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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)
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