def example():
# sample 1, page 101
vmax = 10
r = 40 / (2 * 10)
delta_q = q.delta_q(vmax, r)
vj, tj = q.uniform_midtread_quantizer(vmax, delta_q)
# sample 2, page 101
vmax = 1
r = 20 / (2 * 5)
delta_q = q.delta_q(vmax, r)
vj, tj = q.uniform_midrise_quantizer(vmax, delta_q)
# sample 3, page 85, midrise
vmax = 1
delta_q = 2 * vmax / 8
vj, tj = q.uniform_midrise_quantizer(vmax, delta_q)
n = np.arange(0, 8)
m = np.round(np.sin(2 * np.pi * (np.float(1300) / 8000) * n), decimals=3)
plt.plot(m)
mq, idx = q.quantize(m, vmax, vj, tj)
plt.plot(mq)
# sample 3, page 85, midtread
vj, tj = q.uniform_midtread_quantizer(vmax, delta_q)
mq, idx = q.quantize(m, vmax, vj, tj)
plt.plot(mq)
plt.show()
def exercise_04():
# a)
signal = sawtooth_signal()
vmax = q.vmax(signal)
r = 3
delta_q = q.delta_q(vmax, r)
vj, tj = q.uniform_midrise_quantizer(vmax, delta_q)
mq, idx = q.quantize(signal, vmax, vj, tj)
print("m(q) = {}".format(mq))
plt.plot(signal)
plt.plot(mq)
# plt.plot(xQ)
plt.show()
# b)
# The mp(n) starts with the same element as m(n)
mp = np.copy(mq)
mp = np.insert(mp, 0, signal[0])
mp = np.delete(mp, len(mp) - 1)
# error formula
error = signal - mp
# quantization of error
error_quantified, idx = q.quantize(error, vmax, vj, tj)
plt.hist(error_quantified)
plt.title("Histogram")
plt.show()
# c)
px = metrics.signal_power(signal)
r = np.arange(3, 9)
snr_t = np.arange(len(r), dtype='float')
snr_p = np.arange(len(r), dtype='float')
for i in range(len(r)):
delta_q = q.delta_q(vmax, r[i])
vj, tj = q.uniform_midtread_quantizer(vmax, delta_q)
mq, idx = q.quantize(signal, vmax, vj, tj)
eq = signal - mq
pq = metrics.signal_power(eq)
snr_t[i] = lib.metrics.snr_theoric(r[i], px, vmax)
snr_p[i] = lib.metrics.snr_db(px, pq)
def exercise_02():
filename = 'lab01/som_8_16_mono.wav'
print('2. Reading sound file: {}'.format(filename))
fs, m = wav.read(filename)
vmax = q.vmax(m)
r = np.array([3, 5, 8])
snr = np.arange(len(r), dtype='float')
for i in range(len(r)):
delta_q = q.delta_q(vmax, r[i])
vj, tj = q.uniform_midrise_quantizer(vmax, delta_q)
mq, idx = q.quantize(m, vmax, vj, tj)
filename = 'lab02/som_8_16_quantize_{}bits.wav'.format(r[i])
print('2. r = {} [quantize]; Writing sound file {}'.format(
r[i], filename))
wav.write(filename, fs, mq.astype('int16'))
bin = c.pcm_encode(idx, r[i])
dec = c.pcm_decode(bin)
filename = 'lab02/som_8_16_quantize_encode_decode_dequantize_{}bits.wav'.format(
r[i])
print(
'2. r = {} [quantize > encode > decode > dequantize]; Writing sound file {}'
.format(r[i], filename))
wav.write(filename, fs, q.dequantize(vj, dec).astype('int16'))
p = np.sum(m * m) / len(m)
snr[i] = lib.metrics.snr_theoric(r[i], p, vmax)
print('2. r = {:d}; SNR = {:>7.3f}'.format(r[i], snr[i]))
def exercise_05():
# a)
fs, x = wav.read("som_8_16_mono.wav")
plt.hist(x)
plt.title("Histogram")
plt.show()
# b)
# TODO
# c)
vmax = q.vmax(x)
px = np.sum(x * x) / len(x)
px = lib.metrics.signal_power(x)
r = np.arange(3, 9)
snr_t = np.arange(len(r), dtype='float')
snr_p = np.arange(len(r), dtype='float')
for i in range(len(r)):
delta_q = q.delta_q(vmax, r[i])
vj, tj = q.uniform_midtread_quantizer(vmax, delta_q)
mq = q.quantize(x, vmax, vj, tj)
eq = x - mq
pq = lib.metrics.signal_power(eq)
snr_t = lib.metrics.snr_theoric(r[i], px, vmax)
snr_p = lib.metrics.snr_db(px, pq)
def exercise_01():
signal = lab01.sawtooth_signal()
vmax = q.vmax(signal)
r = 3
delta_q = q.delta_q(vmax, r)
vj, tj = q.uniform_midrise_quantizer(vmax, delta_q)
mq, idx = q.quantize(signal, vmax, vj, tj)
bin = c.pcm_encode(idx, r)
dec = c.pcm_decode(bin)
def exercise_03():
# Hamming parameters
n = 15
r = 11
# Signal quantization
m = lab01.sawtooth_signal()
vmax = q.vmax(m)
delta_q = q.delta_q(vmax, r)
vj, tj = q.uniform_midrise_quantizer(vmax, delta_q)
mq, idx = q.quantize(m, vmax, vj, tj)
# Parity matrix
P = np.array([
[1, 1, 1, 1],
[0, 1, 1, 1],
[1, 0, 1, 1],
[1, 1, 0, 1],
[1, 1, 1, 0],
[0, 0, 1, 1],
[0, 1, 0, 1],
[0, 1, 1, 0],
[1, 0, 1, 0],
[1, 0, 0, 1],
[1, 1, 0, 0],
],
dtype='uint8')
# Encode and codify with Hamming(15, 11)
bin = c.pcm_encode(idx, r)
x = error_control.hamming(bin, P, n, r)
# Simulate channel communication
y = channel.send_with_binomial_noise(x, 0.01)
# Measure the elapsed time to correct errors
from time import time
start_time = time()
# Detect and correct error/noise
y = error_control.correction(y, P)
elapsed_time = time() - start_time
print(
'3. Error correction elapsed time: {:4.3f} s'.format(elapsed_time))
def exercise_05():
# TODO
# a)
fs = 8000
f = 3500
t = np.arange(0, 5 * 1 / f, 1 / fs)
m = np.sin(2 * np.pi * f * t)
r = 3
vmax = q.vmax(m)
delta_q = q.delta_q(vmax, r)
vj, tj = q.uniform_midrise_quantizer(vmax, delta_q)
mq, idx = q.quantize(m, vmax, vj, tj)
x = c.pcm_encode(idx, r)
print(
'5. a) First 4 samples of the signal y(t) = sin(2 * pi * 3500 * t) with fs = {}: {}'
.format(fs, m))
print('5. a) Midrise quantizer with r = 3 codification: {}'.format(
np.ndarray.flatten(x)))
def exercise_04():
# Parity matrix: http://michael.dipperstein.com/hamming/
# Hamming parameters
n = 15
r = 11
# Signal quantization
m = lab01.sawtooth_signal()
vmax = q.vmax(m)
delta_q = q.delta_q(vmax, r)
vj, tj = q.uniform_midrise_quantizer(vmax, delta_q)
mq, idx = q.quantize(m, vmax, vj, tj)
# Parity matrix
P = np.array([
[1, 1, 1, 1],
[0, 1, 1, 1],
[1, 0, 1, 1],
[1, 1, 0, 1],
[1, 1, 1, 0],
[0, 0, 1, 1],
[0, 1, 0, 1],
[0, 1, 1, 0],
[1, 0, 1, 0],
[1, 0, 0, 1],
[1, 1, 0, 0],
],
dtype='uint8')
# Encode and codify with Hamming(15, 11)
bin = c.pcm_encode(idx, r)
x = error_control.hamming(bin, P, n, r)
ber_theoric = np.array([.01, .05, .1, .5, .75, 1])
ber_pratic = np.zeros(shape=(len(ber_theoric), 2))
snr = np.zeros(len(ber_theoric))
for i in range(len(ber_theoric)):
# Channel simulation
y = channel.send_with_binomial_noise(x, ber_theoric[i])
ber_pratic[i, 0] = metrics.ber(x, y)
# Error correction
y = error_control.correction(y, P)
ber_pratic[i, 1] = metrics.ber(bin, y)
# Decode and Dequantize
idx = c.pcm_decode(y)
mq = q.dequantize(vj, idx)
# SNR
e = m - mq
p_error = metrics.signal_power(e)
p = metrics.signal_power(m)
snr[i] = lib.metrics.snr_db(p, p_error)
print(
'4. BERt = {:>6.2f}; BER = {:>6.3f}; BER\' = {:>6.3f}; SNR = {:>6.3f}'
.format(ber_theoric[i], ber_pratic[i, 0], ber_pratic[i, 1],
snr[i]))
def exercise_06():
# Hamming parameters
n = 15
r = 11
# Quantization
from lab01 import lab01
m1 = lab01.sawtooth_signal()
vmax = quantization.vmax(m1)
delta_q = quantization.delta_q(vmax, r)
vj, tj = quantization.uniform_midrise_quantizer(vmax, delta_q)
x1, idx = quantization.quantize(m1, vmax, vj, tj)
# Encoder
P = np.array([
[1, 1, 1, 1],
[0, 1, 1, 1],
[1, 0, 1, 1],
[1, 1, 0, 1],
[1, 1, 1, 0],
[0, 0, 1, 1],
[0, 1, 0, 1],
[0, 1, 1, 0],
[1, 0, 1, 0],
[1, 0, 0, 1],
[1, 1, 0, 0],
],
dtype='uint8')
x2 = codification.pcm_encode(idx, r)
# Error control
x3 = error_control.hamming(x2, P, n, r)
# Digital modulation
a = 1
x4 = modulation.manchester_enconde(x3, a)
# Channel
sigma_squared = np.array([0.5, 1, 2, 4])
for s in sigma_squared:
y1 = channel.send_with_awgn(x4, np.sqrt(s))
# Digital modulation
y2 = modulation.machester_decode(y1, lambda_=0)
# Error control
y3 = error_control.correction(y2, P)
# BER calculation
# TODO: tb = len(x4[0]) ?
tb = len(x4)
eb = metrics.eb_manchester(a, tb)
n0 = s * 2
ber_pratic = metrics.ber(x3, y2)
ber_theoric = metrics.ber_manchester(eb, n0)
# Decoder
y4 = codification.pcm_decode(y3)
# Quantization
m2 = quantization.dequantize(vj, y4)
# Metrics
# TODO: SNR?
plt.plot(m1)
plt.plot(m2)
plt.show()
# Metrics
# snr = np.zeros(len(sigma_squared))
px = metrics.signal_power(m1)
snr_theoric = lib.metrics.snr_theoric(r, px, vmax)
error = m1 - x1
pe = metrics.signal_power(error)
snr_pratic = lib.metrics.snr_db(px, pe)
print('')
def exercise():
# hamming parameters
n = 15
r = 11
# quantization
m1, fs, filename = super_mario_intro('3sec')
# m1, fs, filename = test_wav()
# m1, fs, filename = sawtooth_signal()
filename = 'lab04/{}'.format(filename)
vmax = quantization.vmax(m1)
delta_q = quantization.delta_q(vmax, r)
vj, tj = quantization.uniform_midrise_quantizer(vmax, delta_q)
x1, idx = quantization.quantize(m1, vmax, vj, tj)
# codification
x2 = codification.pcm_encode(idx, r)
# error control
parity_matrix = np.array([
[1, 1, 1, 1],
[0, 1, 1, 1],
[1, 0, 1, 1],
[1, 1, 0, 1],
[1, 1, 1, 0],
[0, 0, 1, 1],
[0, 1, 0, 1],
[0, 1, 1, 0],
[1, 0, 1, 0],
[1, 0, 0, 1],
[1, 1, 0, 0],
],
dtype='uint8')
x3 = error_control.hamming(x2, parity_matrix, n, r)
# digital modulation
x4, coords_o, new_bits = digital_modulation.qam_encode(x3, p=8)
# channel
sigma_square = np.array([0.05, 0.1, 0.2, 0.3])
snr_channel = np.zeros(len(sigma_square))
snr_reception = np.zeros(len(sigma_square))
ber_bc = np.zeros(len(sigma_square))
ber_ac = np.zeros(len(sigma_square))
fig_signal = plt.figure(1)
fig_received_signal = plt.figure(2, figsize=(12, 10))
fig_constellation = plt.figure(3, figsize=(12, 10))
for i in range(len(sigma_square)):
y1 = channel.send_with_awgn(x4, sigma=np.sqrt(sigma_square[i]))
# digital modulation
y2, coords_r, coords_p = digital_modulation.qam_decode(
y1, p=8, rm_bits=new_bits)
# error control
y3 = error_control.correction(y2, parity_matrix)
# codification
y4 = codification.pcm_decode(y3)
# quantization
m2 = quantization.dequantize(vj, y4)
# output
wav.write(filename.format(sigma_square[i]), fs, m2.astype('int16'))
# metrics
ax_received_signal = fig_received_signal.add_subplot(2, 2, i + 1)
ax_constellation = fig_constellation.add_subplot(2, 2, i + 1)
signal_graph(ax_received_signal, m2, sigma_square[i])
constellation_graph(ax_constellation, coords_o, coords_p, coords_r,
sigma_square[i])
p_x4 = metrics.signal_power(x4)
p_y1 = metrics.signal_power(y1)
snr_channel[i] = metrics.snr(p_x4, p_y1)
p_m1 = metrics.signal_power(m1)
p_m2 = metrics.signal_power(m2)
snr_reception[i] = metrics.snr(p_m1, p_m2)
ber_bc[i] = metrics.ber(x3, y2)
ber_ac[i] = metrics.ber(x2, y3)
# metrics
ax_signal = fig_signal.add_subplot(1, 1, 1)
ax_signal.set_title('Transmitted signal')
ax_signal.set_xlabel('time')
ax_signal.set_ylabel('amplitude')
ax_signal.plot(m1)
fig_received_signal.suptitle('Received signal')
fig_constellation.suptitle('16-QAM constellation')
fig_ber_snr = plt.figure(4)
ber_snr_graph(fig_ber_snr.add_subplot(1, 1, 1), ber_ac, ber_bc,
snr_channel, snr_reception, sigma_square)
plt.tight_layout()
plt.show()