International Journal of Engineering Research and Development

ISSN: 2278-067X, Volume 1, Issue 7 (June 2012), PP.27-33

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27
Adaptive Noise Cancellation using Multirate Techniques
Prasheel V. Suryawanshi, Kaliprasad Mahapatro, Vardhman J. Sheth

Maharashtra Academy of Engineering, Alandi (D), Pune 412105, INDIA

AbstractThis paper presents development of a new adaptive structure based on multirate filter and testing the same for
deterministic, speech and music signals. A new class of FIR filtering algorithm based on the multirate approach is proposed.
They not only reduce the computational complexity in FIR filtering, but also retain attractive implementation related
properties such as regularity and multiply-and-accumulate (MAC)-structure. By virtue of the advantages of multirate FIR
filtering algorithm, the proposed scheme can reduce the required computational complexity and reserve the MAC structure.
It is observed that the convergence rate and steady state error is improved. An application of this approach in Adaptive
Noise Canceller is considered.

Keywords Adaptive filter, Multirate filter, Adaptive Noise Cancellation

I. INTRODUCTION
Noise is present in virtually all signals. In some situations it is negligible; in other situations it all but obliterates
the signal of interest. Removing unwanted noise from signals has historically been a driving force behind the development of
signal processing technology, and it continues to be a major application for digital signal processing systems [1].
The usual method of estimating a signal corrupted by additive noise is to pass the composite signal through a filter
that tends to suppress the noise while leaving the signal relatively unchanged. Filters used for the foregoing purpose can be
fixed or adaptive. The design of fixed filters is based on prior knowledge of both the signal and the noise, but adaptive filters
have the ability to adjust their own parameters automatically, and their design requires little or no prior knowledge of signal
or noise characteristics [2][3].
Multirate Signal Processing is the sub-area of DSP concerned with techniques that can be used to efficiently
change the sampling rates within a system. There are many applications where the signal of a given sampling rate needs to
be converted into an equivalent signal with a different sampling rate. The process of decimation and interpolation are the
fundamental operations of interest in multirate signal processing. They allow the sampling frequency to be decreased or
increased without significant undesirable effects of errors such as quantization and aliasing [4][5]. The various aspects of
multirate systems in statistical processing are reported in [6][7][8].
John Shynk [9] presents an overview of several frequency-domain adaptive filters that efficiently process discrete-
time signals using block and multirate filtering techniques. A multirate adaptive filtering structure using VLSI architecture is
reported in [10]. The concept of multistage multirate adaptive filters is discussed in [11][12]. The applications of the
approach in biomedical engineering [13], sub-band filtering [14], Adaptive Line Enhancement [15], Echo cancellation [16]
are well proven. The work by different researchers in this direction is a motivation for working on case study of noise
cancellation. The concept in [15] is extended to the Adaptive Noise Canceller (ANC) configuration, in this paper
The organization of this paper is as follows; the conventional Adaptive Noise Canceller (ANC) is introduced in
section 2. The LMS and RLS algorithm are also briefed. The section 3 describes the proposed structure employing multirate
techniques. Section 4 details the results for different types of signals. Section 5 concludes the paper.
II. ADAPTIVE NOISE CANCELLATION
The main objective in noise cancelling is to produce an optimum estimate of the noise in the contaminated signal
and hence an optimum estimate of the desired signal [4]. The basic adaptive noise-canceller (ANC) schematic is shown in
Fig. 1.

Fig. 1. Adaptive Noise Canceller (ANC)
Adaptive Noise Cancellation using Multirate Techniques
28
A signal is transmitted to a sensor that receives the signal s plus an uncorrelated noise n
0
. The combined signal and
noise, s+n
0
, forms the primary input to the ANC. A second sensor receives a noise n
1
which is uncorrelated with the signal
but correlated in some unknown way with the noise n
0
. This sensor provides the reference input to the ANC. The noise n
1
is
filtered to produce an output y that is a close replica of n
0
. This output is subtracted from the primary input s+n
0
to produce
the output, s+n
0
y.
In the system shown in Fig. 1, the reference input is processed by an adaptive filter that automatically adjusts its
own impulse response through a least-squares algorithm such as LMS that responds to an error signal dependent on the
filters output. Thus with the proper algorithm, the filter can operate under changing conditions and can readjust itself
continuously to minimize the error signal.
In noise-cancelling systems the practical objective is to produce a system output, s+n
0
y, that is a best fit in the
least-squares sense to the signal s. This objective is accomplished by feeding the system output back to the adaptive filter
and adjusting the filter through an adaptive algorithm to minimize the total system output power. Thus in an adaptive noise-
cancelling system, the system output serves as the error signal for the adaptive process.
A. LMS Algorithm
The LMS algorithm, developed by Widrow and his co-workers [2] is based on the steepest descent algorithm
where the weight vector is updated from sample to sample and it does not require prior knowledge of the signal statistics, but
instead uses their instantaneous estimates. The weights obtained by the LMS algorithm are only estimates, but these
estimates improve gradually with time as the weights are adjusted and the filter learns the characteristics of the signal.
Eventually, the weights converge. The condition for convergence is

1
0 < >

max
(1)
where
max
is the maximum eigen value of the input data covariance matrix. The implementation of LMS algorithm
involves iterative computations involving,
filter output;
1
0
( )
N
k k k i
i
n w i x

=
=

(2)
error estimate;
k k k
e y n
.
= (3)
update of filter weights;

1
( ) ( ) 2
k k k k i
w i w i e x
+
= + (4)
The simplicity of the LMS algorithm and ease of implementation, evident from (2), (3) and (4), makes it the
algorithm of first choice in many real-time systems. The LMS algorithm requires approximately 2N+1 multiplications and
2N+1 additions for each new set of input and output samples. Most signal processors are suited to the mainly multiply-
accumulate arithmetic operations involved, making a direct implementation of the LMS algorithm attractive.
B. RLS Algorithm
The RLS (recursive least squares) algorithm is another algorithm for determining the coefficients of an adaptive
filter. In contrast to the LMS algorithm, the RLS algorithm uses information from all past input samples (and not only from
the current tap-input samples) to estimate the (inverse of the) autocorrelation matrix of the input vector [9].
The RLS algorithm is based on the well-known least squares method. With recursive least squares algorithm, the
estimates of
k
W can be updated for each new set of data acquired without repeatedly solving the time-consuming matrix
inversion directly. A suitable RLS algorithm can be obtained by exponentially weighting the data to remove gradually the
effects of old data on
k
W and to allow the tracking of slowly varying signal characteristics. Thus

1 k k k k
W W G e

= + (5)

1 1
1
( )
T
k k k k
P P G x k P

(
=

(6)

1
( )
k
k
k
P x k
G
o

= (7)

1
( )
T
k k k
e y x k W

= (8)

1
( ) ( )
T
k k
x k P x k o

= + (9)
Adaptive Noise Cancellation using Multirate Techniques
29
k
P is essentially a recursive way of computing the inverse matrix
1
T
k k
X X

(

. The argument k emphasizes the
fact that the quantities are obtained at each sample point. The typical value of (forgetting factor) is between 0.98 and 1.
Smaller values assign too much weight to the more recent data, which leads to wildly fluctuating estimates.
The RLS algorithm is computationally more complex than the LMS algorithm. However, due the recursive
updating, the inversion of matrix is not necessary (which would be a considerably higher computational load). The RLS
algorithm typically shows a faster convergence compared to the LMS algorithm. Other advantages are that it produces a
weight vector estimate only at the end data sequence

III. PROPOSED SCHEME
The proposed structure of adaptive noise cancellation scheme using multirate technique is shown in Fig. 2. Starting
with the basic framework for Adaptive filters, a structure has been built eliminating the basic faults arising like
computational complexities, aliasing and spectral gaps.

Fig. 2. Proposed Structure of ANC with Multirate Technique
The H
0
, H
1
, H
a
are the analysis filters and G
0
, G
1
are the reconstruction filters. The decimation and interpolation
factors have been taken as 2 as the number of sub-bands are 2. The proposed scheme achieves a lower computational
complexity, and this design ensures no aliasing components in the output of the system. The system consists of two main
sub-bands and an auxiliary sub-band. The auxiliary sub-band contains the complement of the signals in the main sub-band.
In the fig. 2, H
a
(z) is the analysis filter for the auxiliary sub-band and H
0
(z) and H
1
(z) are the analysis filters for the
main bands. G
0
(z) and G
1
(z) are reconstruction filters for the main bands. These filters are related to each other as;

1 0
( ) ( ) H z H z = (10)

0 1
( ) 2 ( ) G z H z = (11)

1 0
( ) 2 ( ) G z H z = (12)

2 2
0 1
( ) ( ) ( )
m
a
H z z H z H z

(
=

(13)
The coefficients of all filters are calculated and the scheme is tested for different input types.

IV. RESULTS AND ANALYSIS
The proposed scheme using 2 bands with decimation factor of 2, is tested for deterministic signal, speech and
musical signals. The results are compared with conventional ANC.
A. Deterministic Signal
For deterministic signal, 128 samples of signal and noise are considered. Fig. 3 to Fig. 6 shows the convergence
results of the proposed scheme and conventional ANC for a deterministic signal of 10sin(1500t) and noise of 10 sin(312t).


Adaptive Noise Cancellation using Multirate Techniques
30


Fig. 3. Deterministic signal Conventional ANC Fig. 4. Input and output spectra Conventional ANC

Fig. 5. Deterministic signal Proposed Scheme Fig. 6. Input and output spectra Proposed Scheme

It is evident that, the output of the noise canceller exactly matches the desired signal. The update algorithm used is
LMS. The periodogram clearly demonstrates the removal of noise.
B. Speech Signal
For speech signal, 32000 samples with sampling frequency 8 KHz are considered. The noise signal is a sine wave
of 312 Hz. The Algorithm used is LMS. Fig. 7 to Fig. 10 shows the results of the proposed scheme and conventional ANC
for a speech signal.
Fig. 7. Speech signal Conventional ANC Fig. 8. Spectra of Speech Conventional ANC
Adaptive Noise Cancellation using Multirate Techniques
31




Fig. 9. Speech Signal Proposed Scheme Fig. 10. Spectra of Speech signal Proposed Scheme
C. Music Signal
The music signal considered is 8000 samples of piano along with 8000 samples of tabla taken as noise. The
Algorithm used is LMS. Fig. 11 to Fig. 14 shows the results of the proposed scheme and conventional ANC for a music
signal (piano + tabla). Fig. 15 to Fig. 16 shows the results of the proposed scheme for a music signal of closely matched
frequencies (guitar + violin).

Fig. 11. Music signal (Piano + Tabla) Fig. 12. Spectra of Music signal (Piano + Tabla)
Conventional ANC Conventional ANC


Adaptive Noise Cancellation using Multirate Techniques
32
Fig. 13. Music signal (Piano + Tabla) Fig. 14. Spectra of Music signal (Piano + Tabla)
Proposed Scheme Proposed Scheme




















Fig. 15. Music signal (Guitar + Violin) Fig. 16. Spectra of Music signal (Guitar + Violin)
Proposed Scheme Proposed Scheme


The results are encouraging for the proposed multirate adaptive scheme and are indicative of quite less time
(approximately one-fourth) for computation as compared to the conventional ANC structure. Additionally, signals with
closely matched frequencies (eg. violin and guitar) can be effectively segregated using the proposed scheme, which is not
possible with the conventional ANC configuration.
The Table 1 shows the computation time for conventional ANC and the proposed scheme.
TABLE I: COMPUTATION TIME REQUIREMENT
Input Signal Conventional ANC Proposed Scheme
Deterministic 16 ms 4.2 ms
Speech 4.453 sec 1.485 sec
Musical 0.18441 sec 0.134881 sec
V. CONCLUSIONS
This paper proposes a new adaptive noise cancellation structure based on multirate techniques. Noise Cancellation
is chosen as the application because noise is one of the main hindering factors that affect the information signal in any
system. Noise and signal are random in nature. As such, in order to reduce noise, the filter coefficients should change
according to changes in signal behaviour. The adaptive capability will allow the processing of inputs whose properties are
unknown. Multirate techniques can be used to overcome the problem of large computational complexity and slow
convergence rate. The simulations and experiments demonstrate the efficacy of the proposed structure.


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