def synthesis(self, X=None):
"""
Perform time synthesis of frequency domain to real signal using the
inverse DFT.
Parameters
----------
X : numpy array, optional
Complex signal in frequency domain. Default is to use DFT computed
from ``analysis``.
Returns
-------
numpy array
IDFT of ``self.X`` or input if given.
"""
# check for valid input
if X is not None:
if X.shape != self.X.shape:
raise ValueError(
"Invalid input dimensions! Got (%d, %d), expecting (%d, %d)."
% (X.shape[0], X.shape[1], self.X.shape[0], self.X.shape[1])
)
self.X[
:,
] = X
# inverse DFT
if self.transform == "fftw":
self.b[:] = self.X
self.x[
:,
] = self._backward()
elif self.transform == "mkl":
self.x[
:,
] = mkl_fft.irfft_numpy(self.X, self.nfft, axis=self.axis)
else:
self.x[
:,
] = irfft(self.X, self.nfft, axis=self.axis)
# apply window if needed
if self.synthesis_window is not None:
np.multiply(self.synthesis_window, self.x, self.x)
return self.x
a = pyfftw.empty_aligned([nfft, D], dtype="float32")
b = pyfftw.empty_aligned([nfft // 2 + 1, D], dtype="complex64")
c = pyfftw.empty_aligned([nfft, D], dtype="float32")
forward = pyfftw.FFTW(a, b, axes=(0, ))
backward = pyfftw.FFTW(b, c, axes=(0, ), direction="FFTW_BACKWARD")
start_time = time.time()
for k in range(n_trials):
forward()
analysis_time = (time.time() - start_time) / n_trials * 1e6
start_time = time.time()
for k in range(n_trials):
backward()
synthesis_time = (time.time() - start_time) / n_trials * 1e6
print(
"avg fftw w/o class : %f [1e-6 sec], (analysis, synthesis)=(%f, %f) [1e-6 sec]"
% (analysis_time + synthesis_time, analysis_time, synthesis_time))
if mkl_available:
start_time = time.time()
for k in range(n_trials):
X = mkl_fft.rfft_numpy(x)
analysis_time = (time.time() - start_time) / n_trials * 1e6
start_time = time.time()
for k in range(n_trials):
x_r = mkl_fft.irfft_numpy(X)
synthesis_time = (time.time() - start_time) / n_trials * 1e6
print(
"avg mkl w/o class : %f [1e-6 sec], (analysis, synthesis)=(%f, %f) [1e-6 sec]"
% (analysis_time + synthesis_time, analysis_time, synthesis_time))