"""Utils for performing a DFT using numpy.
"""
"""
Copyright 2017 Parag K. Mital. See also NOTICE.md.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""
import numpy as np
from scipy.signal import hann
[docs]def ztoc(re, im):
"""Summary
Parameters
----------
re : TYPE
Description
im : TYPE
Description
Returns
-------
TYPE
Description
"""
return np.sqrt(re**2 + im**2), np.angle(re + im * 1j)
[docs]def ctoz(mag, phs):
"""Summary
Parameters
----------
mag : TYPE
Description
phs : TYPE
Description
Returns
-------
TYPE
Description
"""
return mag * np.cos(phs), mag * np.sin(phs)
[docs]def dft_np(signal, hop_size=256, fft_size=512):
"""Summary
Parameters
----------
signal : TYPE
Description
hop_size : int, optional
Description
fft_size : int, optional
Description
Returns
-------
TYPE
Description
"""
n_hops = len(signal) // hop_size
s = []
hann_win = hann(fft_size)
for hop_i in range(n_hops):
frame = signal[(hop_i * hop_size):(hop_i * hop_size + fft_size)]
frame = np.pad(frame, (0, fft_size - len(frame)), 'constant')
frame *= hann_win
s.append(frame)
s = np.array(s)
N = s.shape[-1]
k = np.reshape(np.linspace(0.0, 2 * np.pi / N * (N // 2), N // 2), [1, N // 2])
x = np.reshape(np.linspace(0.0, N - 1, N), [N, 1])
freqs = np.dot(x, k)
reals = np.dot(s, np.cos(freqs)) * (2.0 / N)
imags = np.dot(s, np.sin(freqs)) * (2.0 / N)
return reals, imags
[docs]def idft_np(re, im, hop_size=256, fft_size=512):
"""Summary
Parameters
----------
re : TYPE
Description
im : TYPE
Description
hop_size : int, optional
Description
fft_size : int, optional
Description
Returns
-------
TYPE
Description
"""
N = re.shape[1] * 2
k = np.reshape(np.linspace(0.0, 2 * np.pi / N * (N // 2), N // 2), [N // 2, 1])
x = np.reshape(np.linspace(0.0, N - 1, N), [1, N])
freqs = np.dot(k, x)
signal = np.zeros((re.shape[0] * hop_size + fft_size,))
recon = np.dot(re, np.cos(freqs)) + np.dot(im, np.sin(freqs))
for hop_i, frame in enumerate(recon):
signal[(hop_i * hop_size): (hop_i * hop_size + fft_size)] += frame
return signal