MelWeightMatrix#
MelWeightMatrix - 17#
Version
name: MelWeightMatrix (GitHub)
domain: main
since_version: 17
function: False
support_level: SupportType.COMMON
shape inference: True
This version of the operator has been available since version 17.
Summary
Generate a MelWeightMatrix that can be used to re-weight a Tensor containing a linearly sampled frequency spectra (from DFT or STFT) into num_mel_bins frequency information based on the [lower_edge_hertz, upper_edge_hertz] range on the mel scale. This function defines the mel scale in terms of a frequency in hertz according to the following formula:
mel(f) = 2595 * log10(1 + f/700)
In the returned matrix, all the triangles (filterbanks) have a peak value of 1.0.
The returned MelWeightMatrix can be used to right-multiply a spectrogram S of shape [frames, num_spectrogram_bins] of linear scale spectrum values (e.g. STFT magnitudes) to generate a “mel spectrogram” M of shape [frames, num_mel_bins].
Attributes
output_datatype: The data type of the output tensor. Strictly must be one of the values from DataType enum in TensorProto whose values correspond to T3. The default value is 1 = FLOAT.
Inputs
num_mel_bins (heterogeneous) - T1: The number of bands in the mel spectrum.
dft_length (heterogeneous) - T1: The size of the original DFT. The size of the original DFT is used to infer the size of the onesided DFT, which is understood to be floor(dft_length/2) + 1, i.e. the spectrogram only contains the nonredundant DFT bins.
sample_rate (heterogeneous) - T1: Samples per second of the input signal used to create the spectrogram. Used to figure out the frequencies corresponding to each spectrogram bin, which dictates how they are mapped into the mel scale.
lower_edge_hertz (heterogeneous) - T2: Lower bound on the frequencies to be included in the mel spectrum. This corresponds to the lower edge of the lowest triangular band.
upper_edge_hertz (heterogeneous) - T2: The desired top edge of the highest frequency band.
Outputs
output (heterogeneous) - T3: The Mel Weight Matrix. The output has the shape: [floor(dft_length/2) + 1][num_mel_bins].
Type Constraints
T1 in ( tensor(int32), tensor(int64) ): Constrain to integer tensors.
T2 in ( tensor(bfloat16), tensor(double), tensor(float), tensor(float16) ): Constrain to float tensors
T3 in ( tensor(bfloat16), tensor(double), tensor(float), tensor(float16), tensor(int16), tensor(int32), tensor(int64), tensor(int8), tensor(uint16), tensor(uint32), tensor(uint64), tensor(uint8) ): Constrain to any numerical types.
Examples
default
import numpy as np
import onnx
node = onnx.helper.make_node(
"MelWeightMatrix",
inputs=[
"num_mel_bins",
"dft_length",
"sample_rate",
"lower_edge_hertz",
"upper_edge_hertz",
],
outputs=["output"],
)
num_mel_bins = np.int32(8)
dft_length = np.int32(16)
sample_rate = np.int32(8192)
lower_edge_hertz = np.float32(0)
upper_edge_hertz = np.float32(8192 / 2)
num_spectrogram_bins = dft_length // 2 + 1
frequency_bins = np.arange(0, num_mel_bins + 2)
low_frequency_mel = 2595 * np.log10(1 + lower_edge_hertz / 700)
high_frequency_mel = 2595 * np.log10(1 + upper_edge_hertz / 700)
mel_step = (high_frequency_mel - low_frequency_mel) / frequency_bins.shape[0]
frequency_bins = frequency_bins * mel_step + low_frequency_mel
frequency_bins = 700 * (np.power(10, (frequency_bins / 2595)) - 1)
frequency_bins = ((dft_length + 1) * frequency_bins) // sample_rate
frequency_bins = frequency_bins.astype(int)
output = np.zeros((num_spectrogram_bins, num_mel_bins))
output.flags.writeable = True
for i in range(num_mel_bins):
lower_frequency_value = frequency_bins[i] # left
center_frequency_point = frequency_bins[i + 1] # center
higher_frequency_point = frequency_bins[i + 2] # right
low_to_center = center_frequency_point - lower_frequency_value
if low_to_center == 0:
output[center_frequency_point, i] = 1
else:
for j in range(lower_frequency_value, center_frequency_point + 1):
output[j, i] = float(j - lower_frequency_value) / float(
low_to_center
)
center_to_high = higher_frequency_point - center_frequency_point
if center_to_high > 0:
for j in range(center_frequency_point, higher_frequency_point):
output[j, i] = float(higher_frequency_point - j) / float(
center_to_high
)
# Expected output
# 1.000000, 1.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
# 0.000000, 0.000000, 1.000000, 1.000000, 0.000000, 0.000000, 0.000000, 0.000000,
# 0.000000, 0.000000, 0.000000, 0.000000, 1.000000, 0.000000, 0.000000, 0.000000,
# 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 1.000000, 0.000000, 0.000000,
# 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 1.000000, 0.000000,
# 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 1.000000,
# 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
# 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
# 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
output = output.astype(np.float32)
expect(
node,
inputs=[
num_mel_bins,
dft_length,
sample_rate,
lower_edge_hertz,
upper_edge_hertz,
],
outputs=[output],
name="test_melweightmatrix",
)