def plot_average_psd(data, window_length, offset, fig=False):
if fig:
plt.figure()
data_ep = np.squeeze(epoch_data(data, window_length, offset))
psd = ama.rfft_psd(data_ep.T, fs)
m = np.mean(psd['PSD'], axis=-1)
mpsd = psd
mpsd['PSD'] = np.reshape(m, [-1, 1])
ama.plot_psd_data(mpsd, f_range=np.array([0, 60]))
def get_psd(self, data):
sample_psd = ama.rfft_psd(data, self.headset_freq)
return sample_psd['freq_axis'], sample_psd['PSD']
def plot_psd(data):
psd = ama.rfft_psd(data, fs)
ama.plot_psd_data(psd, f_range=np.array([0, 60]))
# The Spectograms are scaled to represent the power of the full signal
wavelet_spect_segmented = n_segments * wavelet_spect_segmented
wavelet_spectrogram_power_b = []
wavelet_modulation_spectrogram_power_b = []
# From each Segment of the Spectrogram, compute the Modulation Spectrogram
for i_segment in range(0, n_segments):
wavelet_spectrogram_power_b.append(wavelet_spect_segmented[:,:,i_segment])
# Square Root is obtained to work with the Instantaneous Amplitude
x_tmp_wavelet = np.sqrt(np.squeeze(wavelet_spect_segmented[:,:, i_segment]))
# PSD of the Spectrogram Segment
mod_psd_wavelet = ama.rfft_psd(x_tmp_wavelet, fs)
# Place results in corresponding index
wavelet_modulation_spectrogram_power_b.append(mod_psd_wavelet['PSD'] / mod_psd_wavelet['freq_delta'])
toc = time.time() - tic
print(str(toc) + ' seconds')
# Create dictionaries for Method B, for sake of plotting
wavelet_spectrogram_data_b = deepcopy(wavelet_spectrogram_data_a)
wavelet_modulation_spectrogram_data_b = deepcopy(wavelet_modulation_spectrogram_data_a)
for i_segment in range(0, n_segments):
wavelet_spectrogram_data_b[i_segment]['power_spectrogram'] = wavelet_spectrogram_power_b[i_segment][:,:,np.newaxis]
wavelet_modulation_spectrogram_data_b[i_segment]['power_modulation_spectrogram'] = np.transpose(wavelet_modulation_spectrogram_power_b[i_segment])[:,:,np.newaxis]
energy_x = T * sum(x**2) duration = T * n # Power of the signal power_x = energy_x / duration # A simpler way is power_x_2 = (1 / n) * sum(x**2) # Power in Frequency domain # Power using FFT X = np.fft.fft(x) power_X = float( (1 / n**2) * sum(np.abs(X)**2)) # Power using its PSD from rFFT psd_rfft_r = ama.rfft_psd(x, fs, win_funct = 'boxcar') f_step = psd_rfft_r['freq_delta'] power_psd_rfft_x_rw = f_step * sum(psd_rfft_r['PSD'])[0] plt.figure() ama.plot_psd_data(psd_rfft_r) # Power using its PSD from rFFT psd_rfft_b = ama.rfft_psd(x, fs, win_funct = 'blackmanharris') f_step = psd_rfft_r['freq_delta'] power_psd_rfft_x_bh = f_step * sum(psd_rfft_r['PSD'])[0] plt.figure() ama.plot_psd_data(psd_rfft_b) # Power from STFFT Spectrogram (Hamming window) w_size = 1 * fs w_shift = 0.5 * w_size
ipls] = pls_t_win # _ _ * _ _
if age_limits[0] <= age <= age_limits[1]:
# appends pulse peaks from one file to ALL files list
pls_peaks_all.append(pls_peaks)
ppg_signals_all.append(ppg_signals)
age_all.append(age)
# %% analysis
# concatenate all PPG signals and Pulse peaks
pls_peaks_all_cat = np.concatenate(pls_peaks_all, axis=1)
ppg_signals_all_cat = np.concatenate(ppg_signals_all, axis=1)
# PSD
pls_peaks_psd = ama.rfft_psd(pls_peaks_all_cat, fs, 1024)
ppg_signals_psd = ama.rfft_psd(ppg_signals_all_cat, fs, 1024)
# average across instances
pls_peaks_psd['PSD'] = np.mean(pls_peaks_psd['PSD'], axis=1)[:, None]
ppg_signals_psd['PSD'] = np.mean(ppg_signals_psd['PSD'], axis=1)[:, None]
# compute transfer function
n_fft = 2048
pls_peaks_fft = np.fft.fft(pls_peaks_all_cat, n_fft, axis=0)
ppg_signals_fft = np.fft.fft(ppg_signals_all_cat, n_fft, axis=0)
# adjust for even and odd number of elements
if n_fft % 2 != 0:
# odd case
n_freqs = int((n_fft + 1) / 2)
else:
#%% time <--> frequency
#%% FFT and IFFT of a real-valued signal
xi_rfft = ama.rfft(xi)
xo = ama.irfft(xi_rfft, n)
plt.figure()
fi = plt.subplot(2, 1, 1)
ama.plot_signal(xi, fs, 'Original x(t)')
fo = plt.subplot(2, 1, 2, sharex=fi, sharey=fi)
ama.plot_signal(xo, fs, 'Recovered x(t)')
r = np.corrcoef(np.squeeze(xi), np.squeeze(xo))
print('Correlation: ' + str(r[0, 1]) + '\r\n')
#%% PSD data obtained with rFFT, and its inverse
xi_psd = ama.rfft_psd(xi, fs)
xo = ama.irfft_psd(xi_psd)
plt.figure()
fi = plt.subplot(4, 1, 1)
ama.plot_signal(xi, fs, 'Original x(t)')
fo = plt.subplot(4, 1, 4, sharex=fi, sharey=fi)
ama.plot_signal(xo, fs, 'Recovered x(t)')
plt.subplot(4, 1, (2, 3))
ama.plot_psd_data(xi_psd)
plt.title('PSD of x(t)')
r = np.corrcoef(np.squeeze(xi), np.squeeze(xo))
print('Correlation: ' + str(r[0, 1]) + '\r\n')
#%% time <--> time-frequency
#%% STFT Spectrogram