Synthesized high speed digital filters
A synthesized digital filter and method for synthesizing the digital filter are described herein. In one embodiment of the present invention, the digital filter is made using analog RF components. In another embodiment of the present invention, the digital filter is made using optical components which enables an optical signal to be manipulated in an optical domain without needing to convert the optical signal into an electrical domain.
1. A digital filter comprising a device that synthesizes a digital signal processing difference equation:
H
(
z
)
=
Y
(
z
)
X
(
z
)
=
∑
i
=
0
r
L
i
·
z
-
i
1
+
∑
j
=
1
m
K
j
·
z
-
j
where:
H(z)=Z-transform of filter response
Y(z)=Z-transform of output response
X(z)=Z-trans form of input response
r=Number of input sample coefficients
m=Number of output sample coefficients
L i =Gain (tap weights) for the input sample data
K j =Gain (tap weights) for the output sample data
z −i =Z-transform of the discretized version of an input delayed by i samples
z −j =Z-transform of the discretized version of an output delayed by j samples
said digital filter is synthesized by replacing elements of said digital signal processing difference equation with an optical component as follows:
each memory element z −i and z −j is replaced with a delay unit;
each sum block Σ is replaced with a combiner;
each gain block element L i and K j is replaced with an amplifier or an attenuator; and
each T-junction between each pair of delay units is replaced with a splitter.
2. The digital filter of claim 1 , wherein each delay unit is a piece of optical fiber.
3. The digital filter of claim 1 , wherein each combiner is a tap or an interferometer.
4. The digital filter of claim 1 , wherein each splitter is a tap or an interferometer.
5. The digital filter of claim 1 , wherein:
each amplifier is an semiconductor optical amplifier, an electro-absorptive modulator or an erbium-doped fiber amplifier; and
each attenuator is an optical attenuator if the gain is scaled to a value less than one.
6. The digital filter of claim 1 , wherein said digital filter is an infinite impulse response filter.
7. The digital filter of claim 1 , wherein said digital filter is a finite impulse response filter when m is set to zero.
8. The digital filter of claim 1 , wherein said optical components are incorporated onto a lightwave optical circuit.
9. The digital filter of claim 1 , wherein said digital filter manipulates an optical signal that has a sample rate less than or equal to 500 GHz.
10. The digital filter of claim 1 , wherein said digital filter manipulates an optical signal that has a dynamic sample rate.
11. A method comprising step of synthesizing a digital filter that implements a digital signal processing difference equation:
H
(
z
)
=
Y
(
z
)
X
(
z
)
=
∑
i
=
0
r
L
i
·
z
-
i
1
+
∑
j
=
1
m
K
j
·
z
-
j
where:
H(z)=Z-transform of filter response
Y(z)=Z-trans form of output response
X(z)=Z-trans form of input response
r=Number of input sample coefficients
m=Number of output sample coefficients
L i =Gain (tap weights) for the input sample data
K j =Gain (tap weights) for the output sample data
z −i =Z-transform of the discretized version of an input delayed by i samples
z −j =Z-transform of the discretized version of an output delayed by j samples
said digital filter is synthesized by replacing elements of said digital signal processing difference equation with an optical component in accordance with the following steps:
replacing each memory element z −i and z −j with a delay unit;
replacing each sum block Σ with a combiner;
replacing each gain block element L i and K j with an amplifier or an attenuator; and
replacing each T-junction between each pair of delay units with a splitter.
12. The method of claim 11 , wherein:
each delay unit is a piece of optical fiber;
each combiner is a tap or an interferometer;
each splitter is a tap or an interferometer;
each amplifier is a semiconductor optical amplifier, an electro-absorptive modulator or an erbium doped fiber amplifier; and
each attenuator is an optical attenuator if the gain is scaled to a value less than one.
13. The method of claim 11 , wherein said optical components are incorporated onto a lightwave optical circuit.
14. A digital filter comprising a device that synthesizes a digital signal processing difference equation:
H
(
z
)
=
Y
(
z
)
X
(
z
)
=
∑
i
=
0
r
L
i
·
z
-
i
1
+
∑
j
=
1
m
K
j
·
z
-
j
where:
H(z)=Z-transform of filter response
Y(z)=Z-transform of output response
X(z)=Z-transform of input response
r=Number of input sample coefficients
m=Number of output sample coefficients
L i =Gain (tap weights) for the input sample data
K j =Gain (tap weights) for the output sample data
z −i =Z-fransform of the discretized version of an input delayed by i samples
z −j =Z-transform of the discretized version of an output delayed by j samples
said digital filter is synthesized by replacing elements of said digital signal processing difference equation with an analog component as follows:
each memory element z −i and z −j is replaced with a delay unit that delays a presented voltage for a predetermined amount of time;
each sum block Σ is replaced with an analog power combiner;
each gain block element L i and K j is replaced with an analog amplifier, a resistor divider network or an attenuator; and
each T-junction between each pair of delay units is replaced with an analog power splitter.
15. The digital filter of claim 14 , wherein each delay unit that delays a presented voltage for a predetermined amount of time is a length of cable or a filter.
16. The digital filter of claim 14 , wherein said digital filter is an infinite impulse response filter.
17. The digital filter of claim 14 , wherein said digital filter is a finite impulse response filter when m is set to zero.
18. The digital filter of claim 14 , wherein said digital filter manipulates an optical signal that has a sample rate in the range of 1 GHz.
19. A method comprising step of synthesizing a digital filter that implements a digital signal processing difference equation as follows:
H
(
z
)
=
Y
(
z
)
X
(
z
)
=
∑
i
=
0
r
L
i
·
z
-
i
1
+
∑
j
=
1
m
K
j
·
z
-
j
where:
H(z)=Z-trans form of filter response
Y(z)=Z-transform of output response
X(z)=Z-transform of input response
r=Number of input sample coefficients
m=Number of output sample coefficients
L i =Gain (tap weights) for the input sample data
K j =Gain (tap weights) for the output sample data
z −i =Z-transform of the discretized version of an input delayed by i samples
z −j =Z-transform of the discretized version of an output delayed by j samples
said digital filter is synthesized by replacing each element of said digital signal processing difference equation with an analog component in accordance with the following steps:
replacing each memory element z −i and z −j with a delay unit that delays a presented voltage for a predetermined amount of time;
replacing each sum block Σ with an analog power combiner;
replacing each gain block element L i and K j with an analog amplifier, a resistor divider network or an attenuator; and
replacing each T-junction between each pair of delay units with an analog power splitter.
20. The method of claim 19 , wherein each delay unit that delays a presented voltage for a predetermined amount of time is a length of cable or a filter.
21. The method of claim 19 , wherein said digital filter manipulates an optical signal that has a sample rate in the range of 1 GHz.