TorchComp

Differentiable dynamic range controller in PyTorch.

Installation

pip install torchcomp

Compressor/Expander gain function

This function calculates the gain reduction $g[n]$ for a compressor/expander. It takes the RMS of the input signal $x[n]$ and the compressor/expander parameters as input. The function returns the gain $g[n]$ in linear scale. To use it as a regular compressor/expander, multiply the result $g[n]$ with the signal $x[n]$.

Function signature

def compexp_gain(
    x_rms: torch.Tensor,
    comp_thresh: Union[torch.Tensor, float],
    comp_ratio: Union[torch.Tensor, float],
    exp_thresh: Union[torch.Tensor, float],
    exp_ratio: Union[torch.Tensor, float],
    at: Union[torch.Tensor, float],
    rt: Union[torch.Tensor, float],
) -> torch.Tensor:
    """Compressor-Expander gain function.

    Args:
        x_rms (torch.Tensor): Input signal RMS.
        comp_thresh (torch.Tensor): Compressor threshold in dB.
        comp_ratio (torch.Tensor): Compressor ratio.
        exp_thresh (torch.Tensor): Expander threshold in dB.
        exp_ratio (torch.Tensor): Expander ratio.
        at (torch.Tensor): Attack time.
        rt (torch.Tensor): Release time.

    Shape:
        - x_rms: :math:`(B, T)` where :math:`B` is the batch size and :math:`T` is the number of samples.
        - comp_thresh: :math:`(B,)` or a scalar.
        - comp_ratio: :math:`(B,)` or a scalar.
        - exp_thresh: :math:`(B,)` or a scalar.
        - exp_ratio: :math:`(B,)` or a scalar.
        - at: :math:`(B,)` or a scalar.
        - rt: :math:`(B,)` or a scalar.

    """

Note: x_rms should be non-negative. You can calculate it using $\sqrt{x^2[n]}$ and smooth it with avg.

Equations

$$ x_{\rm log}[n] = 20 \log_{10} x_{\rm rms}[n] $$

$$ g_{\rm log}[n] = \min\left(0, \left(1 - \frac{1}{CR}\right)\left(CT - x_{\rm log}[n]\right), \left(1 - \frac{1}{ER}\right)\left(ET - x_{\rm log}[n]\right)\right) $$

$$ g[n] = 10^{g_{\rm log}[n] / 20} $$

$$ \hat{g}[n] = \begin{rcases} \begin{dcases} \alpha_{\rm at} g[n] + (1 - \alpha_{\rm at}) \hat{g}[n-1] & \text{if } g[n] < \hat{g}[n-1] \\ \alpha_{\rm rt} g[n] + (1 - \alpha_{\rm rt}) \hat{g}[n-1] & \text{otherwise} \end{dcases}\end{rcases} $$

Block diagram

graph TB
    input((x))
    output((g))
    amp2db[amp2db]
    db2amp[db2amp]
    min[Min]
    delay[z^-1]
    zero( 0 )

    input --> amp2db --> neg["*(-1)"] --> plusCT["+CT"] & plusET["+ET"]
    plusCT --> multCS["*(1 - 1/CR)"]
    plusET --> multES["*(1 - 1/ER)"]
    zero & multCS & multES --> min --> db2amp

    db2amp & delay --> ifelse{<}
    output --> delay --> multATT["*(1 - AT)"] & multRTT["*(1 - RT)"]

    subgraph Compressor
        ifelse -->|yes| multAT["*AT"]
        subgraph Attack
            multAT & multATT --> plus1(("+"))
        end

        ifelse -->|no| multRT["*RT"]
        subgraph Release
            multRT & multRTT --> plus2(("+"))
        end
    end

    plus1 & plus2 --> output

Limiter gain function

This function calculates the gain reduction $g[n]$ for a limiter. To use it as a regular limiter, multiply the result $g[n]$ with the input signal $x[n]$.

Function signature

def limiter_gain(
    x: torch.Tensor,
    threshold: torch.Tensor,
    at: torch.Tensor,
    rt: torch.Tensor,
) -> torch.Tensor:
    """Limiter gain function.
    This implementation use the same attack and release time for level detection and gain smoothing.

    Args:
        x (torch.Tensor): Input signal.
        threshold (torch.Tensor): Limiter threshold in dB.
        at (torch.Tensor): Attack time.
        rt (torch.Tensor): Release time.

    Shape:
        - x: :math:`(B, T)` where :math:`B` is the batch size and :math:`T` is the number of samples.
        - threshold: :math:`(B,)` or a scalar.
        - at: :math:`(B,)` or a scalar.
        - rt: :math:`(B,)` or a scalar.

    """

Equations

$$ x_{\rm peak}[n] = \begin{rcases} \begin{dcases} \alpha_{\rm at} |x[n]| + (1 - \alpha_{\rm at}) x_{\rm peak}[n-1] & \text{if } |x[n]| > x_{\rm peak}[n-1] \\ \alpha_{\rm rt} |x[n]| + (1 - \alpha_{\rm rt}) x_{\rm peak}[n-1] & \text{otherwise} \end{dcases}\end{rcases} $$

$$ g[n] = \min(1, \frac{10^\frac{T}{20}}{x_{\rm peak}[n]}) $$

$$ \hat{g}[n] = \begin{rcases} \begin{dcases} \alpha_{\rm at} g[n] + (1 - \alpha_{\rm at}) \hat{g}[n-1] & \text{if } g[n] < \hat{g}[n-1] \\ \alpha_{\rm rt} g[n] + (1 - \alpha_{\rm rt}) \hat{g}[n-1] & \text{otherwise} \end{dcases}\end{rcases} $$

Block diagram

graph TB
    input((x))
    output((g))
    peak((x_peak))
    abs[abs]
    delay[z^-1]
    zero( 0 )

    ifelse1{>}
    ifelse2{<}

    input --> abs --> ifelse1

    subgraph Peak detector
        ifelse1 -->|yes| multAT["*AT"]
        subgraph at1 [Attack]
            multAT & multATT --> plus1(("+"))
        end

        ifelse1 -->|no| multRT["*RT"]
        subgraph rt1 [Release]
            multRT & multRTT --> plus2(("+"))
        end
    end
    
    plus1 & plus2 --> peak
    peak --> delay --> multATT["*(1 - AT)"] & multRTT["*(1 - RT)"] & ifelse1

    peak --> amp2db[amp2db] --> neg["*(-1)"] --> plusT["+T"]
    zero & plusT --> min[Min] --> db2amp[db2amp] --> ifelse2{<}

    subgraph gain smoothing
        ifelse2 -->|yes| multAT2["*AT"]
        subgraph at2 [Attack]
            multAT2 & multATT2 --> plus3(("+"))
        end

        ifelse2 -->|no| multRT2["*RT"]
        subgraph rt2 [Release]
            multRT2 & multRTT2 --> plus4(("+"))
        end
    end

    output --> delay2[z^-1] --> multATT2["*(1 - AT)"] & multRTT2["*(1 - RT)"] & ifelse2

    plus3 & plus4 --> output

Average filter

Function signature

def avg(rms: torch.Tensor, avg_coef: Union[torch.Tensor, float]):
    """Compute the running average of a signal.

    Args:
        rms (torch.Tensor): Input signal.
        avg_coef (torch.Tensor): Coefficient for the average RMS.

    Shape:
        - rms: :math:`(B, T)` where :math:`B` is the batch size and :math:`T` is the number of samples.
        - avg_coef: :math:`(B,)` or a scalar.

    """

Equations

$$\hat{x}_{\rm rms}[n] = \alpha_{\rm avg} x_{\rm rms}[n] + (1 - \alpha_{\rm avg}) \hat{x}_{\rm rms}[n-1]$$

TODO

• CUDA acceleration in Numba
• PyTorch CPP extension
• Native CUDA extension
• Forward mode autograd
• Examples

Citation

If you find this repository useful in your research, please cite our work with the following BibTex entry:

@misc{ycy2024diffapf,
    title={Differentiable All-pole Filters for Time-varying Audio Systems},
    author={Chin-Yun Yu and Christopher Mitcheltree and Alistair Carson and Stefan Bilbao and Joshua D. Reiss and György Fazekas},
    year={2024},
    eprint={2404.07970},
    archivePrefix={arXiv},
    primaryClass={eess.AS}
}