The motive for this article is, in fact, a sad occasion. The world famous radio telescope of the Arecibo Observatory in Puerto Rico has collapsed and cannot be restored. For many years it was the largest radio telescope in the world with a full aperture (diameter 304 m, frequency range up to 10 GHz), with the help of which many discoveries were made. Here in the photo from Wikipedia, it is still working:
Source: en.wikipedia.org/wiki/Arecibo_Observatory
But the text is actually about another event. In 1974, a message to extraterrestrial civilizations was sent into space from this telescope. What and how was encoded in it, details under the cut.
Coding
To begin with, it's interesting to understand how the message was conveyed. As you know, the message size was only 1679 bits (approximately 210 bytes), and it was transmitted at a frequency of 2.38 GHz with a power of 450 kW. Frequency modulation at a rate of 10 bit / s was used for transmission. The number 1679 was not chosen by chance - it is the product of two prime numbers 23 and 73, so there is only one way to expand the picture in the form of a rectangle.
I could not find a ready-made radio message in WAV format, but it is in binary form, and using Python it is easy to generate sound yourself. Those wishing to listen to what the aliens will hear can download and run the code below, which will generate a WAV file. Noise has also been added to the message for added credibility.
generate.py
import scipy.io.wavfile as wav
import scipy.signal as signal
import numpy as np
import matplotlib.pyplot as plt
from PIL import Image
import os
message = """0000001010101000000000000101000001010000000100100010001000100
1011001010101010101010100100100000000000000000000000000000000
0000011000000000000000000011010000000000000000000110100000000
0000000000101010000000000000000001111100000000000000000000000
0000000001100001110001100001100010000000000000110010000110100
0110001100001101011111011111011111011111000000000000000000000
0000010000000000000000010000000000000000000000000000100000000
0000000001111110000000000000111110000000000000000000000011000
0110000111000110001000000010000000001000011010000110001110011
0101111101111101111101111100000000000000000000000000100000011
0000000001000000000001100000000000000010000011000000000011111
1000001100000011111000000000011000000000000010000000010000000
0100000100000011000000010000000110000110000001000000000011000
1000011000000000000000110011000000000000011000100001100000000
0110000110000001000000010000001000000001000001000000011000000
0010001000000001100000000100010000000001000000010000010000000
1000000010000000100000000000011000000000110000000011000000000
1000111010110000000000010000000100000000000000100000111110000
0000000010000101110100101101100000010011100100111111101110000
1110000011011100000000010100000111011001000000101000001111110
0100000010100000110000001000001101100000000000000000000000000
0000000001110000010000000000000011101010001010101010100111000
0000001010101000000000000000010100000000000000111110000000000
0000001111111110000000000001110000000111000000000110000000000
0110000000110100000000010110000011001100000001100110000100010
1000001010001000010001001000100100010000000010001010001000000
0000001000010000100000000000010000000001000000000000001001010
00000000001111001111101001111000"""
def fftnoise(f):
f = np.array(f, dtype='complex')
n_p = (len(f) - 1) // 2
phases = np.random.rand(n_p) * 2 * np.pi
phases = np.cos(phases) + 1j * np.sin(phases)
f[1:n_p+1] *= phases
f[-1:-1-n_p:-1] = np.conj(f[1:n_p+1])
return np.fft.ifft(f).real
def band_limited_noise(min_freq, max_freq, samples, samplerate=1):
freqs = np.abs(np.fft.fftfreq(samples, 1/samplerate))
f = np.zeros(samples)
idx = np.where(np.logical_and(freqs>=min_freq, freqs<=max_freq))[0]
f[idx] = 1
return fftnoise(f)
message = ''.join(i for i in message if i.isdigit())
print("Original message:")
print(message)
print()
# Generate message
fs = 11025
f1, f2 = 3000, 4000
t_sym = 0.1
data = np.zeros(int(fs * t_sym * len(message)))
for p in range(len(message)):
samples = np.linspace(0, t_sym, int(fs * t_sym), endpoint=False)
freq = f2 if message[p] == '1' else f1
data[int(fs * t_sym)*p:int(fs * t_sym)*(p + 1)] = 10000*(0.25*np.sin(2 * np.pi * freq * samples) + band_limited_noise(50, 5000, len(samples), fs))
wav.write('arecibo.wav', fs, np.int16(data))
print("WAV file saved")
For the convenience of listening, I increased the frequency separation, in the original message it was only 10 Hz. Unfortunately, habr does not allow attaching sound files; those who wish can either generate the file themselves or use a temporary link .
By the way, the message was sent in 1974. Right there:
Source: en.wikipedia.org/wiki/Messier_13 The
beautiful star cluster M13 in the constellation Hercules, well known to all astronomy lovers, and accessible for observation even with small telescopes. The cluster is located 22 thousand light years away, so the message will go on for a long time ...
We figured out the coding, now let's imagine that we received such a message - let's see how it can be decoded.
Decoding
The principle of frequency modulation itself is simple - different frequencies correspond to zero and one. On the spectrum, it looks something like this:
There are different ways to decode FSK, as the simplest method, we just filter out one of the frequencies:
fs, data = wav.read('arecibo.wav')
def butter_bandpass(lowcut, highcut, fs, order=5):
nyq = 0.5 * fs
low = lowcut / nyq
high = highcut / nyq
b, a = signal.butter(order, [low, high], btype='band')
return b, a
def butter_bandpass_filter(data, lowcut, highcut, fs, order=5):
b, a = butter_bandpass(lowcut, highcut, fs, order=order)
y = signal.lfilter(b, a, data)
return y
f1, f2 = 3000, 4000
data_f2 = butter_bandpass_filter(data, f2 - 200, f2 + 200, fs, order=3)
plt.plot(data)
plt.plot(data_f2)
plt.xlabel("Time")
plt.ylabel("Amplitude")
plt.title("Signal")
plt.show()
The result suits us quite well:
Of course, the signal that has passed 22 thousand years in space is likely to be slightly weakened, but for simplicity we will assume that the aliens have good
You can easily determine the width of one bit from the picture. We need to output the bits as an image. Because the message was sent to an extraterrestrial civilization - those who, by definition, do not know the "terrestrial" coding systems - transmitting a raster image was the only logical decision. In the constellation Hercules, most likely they do not know what ASCII is or, God forbid, Unicode, but it is most likely possible to display the raster on the screen anywhere in the Galaxy. At least a civilization capable of receiving a digital signal is likely to have some kind of monitor to display it.
We do not know the size of the picture, but we know the size of one bit and we know the size of the entire message. You can just sort out all the possible options, since there are not so many of them:
ss = 1102 # Width of one symbol in samples
for iw in range(12*ss, 25*ss, ss):
w, h = iw, 80
image = Image.new('RGB', (w, h))
px, py = 0, 0
for p in range(data_f2.shape[0]):
image.putpixel((px, py), (0, int(data_f2[p]//32), 0))
px += 1
if px >= w:
px = 0
py += 1
if py >= h:
break
image = image.resize((w//10, 100*h))
image.save("1/image-%d.png" % iw)
For clarity, the picture had to be stretched, because 23 pixels wide by today's standards is, to put it mildly, not enough. The end result is quite visible:
Final Cut:
Unlike the images on Wikipedia , the original image is of course monochrome, there is no color coding in the signal.
A lot of things are encoded in the picture (conditionally, of course), for example, a vertical line 2 pixels wide above a person's head is a DNA spiral (after all, it's obvious, isn't it?). The decoding of the remaining pictograms can be viewed at the link above on Wikipedia.
Conclusion
As you can see, quite a lot of information can be encoded into 210 bytes. In general, the task of sending a signal into deep space is far from simple, because one can only hope for the simplest modulation methods. Will the message reach the addressee? Of course, most likely unlikely. I do not know if the energy of such a "communication line" and the approximate sensitivity of the receiver needed to receive a signal were evaluated when sending it. Yes, this is actually not so important - if such actions inspire someone to explore space, then it was not in vain. Well, we can get the exact answer in 44 thousand years, and I will try to update the text as new data becomes available;)