Communication system using shape-shifted sinusoidal waveforms
A data communication method in which input digital data is received and encoded into an encoded waveform having zero crossings representative of the input digital data. The encoding includes generating the encoded waveform based upon a continuous piecewise function having sinusoidal components. The continuous piecewise function may be used in generating a plurality of symbol waveforms, each of which occupies a period of the encoded waveform and represents bits of the input digital data. The plurality of symbol waveforms are defined so that a value of a phase offset used in the continuous piecewise function is different for each of the plurality of symbol waveforms, thereby resulting in each symbol waveform having a different zero crossing. An encoded analog waveform is generated from a representation of the encoded waveform and transmitted to a receiver.
1. 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 λ 1 and a second half sinusoid corresponding to one half of a second sinusoid of wavelength λ 2 , where λ 1 +λ 2 =λ, and where one of λ 1 and λ 2 is higher than λ and the other one of λ 1 and λ 2 is lower than 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 λ 1 is greater than λ 2 and a second bit value of the input digital data is represented when λ 2 is greater than λ 1 ;
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
<
c
-
/
+
sin
2
π
(
t
-
c
)
λ
2
c
≤
t
<
λ
where c is a root location joining the first half sinusoid and the second half sinusoid; and
generating an encoded analog waveform from a representation of the encoded waveform.
2. 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 λ 1 and a second half sinusoid corresponding to one half of a second sinusoid of wavelength λ 2 , where λ 1 +λ 2 =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 λ 1 is greater than λ 2 and a second bit value of the input digital data is represented when λ 2 is greater than λ 1 ; 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 λ 1 =λ 2 .
3. 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 λ 1 and a second half sinusoid corresponding to one half of a second sinusoid of wavelength λ 2 , where λ 1 +λ 2 =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 λ 1 is greater than λ 2 and a second bit value is represented when λ 2 is greater than λ 1 ;
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.
4. The method of claim 3 further including, for each period of the encoded waveform following the first period:
generating digital symbol samples representing the first half sinusoid and the second half sinusoid for the 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 the period of the encoded waveform based upon a comparison of the first sum of squares and the second sum of squares.
5. The method of claim 3 wherein a first edge of the first integration interval is located a predefined number of degrees before a zero crossing of a sine wave of wavelength λ and wherein a first edge of the second integration interval is located the predefined number of degrees after the zero crossing.
6. The method of claim 3 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 λ 1 =λ 2 .