Communication system using shape-shifted sinusoidal waveforms

A data communication method, the method comprising:

• receiving input digital data;
• encoding the input digital data into an encoded waveform representative of the input digital data wherein the encoded waveform is of a wavelength λ and wherein each period of the encoded waveform includes a first half sinusoid corresponding to one half of a first sinusoid of wavelength λ1 and a second half sinusoid corresponding to one half of a second sinusoid of wavelength λ2, where λ1+λ2=λ, the encoding including generating each period of the encoded waveform so as to represent one bit of the input digital data;
• wherein the first half sinusoid is of a first polarity and the second half sinusoid of a second polarity opposite to the first polarity:
• wherein a first bit value of the input digital data is represented when λ1 is greater than λ2 and a second bit value of the input digital data is represented when λ2 is greater than λ1;
• and
• generating an encoded analog waveform from a representation of the encoded waveform;
• wherein each period of the encoded waveform is represented by a function T(t), where T(t) is given by:
• T
• ⁡
• (
• t
• )
• =
• {
• sin
• ⁡
• (
• 2
• ⁢
• π
• ⁢
• t
• λ
• 1
• )
• ⁢
• 0
• ≤
• t
• &
• ⁢
• t
• <
• c
• -
• sin
• ⁡
• (
• 2
• ⁢
• π
• ⁡
• (
• t
• -
• c
• )
• λ
• 2
• )
• ⁢
• c
• ≤
• t
• &
• ⁢
• t
• <
• λ
• ⁢
• where
• c
• =
• λ
• 2
• ⁢
• (
• 1
• +
• u
• )
• u
• =
• (
• 2
• ⁢
• b
• -
• 1
• )
• ⁢
• s
• λ
• 1
• =
• λ
• ⁡
• (
• 1
• +
• u
• )
• λ
• 2
• =
• λ
• ⁡
• (
• 1
• -
• u
• )
• wherein b represents a value of the input digital data being encoded, c is a root location joining the first half sinusoid and the second half sinusoid, and s represents a change between the root location and a default root location corresponding to λ1=λ2.

A method of recovering input digital data encoded into an encoded waveform of a wavelength λ wherein each period of the encoded waveform includes a first half sinusoid corresponding to one half of a first sinusoid of wavelength λ1 and a second half sinusoid corresponding to one half of a second sinusoid of wavelength λ2, where λ1+λ2=λ, the encoding including generating each period of the encoded waveform so as to represent one bit of the input digital data;

• wherein the first half sinusoid is of a first polarity and the second half sinusoid of a second polarity opposite to the first polarity;
• wherein a first bit value is represented when λ1 is greater than λ2 and a second bit value is represented when λ2 is greater than λ1;
• the method including:
• receiving an encoded analog waveform generated using the encoded waveform;
• generating digital symbol samples representing the first half sinusoid and the second half sinusoid of a first period of the encoded waveform;
• computing a first sum of squares of the digital symbol samples over a first integration interval encompassed by the first half sinusoid;
• computing a second sum of squares of the digital symbol samples over a second integration interval encompassed by the second half sinusoid;
• estimating a bit of the input digital data encoded by a first period of the encoded waveform based upon a comparison of the first sum of squares and the second sum of squares.