问在Numpy中如何从傅里叶变换中恢复振幅和相移？

EN

Amplitude_at_freq = sqrt(real_component_at_freq^2 + imag_component_at_freq^2)
Phase = arctan(imag_component_at_freq/real_component_at_freq)

# Define amplitude, phase, frequency
_A = 4 # Amplitude
_p = 0 # Phase shift
_f = 8 # Frequency

# Construct a simple signal
t = np.linspace(0, 2*np.pi, 1024 + 1)[:-1]
g = _A * np.sin(_f * t + _p) 

# Apply the fourier transform
ff = np.fft.fft(g)

# Get frequency of original signal
ff_ii = np.where(np.abs(ff) > 1.0)[0][0] # Just get one frequency, the other one is just mirrored freq at negative value
print('frequency of:', ff_ii)

# Get the complex vector at that frequency to retrieve amplitude and phase shift
yy = ff[ff_ii] 

# Calculate the amplitude
T = t.shape[0] # domain of x; which we will divide height to get freq amplitude
A = np.sqrt(yy.real**2 + yy.imag**2)/T 
print('amplitude of:', A) 

# Calculate phase shift
phi = np.arctan(yy.imag/yy.real) 
print('phase change:', phi)

>> frequency of: 8
>> amplitude of: 2.0
>> phase change: 1.5707963267948957