Description
In the cpp file Bitcrush.h, the scaleFactor used to multiply the the array to create the representation using new bit depth is 2**bit_depth.
But this will result in a representation with more than the expected bits.
The expected formula is: scaleFactor = (2**new_bit_depth)/2+1
New formula reference
Here is a python code showing the number unique values in the actual and expected representations with a new bit depth
import numpy as np
def generate_audio(bit_depth, verbose=False):
"""
generate a normalized audio with 2**bit_depth unique values
"""
power = 2**bit_depth/2
array = np.arange(-1*power, power+1)
audio = (array/max(array))[1::]
if verbose:
print(f"Input bit_depth: {bit_depth}")
print(f"Possible unique_values: {2**bit_depth}")
print(f"Actual unique_values: {len(np.unique(audio))}")
return audio
audio = generate_audio(bit_depth=16, verbose=True)
new_bit_depth = 4
new_formula_scale = (2**new_bit_depth)/2+1
pedalboard_scale = 2**new_bit_depth
aud_new_formula = np.round(audio*new_formula_scale)/new_formula_scale
aud_pedalboard = np.round(audio*pedalboard_scale)/pedalboard_scale
print(f"Possible unique values with new bitdepth of {new_bit_depth}: {2**new_bit_depth}")
print("Expected unique values with new formula:", len(np.unique(aud_new_formula)))
print("Pedalboard implementation unique values:", len(np.unique(aud_pedalboard)))
Output of the above code
Input bit_depth: 16
Possible unique_values: 65536
Actual unique_values: 65536
Possible unique values with new bitdepth of 4: 16
Expected unique values with new formula: 19
Pedalboard implementation unique values: 33
The error in pedalboard's implementation is huge compared to the new formula.
For a given audio with bit-depth of 16,
Example 1) when new bith depth is 4, pedalboard implementation gives a error of additional 17 unique values
Example 2) when new bith depth is 8, pedalboard implementation gives a error of additional 257 unique values
while the new formula always gives an error of additional 3 unique values