Add functions for displacement conversion

util.py

@@ -7,22 +7,19 @@
 def bounded_frequency_waveform(start_frequency, end_frequency, length=1000, sample_rate=1000):
     # Create an evenly spaced time array
     t = np.linspace(0, 1.0, length, False)  # 1 second
-
     # Generate a random frequency spectrum between the start and end frequencies
     freq = np.linspace(0, sample_rate/2, length//2, False)
     spectrum = np.random.uniform(0, 1, len(freq))
     spectrum = np.where((freq >= start_frequency) & (freq <= end_frequency), spectrum, 0)
-    c = np.random.rayleigh(np.sqrt(4*spectrum*(freq[1]-freq[0])))
-    # See Jiang 2023 ref 28 for why we use the Rayleigh distribution here
+    c = np.random.rayleigh(np.sqrt(spectrum*(freq[1]-freq[0])))
+    # See Phys. Rev. A 107, 042611 (2023) ref 28 for why we use the Rayleigh distribution here
     # Unless we use this distribution, the random noise will not be Gaussian distributed
     phase = np.random.uniform(-np.pi, np.pi, len(freq))
-
     # Use the inverse Fourier transform to convert the frequency domain signal back to the time domain
     # Also include a zero phase component
-    spectrum = np.hstack([spectrum*np.exp(1j*phase), np.zeros_like(spectrum)])
+    spectrum = np.hstack([c*spectrum*np.exp(1j*phase), np.zeros_like(spectrum)])
     y = np.real(ifft(spectrum))
     y = np.fft.fftshift(y)
-
     return t, y
 
 '''
@@ -35,4 +32,46 @@ def linear_convert(data, new_min=-1, new_max=1):
     old_max = np.max(data)
     old_range = old_max - old_min
     new_range = new_max - new_min
-    return new_min + new_range * (data - old_min) / old_range
+    return new_min + new_range * (data - old_min) / old_range
+
+f0 = 257.1722062654443
+Q = 15.680894756413974
+k = 32.638601262518705
+c = -3.219944358492212
+
+'''
+Calculates the expected displacement of the speaker at an inputted drive amplitude 'ampl' 
+for a given frequency 'f', based on the calibration fit at 0.2Vpp. 
+
+@param f: optimal range 20Hz-1kHz
+@param ampl: optimal range 0-0.6V 
+@return: expected displacement in microns 
+'''
+def A(f, ampl):
+    return ampl * (k * f0**2) / np.sqrt((f0**2 - f**2)**2 + f0**2*f**2/Q**2)
+
+'''
+Calculates the phase delay between the speaker voltage waveform and the photodiode response
+at a given frequency 'f'.
+
+@param f: optimal range 20Hz-1kHz
+@return: phase in radians
+'''
+def phase(f):
+    return np.arctan2(f0/Q*f, f**2 - f0**2) + c
+
+'''
+Calculates the corresponding displacement waveform based on the given voltage waveform
+using calibration. 
+'''
+def displacement_waveform(speaker_data, sample_rate, ampl, right=True):
+    fourier_signal = fft(speaker_data)
+    n = speaker_data.size
+    sample_spacing = 1/sample_rate 
+    freq = fftfreq(n, d=sample_spacing) # units: cycles/s = Hz
+
+    # Multiply signal by transfer func in freq domain, then return to time domain
+    converted_signal = fourier_signal * A(freq, ampl) * np.where(freq < 0, np.exp(-1j*phase(-freq)), np.exp(1j*phase(freq)))
+    y = np.real(ifft(converted_signal))
+
+    return y, converted_signal, freq