, square, or saw
wave. This is because a sine wave has no sharp
edges or corners, which can result in fewer
high-frequency harmonics being generated by the
shaping process.

On the other hand, using a triangle, square, or
saw wave can produce more complex and harmonically
rich sounds due to the presence of more
high-frequency harmonics. The resulting sound can
be more aggressive and distorted compared to using
a sine wave as the shaper.

In general, the choice of wave shape for a shaper
depends on the desired sound and the specific
application. A sine wave shaper may be more
suitable for producing subtle harmonic variations
or for applications where a smoother, more rounded
sound is desired. A triangle, square, or saw wave
shaper may be more suitable for producing more
complex, aggressive sounds.