def stft(x, w, N, H):
"""
Analysis/synthesis of a sound using the short-time Fourier transform
x: input sound, w: analysis window, N: FFT size, H: hop size
returns y: output sound
"""
if H <= 0: # raise error if hop size 0 or negative
raise ValueError("Hop size (H) smaller or equal to 0")
M = w.size # size of analysis window
hM1 = int(math.floor((M + 1) / 2)) # half analysis window size by rounding
hM2 = int(math.floor(M / 2)) # half analysis window size by floor
x = np.append(np.zeros(hM2), x) # add zeros at beginning to center first window at sample 0
x = np.append(x, np.zeros(hM1)) # add zeros at the end to analyze last sample
pin = hM1 # initialize sound pointer in middle of analysis window
pend = x.size - hM1 # last sample to start a frame
w = w / sum(w) # normalize analysis window
y = np.zeros(x.size) # initialize output array
while pin <= pend: # while sound pointer is smaller than last sample
# -----analysis-----
x1 = x[pin - hM1:pin + hM2] # select one frame of input sound
mX, pX = dftModel.dft_anal(x1, w, N) # compute dft
# -----synthesis-----
y1 = dftModel.dft_synth(mX, pX, M) # compute idft
y[pin - hM1:pin + hM2] += H * y1 # overlap-add to generate output sound
pin += H # advance sound pointer
y = np.delete(y, range(hM2)) # delete half of first window which was added in stftAnal
y = np.delete(y, range(y.size - hM1, y.size)) # delete half of the last window which as added in stftAnal
return y
def stft_synth(mY, pY, M, H):
"""
Synthesis of a sound using the short-time Fourier transform
mY: magnitude spectra, pY: phase spectra, M: window size, H: hop-size
returns y: output sound
"""
hM1 = int(math.floor((M + 1) / 2)) # half analysis window size by rounding
hM2 = int(math.floor(M / 2)) # half analysis window size by floor
nFrames = mY[:, 0].size # number of frames
y = np.zeros(nFrames * H + hM1 + hM2) # initialize output array
pin = hM1
for i in range(nFrames): # iterate over all frames
y1 = dftModel.dft_synth(mY[i, :], pY[i, :], M) # compute idft
y[pin - hM1:pin + hM2] += H * y1 # overlap-add to generate output sound
pin += H # advance sound pointer
y = np.delete(y, range(hM2)) # delete half of first window which was added in stftAnal
y = np.delete(y, range(y.size - hM1, y.size)) # delete the end of the sound that was added in stftAnal
return y
