Clash Royale CLAN TAG#URR8PPP

Fidelity of sound created from frequency domain data

I know it is possible to create .wav file from frequency domain data (magnitude + phase) but I would like to know how close would that be to the real(orginal) sound ? Does it depend on the frequency step for example (or something else).

Second question:
I need to write a code that takes a frequency domain data (magnitude + phase) to build a wav file.
In order to do so, I started by the following code which creates a fake signal --> fft (at this point I have the kind of input(mag + phase) that I would expect for my target code). But it doesn't seem top work fine, could you please help

import numpy as np
from scipy import pi
import matplotlib.pyplot as plt
#%matplotlib inline
from scipy.fftpack import fft

min=0
max=400

def calculateFFT (timeStep,micDataX,micDataY):

n=micDataX.size

FFT=np.fft.fft(micDataY)
fft_amlitude=2*abs(FFT)/n
fft_phase=np.angle(FFT)
fft_freq= np.fft.fftfreq(n, d=timeStep) #not used created manually (7 lines) check pi_fFreqDomainCreateConstantBW it is kept here to compare sizes
upper_bound=int((n)/2)

return fft_freq[1:upper_bound],fft_amlitude[1:upper_bound],fft_phase[1:upper_bound]


def calculateI_FFT (n,amplitude_spect,phase_spect):

data=list()

for mag,phase in zip(amplitude_spect,phase_spect):
data.append((mag*n/2)*(np.cos(phase)+1j* np.sin(phase)))
full_data=list(data)
i_data=np.fft.irfft(data)
return i_data

#sampling rate and time vector
start_time=0 #sec
end_time= 2
sampling_rate=1000 #Hz
N=(end_time-start_time)*sampling_rate

#Freq domain peaks
peak1_hz=60 # freq of peak
peak1_mag= 25

peak2_hz=270 # freq of peak
peak2_mag= 2

#Vibration data generation
time =np.linspace(start_time,end_time,N)
vib_data=peak1_mag*np.sin(2*pi*peak1_hz*time)+peak2_mag*np.sin(2*pi*peak2_hz*time)

#Data plotting
plt.plot(time[min:max],vib_data[min:max])

# fft
time_step=1/sampling_rate
fft_freq,fft_data,fft_phase=calculateFFT(time_step,time,vib_data)

#ifft
i_data=calculateI_FFT(N,fft_data,fft_phase)

#plotting
plt.plot(time[min:max],i_data[min:max])
plt.xlabel("Time (s)")
plt.ylabel("Vibration (g)")
plt.title("Time domain")


plt.show()


The output signal screenshot is attached (blue for original signal Orange for the reconstructed one)
enter image description here

Thank you!

sound.orig -> FFT -> IFFT -> sound.new

sound.orig

sound.new

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