Signal Processing - May 2017 - 105

−10

−20

−30

MSE

−40

−50

−60

−70

−80
16

64
128
256
Length of the Input Signal

−80
18

512

Amplitude (Uncalibrated, 3/4)
Amplitude (Calibrated, 3/4)
Phase (Uncalibrated, 3/4)
Phase (Calibrated, 3/4)
Amplitude (Uncalibrated, 3/8)
Amplitude (Calibrated, 3/8)
Phase (Uncalibrated, 3/8)
Phase (Calibrated, 3/8)

Figure 3. The MSE performances of decimation in terms of input
signal length.

operations, the overall effectiveness of the
calibration process is decreased.
Similarly, in the interpolation case,
the MSE of amplitude decreases with the
increase of input signal length. In contrast, with the increase of signal length,
the phase errors produced by the uncalibrated approach remain around a constant level and the one with calibration
still achieves significant improvement on
the estimation accuracy. The accuracy
obtained by both the frequency-domainbased SRC and the calibrated one is
decreased when the SRC ratio changes
from 3/4 to 3/8 in Figure 3, or from 4/3 to
8/3 in Figure 4.
Let us compare the performance of
the proposed SRC with the time-domain
SRC methods. In our experiments, the
filter used in the time-domain SRC is
a poly-phase finite impulse response
filter, whose coefficients are calculated
by the Parks-McClellan algorithm.
In the experiments, it is found that the
performance of the time-domain SRC
cannot be substantially improved when
the order of the filter is higher than
500. Therefore, we compare the timedomain methods with the filter orders

72
144
288
Length of the Input Signal

576

Amplitude (Uncalibrated, 4/3)
Amplitude (Calibrated, 4/3)
Phase (Uncalibrated, 4/3)
Phase (Calibrated, 4/3)
Amplitude (Uncalibrated, 8/3)
Amplitude (Calibrated, 8/3)
Phase (Uncalibrated, 8/3)
Phase (Calibrated, 8/3)

Figure 4. The MSE performances of interpolation in terms of input
signal length.

of 100, 300, and 500, respectively. Since
the performances of interpolation and
decimation are similar, the results of
decimation ^ I/D = 3/4h are presented in
Table 1 for brevity. The time-domain
methods can decrease the MSE with
an increase in the length of the filter.
When the length of 500 is used, it can
achieve comparable accuracy with the
uncalibrated frequency-domain SRC.
Among all of the compared methods,
the calibrated frequency-domain SRC
can significantly improve the conversion accuracies of amplitude and phase.
The computational complexities needed by the time-domain method is linearly
proportional to the data length for a given

order of a low-pass filter. For a length of
N data, the uncalibrated and calibrated
frequency-domain methods require the
computational complexities in the orders
of N log N and N 3, respectively. Figure 5 shows the required computation
time by the time-domain method and the
uncalibrated and calibrated frequencydomain methods. The measurements are
made from the simulations by using the
SRC function and fast Fourier transform
function given by the MATLAB software
running on a PC with 3.4-GHz central
processing unit. In addition, the calibrated
frequency-domain method also uses the
CVX MATLAB tool box [9] for calibration. The calibrated frequency-domain

Table 1. The performance comparison of different algorithms for decimation.
Time-Domain SRC

Length (Nx )

Frequency-Domain SRC

100

300

500

Uncalibrated

Calibrated

MSEa (dB)
MSE z (dB)

-6.33
3.36

-19.24
-26.90

-22.69
-31.9

−23.61
−30.44

−43.84
−45.97

256

MSEa (dB)
MSE z (dB)

-7.01
-8.13

-35.53
-21.02

-36.75
-22.05

−39.20
−29.37

−56.54
−44.51

1,024

MSEa (dB)
MSE z (dB)

-6.74
-1.92

-36.73
-18.17

-43.31
-21.73

−53.53
−28.81

−71.68
−45.42

IEEE Signal Processing Magazine

May 2017

105

Table of Contents for the Digital Edition of Signal Processing - May 2017