n_samples_fri = 2 * M + 1 # also number of FS coefficients
# subsampling
skip = n_samples // n_samples_fri
sub_idx = np.arange(0, n_samples, skip).astype(np.int)
n_samples_fri = len(sub_idx)
M = (n_samples_fri - 1) // 2
oversample_fact = M / K
print("Oversample factor : %f" % oversample_fact)
t_samp_sub = t_samp[sub_idx]
# fourier coefficients - ideal low pass by only using this coefficients
fs_ind_base = np.arange(-M, M + 1)
fs_ind = fs_ind_base + fs_ind_center # around center frequency
""" Pulse estimate """
H_tot = total_freq_response(fs_ind / period, center_freq, bw_pulse,
n_cycles)
# "TGC" of sorts
atten = 2 * np.pi * time2distance(t_samp_sub + t0, speed_sound)
""" Sweep though all channels """
rx_echoes = np.zeros((n_elem_tx, n_points))
amplitudes = np.zeros((n_elem_tx, n_points))
resynth_score = np.zeros(n_elem_tx)
start_time = time.time()
print()
for chan_idx in range(n_elem_tx):
print("CHANNEL %d/%d" % (chan_idx + 1, n_elem_tx))
y_samp = ndt_rawdata[min_samp:max_samp, chan_idx]
samp_bw = n_samples / period
Ts = 1 / samp_bw
y_samp, t_samp = sample_iq(ck, tk, period, samp_bw, center_freq, bw, n_cycles,
bwr)
"""
Estimate FS coefficients of sum of diracs
"""
freqs_fft = np.fft.fftfreq(n_samples, Ts)
increasing_order = np.argsort(freqs_fft)
freqs_fft = freqs_fft[increasing_order]
Y = (np.fft.fft(y_samp))[increasing_order] / n_samples
# equalize
freqs = freqs_fft + center_freq
H_tot = total_freq_response(freqs, center_freq, bw, n_cycles, bwr)
fs_coeff_hat = Y / H_tot
"""
FRI recovery
"""
ann_filt = compute_ann_filt(fs_coeff_hat, n_diracs)
tk_hat = estimate_time_param(ann_filt, period)
ck_hat = estimate_amplitudes(fs_coeff_hat, freqs, tk_hat, period)
"""
Evaluate
"""
evaluate_recovered_param(ck, tk, ck_hat, tk_hat)
"""
Plot measured data, alongside typical RF data
"""
y_rf, t_rf = sample_rf(ck, tk, period, samp_freq, center_freq, bw, n_cycles,
def process_fig2p10(n_diracs,
period,
snr_db,
center_freq,
bw,
n_cycles,
bwr,
samp_freq,
cadzow_iter,
oversample_fact,
viz=False,
seed=0):
"""
Fig. 2.8-2.9
"""
# create FRI parameters
ck, tk = create_pulse_param(n_diracs, period=period, seed=seed)
# set oversampling
M = oversample_fact * n_diracs
n_samples = 2 * M + 1
samp_bw = n_samples / period
Ts = 1 / samp_bw
# oversample
y_samp, t_samp = sample_iq(ck, tk, period, samp_bw, center_freq, bw,
n_cycles, bwr)
y_noisy = add_noise(y_samp, snr_db, seed=seed)
# estimate fourier coefficients
freqs_fft = np.fft.fftfreq(n_samples, Ts)
increasing_order = np.argsort(freqs_fft)
freqs_fft = freqs_fft[increasing_order]
freqs = freqs_fft + center_freq
H_tot = total_freq_response(freqs, center_freq, bw, n_cycles, bwr)
fs_coeff_hat = estimate_fourier_coeff(y_noisy, t_samp, H=H_tot)
# denoising + recovery
fs_coeff_clean = cadzow_denoising(fs_coeff_hat,
n_diracs,
n_iter=cadzow_iter)
ann_filt = compute_ann_filt(fs_coeff_clean, n_diracs)
tk_hat = estimate_time_param(ann_filt, period)
ck_hat = estimate_amplitudes(fs_coeff_clean, freqs, tk_hat, period)
# compute errors
tk_err = compute_srr_db_points(tk, tk_hat)
y_rf, t_rf = sample_rf(ck, tk, period, samp_freq, center_freq, bw,
n_cycles, bwr)
y_rf_resynth, t_rf = sample_rf(ck_hat, tk_hat, period, samp_freq,
center_freq, bw, n_cycles, bwr)
sig_err = compute_srr_db(y_rf, y_rf_resynth)
print()
print("%d Diracs, %.02fx oversampling:" % (n_diracs, oversample_fact))
print("Locations SRR : %.02f dB" % tk_err)
print("Resynthesized error : %.02fdB" % sig_err)
"""visualize"""
if viz:
import matplotlib.pyplot as plt
time_scal = 1e5
plt.figure()
baseline = plt.stem(time_scal * tk,
ck,
'g',
markerfmt='go',
label="True")[2]
plt.setp(baseline, color='g')
baseline.set_xdata([0, time_scal * period])
baseline = plt.stem(time_scal * tk_hat,
ck_hat,
'r',
markerfmt='r^',
label="Estimate")[2]
plt.setp(baseline, color='r')
baseline.set_xdata(([0, time_scal * period]))
plt.xlabel("Time [%s seconds]" % str(1 / time_scal))
plt.xlim([0, time_scal * period])
plt.legend(loc='lower right')
plt.grid()
plt.tight_layout()
ax = plt.gca()
ax.axes.yaxis.set_ticklabels([])
# resynthesized signal
plt.figure()
plt.plot(time_scal * t_rf, y_rf, label="True", alpha=0.65)
plt.plot(time_scal * t_rf, y_rf_resynth, label="Estimate", alpha=0.65)
plt.xlim([0, time_scal * period])
plt.grid()
plt.xlabel("Time [%s seconds]" % str(1 / time_scal))
plt.tight_layout()
plt.legend(loc='lower right')
ax = plt.gca()
ax.axes.yaxis.set_ticklabels([])