From 91f66894688bf078f8ddba49e54b5f02269e2511 Mon Sep 17 00:00:00 2001 From: Anton Schirg Date: Sat, 21 Oct 2017 14:57:32 +0200 Subject: [PATCH] New modulation --- LICENSE | 347 +++++++++++++++++++++++++++++++++++++++++++++++ analyse_audio.py | 284 +++++++++++++++++++++++++++++++++++++- default.nix | 19 +++ 3 files changed, 649 insertions(+), 1 deletion(-) create mode 100644 default.nix diff --git a/LICENSE b/LICENSE index be1bebd..12849c6 100644 --- a/LICENSE +++ b/LICENSE @@ -1,3 +1,350 @@ +This software is licensed under the GNU GPL because it contains parts from https://github.com/kit-cel/lecture-examples. +The rest of the software is also licensed under MIT License (see further down) + +GNU GENERAL PUBLIC LICENSE + Version 2, June 1991 + + Copyright (C) 1989, 1991 Free Software Foundation, Inc., + 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The licenses for most software are designed to take away your +freedom to share and change it. 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If this is what you want to do, use the GNU Lesser General +Public License instead of this License. + +------------------ + +For parts not marked as EXTERNAL: + The MIT License (MIT) Copyright (c) 2013 Anton Schirg diff --git a/analyse_audio.py b/analyse_audio.py index 138dd70..41b2935 100644 --- a/analyse_audio.py +++ b/analyse_audio.py @@ -1,3 +1,5 @@ +# Contains code form https://github.com/kit-cel/lecture-examples/blob/master/nt1/vorlesung marked with EXTERNAL licensed under GPL + import numpy as np import scipy_signal @@ -101,6 +103,234 @@ def generate_signal(bits, chunk_length, sample_rate, frequency): return data +# EXTERNAL +######################## +# find impulse response of an RC filter +######################## +def get_rc_ir(K, n_up, t_symbol, r): + + ''' + Determines coefficients of an RC filter + + Formula out of: K.-D. Kammeyer, Nachrichtenübertragung + At poles, l'Hospital was used + + NOTE: Length of the IR has to be an odd number + + IN: length of IR, upsampling factor, symbol time, roll-off factor + OUT: filter coefficients + ''' + + # check that IR length is odd + assert K % 2 == 1, 'Length of the impulse response should be an odd number' + + # map zero beta to close-to-zero + if r == 0: + r = 1e-32 + + + # initialize output length and sample time + rc = np.zeros( K ) + t_sample = t_symbol / n_up + + + # time indices and sampled time + k_steps = np.arange( -(K-1) / 2.0, (K-1) / 2.0 + 1 ) + t_steps = k_steps * t_sample + + for k in k_steps.astype(int): + + if t_steps[k] == 0: + rc[ k ] = 1. + + elif np.abs( t_steps[k] ) == t_symbol / ( 2.0 * r ): + rc[k] = np.sin(np.pi/(2*r)) / (np.pi/(2*r)) * np.pi / 4 + # rc[ k ] = r * np.sin( np.pi / r ) + # + else: + rc[ k ] = np.sin( np.pi * t_steps[k]/t_symbol ) / (np.pi * t_steps[k]/t_symbol) \ + * np.cos( r * np.pi * t_steps[k] / t_symbol ) \ + / ( 1.0 - ( 2.0 * r * t_steps[k] / t_symbol )**2 ) + # rc[ k ] = np.sin( np.pi * t_steps[k]/t_symbol ) / np.pi / t_steps[k] \ + # * np.cos( r * np.pi * t_steps[k] / t_symbol ) \ + # / ( 1.0 - ( 2.0 * r * t_steps[k] / t_symbol )**2 ) + + return rc + + +######################## +# find impulse response of an RRC filter +######################## +def get_rrc_ir(K, n_up, t_symb, r): + + ''' + Determines coefficients of an RRC filter + + Formula out of: J. Huber, Trelliscodierung, Springer, 1992, S. 15 + At poles, values of wikipedia.de were used (without cross-checking) + + NOTE: Length of the IR has to be an odd number + + IN: length of IR, upsampling factor, symbol time, roll-off factor + OUT: filter ceofficients + ''' + + assert K % 2 != 0, "Filter length needs to be odd" + + if r == 0: + r = 1e-32 + + # init + rrc = np.zeros(K) + t_sample = t_symb/n_up + + + i_steps = np.arange( 0, K) + k_steps = np.arange( -(K-1)/2.0, (K-1)/2.0 + 1 ) + t_steps = k_steps*t_sample + + for i in i_steps: + + if t_steps[i] == 0: + rrc[i] = 1.0/np.sqrt(t_symb) * (1.0 - r + 4.0 * r / np.pi ) + + elif np.abs( t_steps[i] ) == t_symb/4.0/r: + rrc[i] = r/np.sqrt(2.0*t_symb)*((1+2/np.pi)*np.sin(np.pi/4.0/r)+ \ + ( 1.0 - 2.0/np.pi ) * np.cos(np.pi/4.0/r) ) + + else: + rrc[i] = 1.0/np.sqrt(t_symb)*( np.sin( np.pi*t_steps[i]/t_symb*(1-r) ) + \ + 4.0*r*t_steps[i]/t_symb * np.cos( np.pi*t_steps[i]/t_symb*(1+r) ) ) \ + / (np.pi*t_steps[i]/t_symb*(1.0-(4.0*r*t_steps[i]/t_symb)**2.0)) + + return rrc +# END EXTERNAL + +import matplotlib +matplotlib.use('TkAgg') +import matplotlib.pyplot as plt + +# EXTERNAL +def generate_constellation_points(M): + return [ np.exp( 1j * 2 * np.pi * m / M + 1j * np.pi / M ) for m in range( M ) ] +# END EXTERNAL + +def generate_rc_filter(n_up, symbol_time): + syms_per_filt = 4 + K_filt = 2 * syms_per_filt * n_up + 1 + rc = get_rc_ir(K_filt, n_up, symbol_time, 0.33) + return rc / np.linalg.norm(rc) + +def generate_rrc_filter(n_up, symbol_time): + syms_per_filt = 4 + K_filt = 2 * syms_per_filt * n_up + 1 + rrc = get_rrc_ir(K_filt, n_up, symbol_time, 0.33) + #return rrc / np.linalg.norm(rrc) + return rrc / rrc[int(rrc.shape[0] / 2)] + +def generate_signal_new(symbols, n_up, sr, frequency): + M = 4 + constellation_points = generate_constellation_points(M) + + plt.plot(np.real(constellation_points), np.imag(constellation_points), 'o') + for i, xy in enumerate(zip(np.real(constellation_points), np.imag(constellation_points))): + plt.annotate(str(i), xy=xy, textcoords='data') + plt.show() + + s = [ constellation_points[symbol] for symbol in symbols ] + n_symbols = len(s) + symbol_time = n_up / sr + + rect = np.ones(n_up) + + rrc = generate_rrc_filter(n_up, symbol_time) * 0.7 + + plt.plot(rrc) + print(rrc.shape) + +# EXTERNAL + s_up = np.zeros(n_symbols * n_up, dtype=np.complex128) + s_up[::n_up] = s + s_up = np.convolve(rrc, s_up) + + plt.plot(np.abs(s_up)) + plt.show() + + plt.plot( np.real( s_up ), np.imag( s_up ), linewidth=2.0 ) + plt.grid( True ) + plt.xlabel( '$\mathrm{Re}\\{s(t)\\}$' ) + plt.ylabel(' $\mathrm{Im}\\{s(t)\\}$' ) + plt.title( 'QPSK signal' ) + plt.show() +# END EXTERNAL + + t = np.linspace(0, s_up.shape[0]/sr, s_up.shape[0]) + carrier = np.exp(-1j*2*np.pi*frequency*t) + + modulated = np.real(s_up * carrier) + print(modulated.shape) + + #plt.plot(modulated) + #plt.show() + + return modulated + +def demodulate_signal(signal, n_data_symbols, n_up, sr, frequency): + M = 4 + constellation_points = generate_constellation_points(M) + symbol_time = n_up / sr + n_symbols = n_data_symbols + 8 + 1 # 8 for rc, 1 for differential + + signal = signal[:n_symbols * n_up] + + t = np.linspace(0, n_symbols * symbol_time, n_symbols * n_up) + dem_carrier = np.exp(1j*2*np.pi*frequency*t) + + demodulated = signal * dem_carrier + + rrc = generate_rrc_filter(n_up, symbol_time) + rrc /= np.linalg.norm(rrc) + demodulated = np.convolve(demodulated, rrc[::-1]) + + sampled = demodulated[::n_up] + sampled = sampled[8:-8] #remove 2x rc length at sides + + diff_dec = differential_decode_symbols(sampled) + + +# EXTERNAL + plt.plot( np.real( demodulated ), np.imag( demodulated ), linewidth=2.0 ) + plt.grid( True ) + plt.xlabel( '$\mathrm{Re}\\{s(t)\\}$' ) + plt.ylabel(' $\mathrm{Im}\\{s(t)\\}$' ) + plt.title( 'Demodulated QPSK signal' ) + plt.show() + + plt.plot( np.real( diff_dec ), np.imag( diff_dec ), 'o', linewidth=2.0 ) + for i, xy in enumerate(zip(np.real(diff_dec), np.imag(diff_dec))): + plt.annotate(str(i), xy=xy, textcoords='data') + plt.grid( True ) + plt.xlabel( '$\mathrm{Re}\\{s(t)\\}$' ) + plt.ylabel(' $\mathrm{Im}\\{s(t)\\}$' ) + plt.title( 'Demodulated QPSK signal' ) + plt.show() +# END EXTERNAL + + symbols = [] + for s in diff_dec: + upper = np.imag(s) > 0 + right = np.real(s) > 0 + if upper and right: + symbols.append(0) + if upper and not right: + symbols.append(1) + if not upper and not right: + symbols.append(2) + if not upper and right: + symbols.append(3) + + return symbols + def generate_chirp(f0, f1, duration, sample_rate): ts = np.linspace(0, duration, duration * sample_rate) @@ -117,6 +347,24 @@ def check_checksum(data): return checksum == data[3] +def differential_encode_symbol_nums(symbol_nums, M): + encoded = [0] + last = 0 + for s in symbol_nums: + enc = (s + last) % M + last = enc + encoded.append(enc) + return encoded + + +def differential_decode_symbols(symbols): + last = symbols[0] + decoded = np.zeros(symbols.shape[0] - 1, dtype=np.complex128) + for i, s in enumerate(symbols[1:]): + decoded[i] = s / last * (1+1j) + last = s + return decoded + def find_sync_signal(data, sr, sync_signal): """ @@ -129,4 +377,38 @@ def find_sync_signal(data, sr, sync_signal): def bandpass(data, f, pass_width, sr): filter_array = scipy_signal.firwin(128, [f-pass_width, f+pass_width], pass_zero=False, nyq=sr/2) data2 = scipy_signal.fftconvolve(data, filter_array, mode='same') - return data2 \ No newline at end of file + return data2 + +if __name__ == "__main__": + import scipy_wavfile as wavfile + import random + + random.seed(1337) + data = [random.randint(0, 3) for _ in range(64)] + + print([9] + data) + + diff_data = differential_encode_symbol_nums(data, 4) + print(diff_data) + + sync_signal = generate_chirp(2000, 4000, 0.3, 48000) + + data_signal = generate_signal_new(diff_data, 256, 48000, 4000) + signal = np.append(sync_signal, data_signal) + wavfile.write("test_new.wav", 48000, (signal * np.iinfo(np.int16).max).astype(np.int16)) + + sr, signal = wavfile.read("test_new_rec_rcc_bad.wav") + assert sr == 48000 + signal = (signal[:,0]).astype(np.float) / np.iinfo(np.int16).max + print("read length ", signal.shape) + + end_of_sync = find_sync_signal(signal, 48000, sync_signal) + print("end of sync: ", end_of_sync) + demod_data = demodulate_signal(signal[end_of_sync:], 64, 256, 48000, 4000) + ser = sum([int(orig != demod) for orig, demod in zip(data, demod_data)])/len(data) + + print(data) + print(len(data)) + print(demod_data) + print(len(demod_data)) + print("SER: {}".format(ser)) diff --git a/default.nix b/default.nix new file mode 100644 index 0000000..3cacf70 --- /dev/null +++ b/default.nix @@ -0,0 +1,19 @@ +let + pkgs = import {}; + stdenv = pkgs.stdenv; + pypkgs = pkgs.python36Packages; +in rec { + audiosync = stdenv.mkDerivation rec { + name = "audiosync"; + src = ./.; + nativeBuildInputs = [ pkgs.pkgconfig ]; + buildInputs = [ + pypkgs.numpy + pypkgs.tkinter + pkgs.ffmpeg + +#Debug + pypkgs.matplotlib + ]; + }; +}