Signal Processing - May 2017 - 101

TIPS & Tricks
Lifan Zhao, Xiumei Li, Lu Wang,
and Guoan Bi

Autocalibrated Sampling Rate Conversion
in the Frequency Domain

x (n )

Up-Sampling
↑I

Low-Pass
Filter

Down-Sampling
D

SRC has been an indispensable operation in various digital signal processing
applications to achieve acceptable performance at affordable processing costs
[1]. In the literature, various approaches
have been reported to carry out the SRC
either in the time or frequency domain,
as illustrated in Figure 1. The timedomain SRC requires processing operations including up-sampling, low-pass
filtering, and down-sampling as shown
in Figure 1(a). Although various methods have been reported to implement the

increasing the conversion accuracy on
the outputs of the SRC. Because these
errors are relatively small and randomly
distributed, we may consider them as
perturbations. Inspired by the recent
success of the sparse representation
(SR) technique, let us develop a simple
sparsity-based method in this article
to autocalibrate the perturbations produced by the frequency-domain SRC
method [3] to improve the conversion
accuracy. This autocalibration method
can be used as an additional measure for
accuracy improvement after all of the
possible wisdoms have been exhausted
for implementing the frequency-domain
SRC. Our formulation is different from
the autocalibration problem in other SR
problems [5] because sparsity assumption of the DFT coefficients is generally not valid in SRC applications. To
properly facilitate error estimation in
the frequency domain, sparsity in timedomain errors, which is a unique characteristic of frequency-domain SRC, is
properly exploited. Simulated experimental results demonstrate that the conversion

y (n )

(a)
x (n )

Spectrum
Manipulation

DFT

Inverse DFT

Introduction

SRC, the success largely depends on carefully rearranging the up-/down-samplers
and subfiltering functions to collectively
perform the desired conversion process
[1]. In contrast, the frequency-domain
SRC directly manipulates the DFT of the
input signal, as shown in Figure 1(b) [2],
[3]. In this method, the output of the SRC
is obtained by the inverse DFT (IDFT) of
the manipulated DFT of the input signal
[2], [4]. Although useful rules of manipulating the DFT have been given for
achieving better conversion accuracy [2],
[3], the optimal selection criteria for minimizing the conversion errors remains an
open problem.
In spite of careful design efforts on
various methods of implementing the
SRC, there always exist conversion
errors that are defined as the differences between the obtained and the ideal
SRC outputs. In various applications
including digital audio, communication, and multimedia systems, SRC with
high accuracy is often desired. Therefore, it is of significant importance to
investigate the possibilities of further

↑

requency-domain sampling rate conversion (SRC) can be conveniently
implemented by manipulating the
discrete Fourier transform (DFT) of the
input signal. This method has achieved
the advantages of using less computation
to obtain more accurate converted output.
Conversion errors are mainly produced
from the formulation process of the
DFT of the output signal. This article
presents a sparsity-based scheme to appropriately and automatically calibrate
the conversion errors to make further
improvement on the conversion accuracy at the cost of more computational
complexity. The experimental results
demonstrate that the proposed scheme
can significantly decrease the meansquare errors (MSEs) and is particularly
effective on minimizing the MSEs of
phase spectrum.

y (n )

(b)
Digital Object Identifier 10.1109/MSP.2017.2671412
Date of publication: 26 April 2017

Figure 1. The steps of SRC: (a) the time-domain method and (b) the frequency-domain method.
IEEE Signal Processing Magazine

May 2017

101

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