How to encode/decode complex number to bitstream in MATLAB?

Question

How to compress a complex number like 0.0332815625326639 + 0.000694052654051097i into a bit stream and then decode it to get back the same number?

Answer 1

To generate the bitstream, you can use the following approach:

1. Separate real and imaginary part.
2. Convert the number into its hexadecimal representation with num2hex and use each character as one row (transpose it with .').
3. Convert each row to a decimal with hex2dec. This is needed for the next step.
4. Create the binary representation for each decimal with dec2bin. We need to set a minimal length of 4 since one character in hex occupies 4 bits.
5. Put the values of each row after each other. Now we have converted the hex-string into its binary representation of length 64.
6. Append the imaginary part after the real part which gives us a bitstream of length 128.

To decode the bitstream and get the number back, you can reverse the steps above:

1. Split the bitstream in two junks of length 64. The first is the real part (1:64), the second represents the imaginary part (65:128).
2. Reshape the string to form rows of four characters.
3. Convert the rows to a decimal number with bin2dec.
4. Convert the decimal numbers to their hex-representation with dec2hex.
5. Convert the hexadecimal string back to the original number with hex2num.
6. Use complex to get a complex number consisting of the real and imaginary part. You could use realpart+imagpart*i as well.

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Now let's see the code for all of that:

function the_demo

x = 0.0332815625326639 + 0.000694052654051097i;

bitstream = cb_encode(x)
value = cb_decode(bitstream)

check = x-value    % see if we succeeded


function bin = cb_encode(x)
a1 = dec2bin(hex2dec(num2hex(real(x)).'),4);
a2 = dec2bin(hex2dec(num2hex(imag(x)).'),4);
bin = [reshape(a1.',1,[]),reshape(a2.',1,[])];

function y = cb_decode(bin)
b1 = reshape(bin(1:64),4,[]).';
b1 = hex2num(dec2hex(bin2dec(b1)).');
b2 = reshape(bin(65:128),4,[]).';
b2 = hex2num(dec2hex(bin2dec(b2)).');
y = complex(b1,b2);

Running this, gives the following output:

>> the_demo
bitstream =
00111111101000010000101001000111111011010100011001101111101000000011111101000110101111100010001010111001101101011000000000110010
value =
   0.0333 + 0.0007i
check =
     0