Method to linearize the output from an ADC
A method is disclosed of compensating the output of an ADC for non-linearity in the response of the ADC. The method comprises converting an analog input signal to uncorrected digital ADC output samples, applying a vector of correction variables to each of a block of uncorrected ADC output samples to provide a block of corrected ADC samples, and iteratively minimizing a measure of the spectral flatness of the block of corrected ADC samples with response to the vector of correction variables.
1. A method of compensating an output of an Analog-to-Digital Converter (ADC) for non-linearity in a response of the ADC, the method comprising:
converting an analog input signal to uncorrected digital ADC output samples;
applying a vector of correction variables to each of a block of the uncorrected digital ADC output samples and producing a block of corrected ADC samples; and
iteratively minimizing a measure of a spectral flatness of the produced block of corrected ADC samples with respect to the vector of correction variables.
2. The method according to claim 1 , wherein the analog input signal comprises a plurality of frequencies.
3. The method according to claim 1 , wherein the ADC is a sigma delta ADC comprising a quantizer and a DAC which together form a loop filter.
4. The method according to claim 3 , wherein the step of iteratively minimizing the measure of the spectral flatness of the produced block of corrected ADC samples with respect to the vector of correction variables comprises:
estimating a mismatch function V of the quantizer and a mismatch function W of the DAC;
estimating an impulse response h of the loop filter determining a first impulse response f and a second impulse response g, wherein f and g follow the follow relationships:
f
(
k
)
=
δ
(
k
)
-
∑
i
=
1
P
h
(
i
)
f
(
k
-
i
)
g
k
+
1
=
∑
i
=
1
P
h
i
f
k
-
i
wherein δ is the Kronecker-delta function, and iteratively subtracting a correction sample e from the uncorrected ADC output samples, wherein e obeys the relationship
e
(
k
)
=
∑
s
=
10
L
-
1
V
(
y
(
k
)
)
*
f
(
k
)
+
W
(
y
(
k
)
)
*
g
(
k
)
,
wherein * denotes the convolution of two functions.
5. The method according to claim 4 , wherein the measure of spectral flatness is the spectral flatness λ( ) of a spectrum {right arrow over (Z)} according to:
λ
(
Z
→
)
=
exp
(
1
N
∑
i
log
(
Z
i
2
)
)
1
N
∑
i
Z
i
2
.
6. The method according to claim 4 , wherein the measure of spectral flatness is given by a generalized spectral flatness of the spectrum {right arrow over (Z)}:
λ
p
,
q
(
Z
→
)
=
(
1
N
∑
i
Z
i
p
)
1
p
(
1
N
∑
i
Z
i
q
)
1
q
.
7. The method according to claim 4 , wherein the compensation is applied over a frequency range of at least −200 MHz to 200 MHz.
8. The method according to claim 4 , wherein the compensation is applied over a frequency range of at least approximately 0 Hz to at least approximately 20 MHz.
9. The method of claim 1 , wherein the step of iteratively minimizing further comprises:
selectively applying incremental steps to correction variables.
10. The method of claim 9 , further comprising:
following incremental steps that lower the measure of the spectral flatness and discarding other incremental steps.
11. The method of claim 1 , wherein the step of iteratively minimizing further comprises:
performing gradient-descent minimization.
12. The method of claim 11 , further comprising:
evaluating a gradient numerically.