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| # File under the MIT license, see https://github.com/adefossez/julius/LICENSE for details. | |
| # Author: adefossez, 2020 | |
| """ | |
| Signal processing or PyTorch related utilities. | |
| """ | |
| import math | |
| import typing as tp | |
| import torch | |
| from torch.nn import functional as F | |
| def sinc(x: torch.Tensor): | |
| """ | |
| Implementation of sinc, i.e. sin(x) / x | |
| __Warning__: the input is not multiplied by `pi`! | |
| """ | |
| return torch.where(x == 0, torch.tensor(1., device=x.device, dtype=x.dtype), torch.sin(x) / x) | |
| def pad_to(tensor: torch.Tensor, target_length: int, mode: str = 'constant', value: float = 0): | |
| """ | |
| Pad the given tensor to the given length, with 0s on the right. | |
| """ | |
| return F.pad(tensor, (0, target_length - tensor.shape[-1]), mode=mode, value=value) | |
| def hz_to_mel(freqs: torch.Tensor): | |
| """ | |
| Converts a Tensor of frequencies in hertz to the mel scale. | |
| Uses the simple formula by O'Shaughnessy (1987). | |
| Args: | |
| freqs (torch.Tensor): frequencies to convert. | |
| """ | |
| return 2595 * torch.log10(1 + freqs / 700) | |
| def mel_to_hz(mels: torch.Tensor): | |
| """ | |
| Converts a Tensor of mel scaled frequencies to Hertz. | |
| Uses the simple formula by O'Shaughnessy (1987). | |
| Args: | |
| mels (torch.Tensor): mel frequencies to convert. | |
| """ | |
| return 700 * (10**(mels / 2595) - 1) | |
| def mel_frequencies(n_mels: int, fmin: float, fmax: float): | |
| """ | |
| Return frequencies that are evenly spaced in mel scale. | |
| Args: | |
| n_mels (int): number of frequencies to return. | |
| fmin (float): start from this frequency (in Hz). | |
| fmax (float): finish at this frequency (in Hz). | |
| """ | |
| low = hz_to_mel(torch.tensor(float(fmin))).item() | |
| high = hz_to_mel(torch.tensor(float(fmax))).item() | |
| mels = torch.linspace(low, high, n_mels) | |
| return mel_to_hz(mels) | |
| def volume(x: torch.Tensor, floor=1e-8): | |
| """ | |
| Return the volume in dBFS. | |
| """ | |
| return torch.log10(floor + (x**2).mean(-1)) * 10 | |
| def pure_tone(freq: float, sr: float = 128, dur: float = 4, device=None): | |
| """ | |
| Return a pure tone, i.e. cosine. | |
| Args: | |
| freq (float): frequency (in Hz) | |
| sr (float): sample rate (in Hz) | |
| dur (float): duration (in seconds) | |
| """ | |
| time = torch.arange(int(sr * dur), device=device).float() / sr | |
| return torch.cos(2 * math.pi * freq * time) | |
| def unfold(input, kernel_size: int, stride: int): | |
| """1D only unfolding similar to the one from PyTorch. | |
| However PyTorch unfold is extremely slow. | |
| Given an input tensor of size `[*, T]` this will return | |
| a tensor `[*, F, K]` with `K` the kernel size, and `F` the number | |
| of frames. The i-th frame is a view onto `i * stride: i * stride + kernel_size`. | |
| This will automatically pad the input to cover at least once all entries in `input`. | |
| Args: | |
| input (Tensor): tensor for which to return the frames. | |
| kernel_size (int): size of each frame. | |
| stride (int): stride between each frame. | |
| Shape: | |
| - Inputs: `input` is `[*, T]` | |
| - Output: `[*, F, kernel_size]` with `F = 1 + ceil((T - kernel_size) / stride)` | |
| ..Warning:: unlike PyTorch unfold, this will pad the input | |
| so that any position in `input` is covered by at least one frame. | |
| """ | |
| shape = list(input.shape) | |
| length = shape.pop(-1) | |
| n_frames = math.ceil((max(length, kernel_size) - kernel_size) / stride) + 1 | |
| tgt_length = (n_frames - 1) * stride + kernel_size | |
| padded = F.pad(input, (0, tgt_length - length)).contiguous() | |
| strides: tp.List[int] = [] | |
| for dim in range(padded.dim()): | |
| strides.append(padded.stride(dim)) | |
| assert strides.pop(-1) == 1, 'data should be contiguous' | |
| strides = strides + [stride, 1] | |
| return padded.as_strided(shape + [n_frames, kernel_size], strides) | |