def _test_fft(size):
input = _random_vector(size)
refout = _naive_dft(input, False)
actualout = fft.transform(input, False)
err = _log10_rms_err(refout, actualout)
actualin = fft.transform(refout, True)
actualin = [(x / size) for x in actualin]
err = max(_log10_rms_err(input, actualin), err)
print("fftsize={:4d} logerr={:5.1f}".format(size, err))
def _test_fft(size):
input = _random_vector(size)
refout = _naive_dft(input, False)
actualout = fft.transform(input, False)
err = _log10_rms_err(refout, actualout)
actualin = fft.transform(refout, True)
actualin = [(x / size) for x in actualin]
err = max(_log10_rms_err(input, actualin), err)
print("fftsize={:4d} logerr={:5.1f}".format(size, err))
def regressionCoefficients(wav_data, thres):
# smoothen the signal
wav1 = smoothing(wav_data)
L1 = len(wav1)
ff1 = linspace(0, 8000, L1)
f1 = linspace(0, 4000, L1 // 2)
xx1 = transform(wav1,False)
xx1 = np.abs(real(xx1)) // L1
x1 = 2 * xx1[0:L1 // 2]
max1 = max(x1)
# x1 = 2 * xx1[0:L1 // 2]
# max1 = max(x1)
x1 = x1 / max1
# find peaks above threshold of 20%
peaks1 = findpeaks(x1, 50, thres)
plt.plot(f1, x1)
# plot peaks
plt.plot(f1[peaks1], x1[peaks1], 'ro')
plt.show()
freq1 = f1[peaks1]
# Regression Coefficients
coef1 = x1[peaks1] * max1
return coef1
def inverse_transform(vector):
n = len(vector)
factor = -1j * cmath.pi / (len(vector) * 2)
temp = [(val if i > 0 else val / 2.0) * cmath.exp(i * factor)
for (i, val) in enumerate(vector)]
temp = fft.transform(temp, False)
temp = [val.real for val in temp]
result = [None] * n
result[::2] = temp[:(n + 1) // 2]
result[-1 - len(vector) % 2::-2] = temp[(n + 1) // 2:]
return result
def inverse_transform(vector): n = len(vector) factor = -1j * cmath.pi / (len(vector) * 2) temp = [(val if i > 0 else val / 2.0) * cmath.exp(i * factor) for (i, val) in enumerate(vector)] temp = fft.transform(temp, False) temp = [val.real for val in temp] result = [None] * n result[ : : 2] = temp[ : (n + 1) // 2] result[-1 - len(vector) % 2 : : -2] = temp[(n + 1) // 2 : ] return result
def update_fftplot(self):
"""Continually plots the FFT (absolute value of the complex output) of
the EEG graph. Takes half the FFT plot due to symmetry and the Nyquist
sampling limit.
"""
self.fft_plot_ref = None
while self._run_thread:
self.fft = my_fft.transform(np.asarray(self.ydata), False)
if self.fft_plot_ref is not None:
self.fft_plot_ref.remove()
self.fft_plot_ref, = self.fft_canvas.axes.plot(
self.bins[:(self.n_data >> 1)],
np.abs(self.fft[:(self.n_data >> 1)]), '#00FF7F', linewidth=1)
self.fft_canvas.draw()
# TODO: slider of the fft frequency
time.sleep(0.1)
def shiftallpeaks(peaks1, peaks2, wav_data3):
""" Shift all peaks paramaters(peaks1,peaks2,wav_data3)
"""
n = len(peaks1)
x3 = transform(wav_data3,False)
new = zeros(len(x3) // 2)
new = new.astype(dtype=np.complex)
Peaks1 = zeros(n + 2)
Peaks1[1:n + 1] = peaks1
Peaks1[n + 1] = len(x3) // 2
Peaks1 = Peaks1.astype(np.int16)
Peaks2 = zeros(n + 2)
Peaks2[1:n + 1] = peaks2
Peaks2[n + 1] = len(x3) // 2
Peaks2 = Peaks2.astype(np.int16)
for j in range(0, n + 1):
k = 0
for i in range(Peaks2[j], Peaks2[j + 1]):
index = Peaks1[j] + np.floor(scale[j + 1] * k)
k += 1
index = int(index)
new[i] = x3[index]
# run this if you wish to replace duplicates with zeros
for j in range(len(new) - 1):
if new[j] == new[j + 1]:
new[j] = 0.0
return new
# plot best fit line to coefficients
xaxis = linspace(0, C1[-1], 1000)
yaxis = linspace(0, 0, 1000)
for i in range(0, 1000):
for j in range(n):
yaxis[i] += coef[j] * xaxis[i] ** (n - j - 1)
plt.plot(X, Y, 'ro')
plt.plot(xaxis, yaxis)
# find FFT of third audio sample
L3 = len(wav_data3)
ff3 = linspace(0, 8000, L3)
f3 = linspace(0, 4000, L3 // 2)
xx3 = transform(wav_data3,False)
xx3 = np.abs(real(xx3)) // L3
x3 = 2 * xx3[0:L3 // 2]
# push coefficients through regression model found from vector "coef"
n = len(coef)
ynew = linspace(0, 0, L3 // 2)
for i in range(L3 // 2):
for j in range(n):
ynew[i] += coef[j] * x3[i] ** (n - j - 1)
# plot the transformation of the coefficients
plt.plot(f3, yaxis)
plt.show()
def transform(vector):
temp = vector[::2] + vector[-1 - len(vector) % 2::-2]
temp = fft.transform(temp, False)
factor = -1j * cmath.pi / (len(vector) * 2)
return [(val * cmath.exp(i * factor)).real for (i, val) in enumerate(temp)]
def _test_fft(size):
input = _random_vector(size)
refout = _naive_dft(input)
actualout = fft.transform(input)
print("fftsize={:4d} logerr={:5.1f}".format(
size, _log10_rms_err(refout, actualout)))
def _test_fft(size):
input = _random_vector(size)
refout = _naive_dft(input)
actualout = fft.transform(input)
print("fftsize={:4d} logerr={:5.1f}".format(size, _log10_rms_err(refout, actualout)))
import fft
import complexity
HARMONIC_NUM = 10
FREQUENCY_LIMIT = 2700
TIME_INTERVALS_NUM = 256
COMPARISON_INTERVALS_NUM = 2 ** 10
COMPLEXITY_INTERVALS_NUM = 2 ** 15
plt.style.use("dark_background")
fig, (ax1, ax2, ax3) = plt.subplots(3, 1)
f = np.linspace(0, FREQUENCY_LIMIT, TIME_INTERVALS_NUM)
signal = signal_generator.generate(HARMONIC_NUM, FREQUENCY_LIMIT, TIME_INTERVALS_NUM)
spectrumNumPy = abs(np.fft.fft(signal))
spectrumFFT = abs(fft.transform(signal))
ax1.plot(f, spectrumNumPy, color="blue")
ax1.set_title("numpy")
ax2.plot(f, spectrumFFT, color="blue")
ax2.set_title("my fft")
counts = [1 << i for i in range(1, int(np.log2(COMPLEXITY_INTERVALS_NUM))+1)]
time = complexity.comparativeBenchmark(COMPLEXITY_INTERVALS_NUM)(fft.transform)
ax3.plot(counts, time, color="green", marker=".")
ax3.set_title("Algorithm complexity")
ax3.set_xlabel("Number of discrete intervals in signal")
ax3.set_ylabel("Time")
fig2, ax4 = plt.subplots()
benchmark = complexity.comparativeBenchmark(COMPARISON_INTERVALS_NUM)
counts = [1 << i for i in range(1, int(np.log2(COMPARISON_INTERVALS_NUM))+1)]
FILENAME1 = "source.wav" FILENAME2 = "target.wav" FILENAME3 = "thirdsample.wav" rate1, wav_data1 = wavfile.read(FILENAME1) rate2, wav_data2 = wavfile.read(FILENAME2) rate3, wav_data3 = wavfile.read(FILENAME3) wav1 = smoothing(wav_data1) wav2 = smoothing(wav_data2) wav3 = smoothing(wav_data3) L1 = len(wav1) f1 = linspace(0, 8000, L1) x1 = transform(wav1,False) # x1 = np.fft.fft(wav1) X1 = np.abs(x1) / L1 # magnitude of coefficient of FFT of source voice L2 = len(wav2) f2 = linspace(0, 8000, L2) # x2 = np.fft.fft(wav2) x2 = transform(wav2,False) X2 = np.abs(x2) / L2 # magnitude of coefficient of FFT of target voice to be replicated ratio = abs(x2) / abs(x1) # ratio of coefficients r=d/c Freq = linspace(0, 8000, L1) plt.plot(Freq, ratio) # plot ratio over double sided FFT spectrum # This will help us cut down on the ratio . # You need to pick values of h>1. # The closer to 1 , the more it shrinks
def transform(vector): temp = vector[ : : 2] + vector[-1 - len(vector) % 2 : : -2] temp = fft.transform(temp, False) factor = -1j * cmath.pi / (len(vector) * 2) return [(val * cmath.exp(i * factor)).real for (i, val) in enumerate(temp)]