Method and a demodulator for demodulating a position error signal from a readback servo signal
View Patent ↗According to embodiments of the present invention, a method for demodulating a position error signal from a readback servo signal having a first frequency associated with a first servo track of a storage medium and a second frequency associated with a second servo track adjacent to the first servo track is provided. The method includes sampling the readback servo signal at successive time instants to provide a sequence of samples, computing a Discrete Fourier Transform based on the sequence of samples, and providing a measurement indicative of the position error signal based on the Discrete Fourier Transform. According to further embodiments of the present invention, a demodulator is also provided.
1. A method for demodulating a position error signal from a readback servo signal having a first frequency associated with a first servo track of a storage medium and a second frequency associated with a second servo track adjacent to the first servo track, the method comprising:
sampling the readback servo signal at successive time instants to provide a sequence of samples;
applying a window of a predetermined length to the sequence of samples to form a windowed sequence of samples, wherein the predetermined length is less than a length of the sequence of samples;
computing a Discrete Fourier Transform based on the windowed sequence of samples; and
providing a measurement indicative of the position error signal based on the Discrete Fourier Transform.
2. The method as claimed in claim 1 ,
wherein the window is a sliding window of the predetermined length samples so as to form respective windowed sequences of samples;
wherein computing the Discrete Fourier Transform comprises computing a respective Discrete Fourier Transform based on each respective windowed sequence of samples, and
wherein providing the measurement comprises providing a respective measurement indicative of the position error signal based on the respective Discrete Fourier Transform.
3. The method as claimed in claim 2 , wherein for two consecutive windowed sequences of samples of the respective windowed sequences of samples, computing the Discrete Fourier Transform comprises computing a respective Discrete Fourier Transform of a succeeding windowed sequence of samples of the two consecutive windowed sequences of samples based on a respective Discrete Fourier Transform computed based on a preceding windowed sequence of samples of the two consecutive windowed sequences of samples.
4. The method according to claim 1 , wherein providing the measurement comprises computing a difference between an absolute value of a component of the Discrete Fourier Transform corresponding to the first frequency and an absolute value of a component of the Discrete Fourier Transform corresponding to the second frequency.
5. The method according to claim 1 , wherein the measurement is expressed as:
PES m =|X k m | k=f1 −|X k m | k=f2
where
PES m is the position error signal at time instant m,
|X k m | k=f1 represents the absolute value of the Discrete Fourier Transform component of the readback servo signal corresponding to frequency f 1 , at time instant m,
|X k m | k=f2 represents the absolute value of the Discrete Fourier Transform component of the readback servo signal corresponding to frequency f 2 , at time instant m,
f 1 is the first frequency,
f 2 is the second frequency.
6. The method as claimed in claim 1 ,
wherein the window is a sliding window of the predetermined length so as to form respective windowed sequences of samples;
wherein for two consecutive windowed sequences of samples of the respective windowed sequences of samples, computing the Discrete Fourier Transform comprises computing a first Discrete Fourier Transform based on a preceding windowed sequence of samples of the two consecutive windowed sequences of samples, and further comprising computing a second Discrete Fourier Transform corresponding to a succeeding windowed sequence of samples of the two consecutive windowed sequences of samples based on the first Discrete Fourier Transform; and
wherein providing the measurement comprises providing a respective measurement indicative of the position error signal based on the first Discrete Fourier Transform and the second Discrete Fourier Transform respectively.
7. The method as claimed in claim 6 , wherein computing the second Discrete Fourier Transform comprises:
performing a complex multiplication based on the first Discrete Fourier Transform; and
performing a summation based on
a sample of a succeeding windowed sequence of samples of the two consecutive windowed sequences of samples at a time instant the second Discrete Fourier Transform is to be computed, and
another sample at a final time instant within the succeeding windowed sequence of samples.
8. The method as claimed in claim 6 , wherein the second Discrete Fourier Transform is computed as:
X
k
n
+
1
=
ⅇ
j
2
π
k
w
X
k
n
+
(
x
n
+
1
-
x
n
-
w
+
1
)
where
X k n is the first Discrete Fourier Transform,
X k n+1 is the second Discrete Fourier Transform,
x n+1 is a sample at the time instant the second Discrete Fourier Transform is to be computed,
X n−w+1 is a sample at the final time instant within a succeeding windowed sequence of samples of the two consecutive windowed sequences of samples,
w is the predetermined length,
k is frequency.
9. A demodulator for demodulating a position error signal from a readback servo signal having a first frequency associated with a first servo track of a storage medium and a second frequency associated with a second servo track adjacent to the first servo track, the demodulator comprising:
a sampling circuit configured to sample the readback servo signal at successive time instants to provide a sequence of samples;
a computing circuit configured to apply a window of a predetermined length to the sequence of samples to form a windowed sequence of samples, wherein the predetermined length is less than a length of the sequence of samples,
wherein the computing circuit is further configured to compute a Discrete Fourier Transform based on the windowed sequence of samples, and further configured to provide a measurement indicative of the position error signal based on the Discrete Fourier Transform.
10. The demodulator as claimed in claim 9 , wherein the window is a sliding window of the predetermined length so as to form respective windowed sequences of samples, wherein the computing circuit is configured to compute a respective Discrete Fourier Transform based on each respective windowed sequence of samples, and further configured to provide a respective measurement indicative of the position error signal based on the respective Discrete Fourier Transform.
11. The demodulator as claimed in claim 10 , wherein for two consecutive windowed sequences of samples of the respective windowed sequences of samples, the computing circuit is configured to compute a respective Discrete Fourier Transform of a succeeding windowed sequence of samples of the two consecutive windowed sequences of samples based on a respective Discrete Fourier Transform computed based on a preceding windowed sequence of samples of the two consecutive windowed sequences of samples.
12. The demodulator as claimed in claim 9 , wherein the computing circuit is configured to compute a difference between an absolute value of a component of the Discrete Fourier Transform corresponding to the first frequency and an absolute value of a component of the Discrete Fourier Transform corresponding to the second frequency.
13. The demodulator according to claim 9 , wherein the measurement is expressed as:
PES m =|X k m | k=f1 −|X k m | k=f2
where
PES m is the position error signal at time instant m,
|X k m | k=f1 represents the absolute value of the Discrete Fourier Transform component of the readback servo signal corresponding to frequency f 1 , at time instant m,
|X k m | k=f2 represents the absolute value of the Discrete Fourier Transform component of the readback servo signal corresponding to frequency f 2 , at time instant m,
f 1 is the first frequency,
f 2 is the second frequency.
14. The demodulator as claimed in claim 9 ,
wherein the window is a sliding window of the predetermined length so as to form respective windowed sequences of samples;
wherein for two consecutive windowed sequences of samples of the respective windowed sequences of samples, the computing circuit is configured to compute a first Discrete Fourier Transform based on a preceding windowed sequence of samples of the two consecutive windowed sequences of samples, further configured to compute a second Discrete Fourier Transform corresponding to a succeeding windowed sequence of samples of the two consecutive windowed sequences of samples based on the first Discrete Fourier Transform, and further configured to provide a respective measurement indicative of the position error signal based on the first Discrete Fourier Transform and the second Discrete Fourier Transform respectively.
15. The demodulator as claimed in claim 14 , wherein, for computing the second Discrete Fourier Transform, the computing circuit is configured to perform a complex multiplication based on the first Discrete Fourier Transform, and further configured to perform a summation based on
a sample of a succeeding windowed sequence of samples of the two consecutive windowed sequences of samples at a time instant the second Discrete Fourier Transform is to be computed, and
another sample at a final time instant within the succeeding windowed sequence of samples.
16. The demodulator as claimed in claim 14 , wherein the second Discrete Fourier Transform is computed as:
X
k
n
+
1
=
ⅇ
j
2
π
k
w
X
k
n
+
(
x
n
+
1
-
x
n
-
w
+
1
)
where
X k n is the first Discrete Fourier Transform,
X k n+1 is the second Discrete Fourier Transform,
x n+1 is a sample at the time instant the second Discrete Fourier Transform is to be computed,
X n−w+1 is a sample at the final time instant within a succeeding windowed sequence of samples of the two consecutive windowed sequences of samples,
w is the predetermined length,
k is frequency.