Signal Processing - May 2017 - 104
10
y (n )
y (n )
5
5
5
0
0
0
20
30
40
0
20
30
Y (k )
40
0
"
0
20
20
10
10
10
20
30
0
40
∠Y (k )
2
10
20
30
0
40
"
10
∠Y (k )
2
0
0
0
-1
-1
-2
-2
-2
20
30
(a)
40
10
20
30
40
∠Y ′(k )
1
-1
10
40
Y ′(k )
2
1
1
20
30
Y (k )
20
0
y ′(n )
10
"
10
10
20
30
(b)
40
10
20
30
40
(c)
Figure 2. An example of the uncalibrated and calibrated SRC performance (N x = 64, I/D = 3/4) . (a) The time-domain ideal output sequence y (n), the
amplitude, and the phase of its corresponding DFT; (b) the uncalibrated time-domain output sequence yt (n), the amplitude, and the phase of its corresponding DFT; and (c) the calibrated time-domain output sequence y l(n), the amplitude, and the phase of its corresponding DFT.
alternating direction method of multipliers [8], which will not be discussed
further for brevity.
Experimental results
In this section, we evaluate the accuracy
performance of the proposed optimization scheme in terms of the MSE. The
amplitude MSE is defined as
MSE a = 10 log
y - F - 1 Yl
Ny
2
2
(12)
and the phase MSE of the spectrum is
defined as
MSE z = 10 log
angle (Y) - angle (Yl )
Ny
2
2
.
(13)
In the following experiments, CVX
package [9] is used for the optimization.
In our experiments, the e 1 can all be set
to the value within 3-4 for various cases.
Figure 2 presents an example to demonstrate the outputs of the SRC before and
104
after the calibration process in the time
and frequency domains. As seen from this
figure, the proposed calibration process
can obtain a more accurate estimation
for both the time-domain amplitude and
frequency-domain phase. In particular,
the calibration method can reconstruct
the DFT phase of the calibrated output. In
the last row of Figure 2, the phase of the
calibrated DFT, +Y l(k), is much similar
to the ideal one, +Y (k), compared to that
of the uncalibrated DFT, +Yt (k).
The quantitative performance evaluation is presented in Figures 3 and 4 for
decimation and interpolation, respectively. For both decimation and interpolation, the MSE of amplitude decreases
as input signal length increases. This is
because the number of available samples
used for calibration in (7) increases with
the sequence length to enhance the calibration effects. The MSE of the phase,
however, remains about the same level for
different input signal lengths. Since the
IEEE Signal Processing Magazine
|
May 2017
|
number of the manipulated frequencydomain parameters increases with
the increase of signal length by a similar amount, the MSE of the phase is not
decreased with the increase of sequence
length. In general, the proposed calibration method can consistently obtain significant reduction of conversion errors
in both the time-domain amplitude and
frequency-domain phase, which validates its robustness of conversion accuracy performance.
The accuracy is degraded when the
SRC factor decreases from 3/4 to 3/8. This
can be explained by considering the number of samples that are ignored or inserted
according to (1) or (2) has increased. For
example, the number of points being
truncated by (1) or being inserted with
a value of C 2 in (2) is doubled so that
the errors produced by yt (k) are accordingly increased. Because the calibration
process has to cope with more errors
produced by the ignoring or inserting
Table of Contents for the Digital Edition of Signal Processing - May 2017
Signal Processing - May 2017 - Cover1
Signal Processing - May 2017 - Cover2
Signal Processing - May 2017 - 1
Signal Processing - May 2017 - 2
Signal Processing - May 2017 - 3
Signal Processing - May 2017 - 4
Signal Processing - May 2017 - 5
Signal Processing - May 2017 - 6
Signal Processing - May 2017 - 7
Signal Processing - May 2017 - 8
Signal Processing - May 2017 - 9
Signal Processing - May 2017 - 10
Signal Processing - May 2017 - 11
Signal Processing - May 2017 - 12
Signal Processing - May 2017 - 13
Signal Processing - May 2017 - 14
Signal Processing - May 2017 - 15
Signal Processing - May 2017 - 16
Signal Processing - May 2017 - 17
Signal Processing - May 2017 - 18
Signal Processing - May 2017 - 19
Signal Processing - May 2017 - 20
Signal Processing - May 2017 - 21
Signal Processing - May 2017 - 22
Signal Processing - May 2017 - 23
Signal Processing - May 2017 - 24
Signal Processing - May 2017 - 25
Signal Processing - May 2017 - 26
Signal Processing - May 2017 - 27
Signal Processing - May 2017 - 28
Signal Processing - May 2017 - 29
Signal Processing - May 2017 - 30
Signal Processing - May 2017 - 31
Signal Processing - May 2017 - 32
Signal Processing - May 2017 - 33
Signal Processing - May 2017 - 34
Signal Processing - May 2017 - 35
Signal Processing - May 2017 - 36
Signal Processing - May 2017 - 37
Signal Processing - May 2017 - 38
Signal Processing - May 2017 - 39
Signal Processing - May 2017 - 40
Signal Processing - May 2017 - 41
Signal Processing - May 2017 - 42
Signal Processing - May 2017 - 43
Signal Processing - May 2017 - 44
Signal Processing - May 2017 - 45
Signal Processing - May 2017 - 46
Signal Processing - May 2017 - 47
Signal Processing - May 2017 - 48
Signal Processing - May 2017 - 49
Signal Processing - May 2017 - 50
Signal Processing - May 2017 - 51
Signal Processing - May 2017 - 52
Signal Processing - May 2017 - 53
Signal Processing - May 2017 - 54
Signal Processing - May 2017 - 55
Signal Processing - May 2017 - 56
Signal Processing - May 2017 - 57
Signal Processing - May 2017 - 58
Signal Processing - May 2017 - 59
Signal Processing - May 2017 - 60
Signal Processing - May 2017 - 61
Signal Processing - May 2017 - 62
Signal Processing - May 2017 - 63
Signal Processing - May 2017 - 64
Signal Processing - May 2017 - 65
Signal Processing - May 2017 - 66
Signal Processing - May 2017 - 67
Signal Processing - May 2017 - 68
Signal Processing - May 2017 - 69
Signal Processing - May 2017 - 70
Signal Processing - May 2017 - 71
Signal Processing - May 2017 - 72
Signal Processing - May 2017 - 73
Signal Processing - May 2017 - 74
Signal Processing - May 2017 - 75
Signal Processing - May 2017 - 76
Signal Processing - May 2017 - 77
Signal Processing - May 2017 - 78
Signal Processing - May 2017 - 79
Signal Processing - May 2017 - 80
Signal Processing - May 2017 - 81
Signal Processing - May 2017 - 82
Signal Processing - May 2017 - 83
Signal Processing - May 2017 - 84
Signal Processing - May 2017 - 85
Signal Processing - May 2017 - 86
Signal Processing - May 2017 - 87
Signal Processing - May 2017 - 88
Signal Processing - May 2017 - 89
Signal Processing - May 2017 - 90
Signal Processing - May 2017 - 91
Signal Processing - May 2017 - 92
Signal Processing - May 2017 - 93
Signal Processing - May 2017 - 94
Signal Processing - May 2017 - 95
Signal Processing - May 2017 - 96
Signal Processing - May 2017 - 97
Signal Processing - May 2017 - 98
Signal Processing - May 2017 - 99
Signal Processing - May 2017 - 100
Signal Processing - May 2017 - 101
Signal Processing - May 2017 - 102
Signal Processing - May 2017 - 103
Signal Processing - May 2017 - 104
Signal Processing - May 2017 - 105
Signal Processing - May 2017 - 106
Signal Processing - May 2017 - 107
Signal Processing - May 2017 - 108
Signal Processing - May 2017 - 109
Signal Processing - May 2017 - 110
Signal Processing - May 2017 - 111
Signal Processing - May 2017 - 112
Signal Processing - May 2017 - Cover3
Signal Processing - May 2017 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201809
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201807
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201805
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201803
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201801
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0917
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0717
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0517
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0317
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0916
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0716
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0516
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0316
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0915
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0715
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0515
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0315
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0914
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0714
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0514
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0314
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0913
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0713
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0513
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0313
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0912
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0712
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0512
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0312
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0911
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0711
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0511
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0311
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0910
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0710
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0510
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0310
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0909
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0709
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0509
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0309
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1108
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0908
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0708
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0508
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0308
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0108
https://www.nxtbookmedia.com