design of normalized subband adaptive filter for … · design of normalized subband adaptive...

DESIGN OF NORMALIZED SUBBAND ADAPTIVE FILTER FOR

ACOUSTIC ECHO CANCELLATION

Pavya.S, Graduate Student Member IEEE,

[email protected],

K.S.Rangasamy college of technology,

Tiruchengode,tamilnadu,India

P.Babu,Associate professor(ECE),

[email protected],

K.S. Rangasamy College of Technology,

Tiruchengode, Tamilnadu, India

ABSTRACT: In hands-free telephones and

teleconferencing systems, acoustic echo cancellers are

required, which are often implemented by adaptive

filters. In these applications, the speech input signal of

the adaptive filter is highly correlated and the impulse

response of the echo path is very long. These

characteristics will slow down the convergence rate of

the adaptive filter if the well-known normalized

leastmean- square (NLMS) algorithm is used. The

normalized subband adaptive filter (NSAF) offers a

good solution to this problem because of its

decorrelating property. This paper proposes a VHDL

implementation of normalized subband adaptive filter

structure(NSAF) adaptive algorithm.the experiment

result shows that the power consumed by subband is lower than that of full band.

Index Terms — Acoustic echo canceller, adaptive

combination, normalized subband adaptive filter

(NSAF), hands-free telephone, teleconferencing system

Cascade intergrator-comb filter (CIC).

I.INTRODUCTION

A common problem encountered in hands-free

telephones and teleconferencing systems is the presence

of echoes which are generated acoustically by the

coupling between the loudspeaker and the microphone

via the impulse response of a room [1]. Removal of

these echoes requires the precise knowledge of the

impulse response of the acoustic echo path, which may

be time varying. In recent years, there has been a great interest in the use of adaptive filters as acoustic echo

cancellers to remove echoes [2], [3]. An adaptive filter

can be characterized by its structure and adaptive

filtering algorithm [4]. The transversal filter with the

well-known normalized least-mean-square (NLMS)

algorithm is one of the most popular adaptive filters

because of its simplicity and robust performance [5],

[6]. In acoustic echo cancellation (AEC) applications,

however, the speech input signal of the adaptive filter is

highly correlated and the impulse response of the

acoustic echo path is very long. These two

characteristics will slow down the convergence rate of

the acoustic echo canceller if the NLMS-based adaptive

filter is used to remove echoes.

One technique to solve the above problem is

subband adaptive filtering. In conventional subband

adaptive filters (SAFs), each subband uses an individual

adaptive subfilter in its own adaptation loop, which

decreases the convergence rate of SAFs because of the

aliasing and band-edge effects [7]. To solve these

structural problems, a family of SAFs based on a new

structure has been proposed [8]–[10]. In [8], Courville

and Duhamel derived an SAF using a weighted

criterion. Based on the polyphase decomposition,

Pradhan and Reddy [9] derived another SAF using a

similar weighted criterion. In [10], Lee and Gan

presented a normalized SAF (NSAF) from the principle of minimum disturbance, with its complexity close to

that of the NLMS-based adaptive filter. The NSAF can

be viewed as a subband generalization of the

NLMSbased adaptive filter. Its central idea is to use the

subband signals, normalized by their respective

subband input variances, to update the tap weights of a

fullband adaptive filter. This strategy leads to the

decorrelating property of the NSAF [11]. Although

these SAFs can obtain fast convergence rate when

applied to AEC applications, they all require a tradeoff

between fast convergence rate and small steady-state

mean-square error (MSE) because of the use of a fixed

stepsize. Several studies have shown that the set-

membership, variable regularization parameter, and

variable step-size parameter versions of the NSAF can

offer possible schemes to overcome the conflicting

requirements of fast convergence rate and small steady-state MSE [12]–[14]. However, they all need to

estimate the system noise power in advance, which

increases the complexity of the system.

Recently, an adaptive combination of fullband

adaptive filters has been proposed in [15], and its mean

square error has been analyzed in [16]. The merit of

this combination is that it can obtain both fast

convergence rate and small steady-state MSE without

estimate of the system noise power. More recently, a

combination of subband adaptive filters for AEC has

been proposed [17], which is based on a conventional

subband structure. In this paper, we propose a new

Pavya S et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 1232-1236

IJCTA | MAY-JUNE 2012 Available [email protected]

1232

ISSN:2229-6093

mailto:[email protected]

[email protected],

subband adaptive combination scheme to deal with the

tradeoff problem encountered in acoustic echo

cancellers which are implemented by NSAFs. The

proposed combination is carried out in subband domain

and the mixing parameter that controls the combination

is adapted by means of a stochastic gradient algorithm

which employs the sum of squared subband errors as

the cost function. The section is splited as II.NSAF

structure III.Filter Bank IV.CIC decimator V.CIC interpolator VI.simulation results

Fig 1: Block Diagram of NSAF

II.NSAF STRUCTURE An N-channel analysis filter bank is a structure

transforming an input signal to a set of N subband

signals. A corresponding N-channel synthesis filter

bank transforms N subband channels to a full band

signal, in other words the inverse operation takes place. All subbands have equal bandwidth and the same

decimation and interpolation factors.

In this architecture both the microphone

signal d(n) and the far-end signal u(n) are partitioned

into N sub band signals via the analysis filters Hi(z ),i=

0,1, …N-1 The sub band signals di( n) and yi( n) for i =

0,1,…N −1 are all critically decimated to a lower

sampling rate. The decimated subband error signals are

then defined as eid(n)=di,d(n)-yi,d(n) , i=0,1,…..,N-1

Here we use the variable n and k to index the original

and decimated sequences.

III.FILTER BANK A filter bank is a set of bandpass filters with a

common input for the analysis filter bank or a summed

output for the synthesis filter bank.Figure 2 shows an

N-channel (or N-band) filter bank using z-domain

notation, where Hi(z) and Gi(z) are the analysis and

Fig 2: NSAF Structure

synthesis filters, respectively, and the variable i = 0, 1, .

. .,N – 1 is used as the subband index. The analysis

filter bank partitions the incoming signal X(z) into N

subband signals Xi(z), each occupying a portion of the

original frequency band. The synthesis filter bank

reconstructs the output signal Y(z) from N subband

signals Yi(z) to approximate the input signal.

A filter bank is called a uniform filter bank if

the center frequencies of bandpass filters are uniformly

spaced and all filters have equal bandwidth. By decomposing a fullband signal using an N-channel

uniform filter bank, each subband signal Xi(z) contains

only 1/N of the original spectral band. Since the

bandwidth of the subband signals Xi(z) is 1/N of the

original signal X(z), these subband signals can be

decimated to 1/N of the original sampling rate while

preserving the original information. A filter bank is

called a critically (or maximally) decimated filter

bank,if the decimation factor is equal to the number of

subbands, i.e. D = N. Critical decimation preserves the

effective sampling rate with N decimated subband

signals, Xi,D(z), each with 1/N of the original sampling

+

_

Echo path Analysis

filter

CIC

decimator

Noise

Analysis

filter

Adaptive

filter

CIC

decimator

Output bit error

ratio

Synthesis

filter

CIC

interpolator

+

Σ i/p



1233

ISSN:2229-6093

rate, so that the total number of subband samples is

identical to that of the fullband signal X(z). In the

synthesis section, the decimated subband signals

Xi,D(z) are interpolated by the same factor before being

combined by the synthesis filter bank. Therefore, the

original sampling rate is restored in the reconstructed

fullband signal Y(z).

IV.CIC DECIMATOR

Cascaded integrator-comb (CIC), or

Hogenauer filters, are multirate filters used for realizing

large sample rate changes in digital systems. Both

decimation and interpolation structures are supported

by the Core. CIC filters are multiplierless structures,

consisting of only adders, subtractors and registers.

They are typically employed in applications that have a

large excess sample rate. That is, the system sample

rate is much larger than the bandwidth occupied by the

signal. CIC filters are frequently used in digital down-

converters (DDCs) and digital up-converters. Figure 1

shows the basic structure for a CIC decimation filter.

The integrator section consists of N ideal integrator

stages operating at the high sampling rate fs. Each stage

is implemented as a one-pole filter with a unity

feedback coefficient The transfer functions for a single integrator is

Hi(z)=1/1-z-1

(1)

Fig 3: CIC Decimator

The comb section operates at the low sampling

rate fs/R where R is the integer rate change factor. This

section consists of comb stages with a differential delay

of M samples per stage. The differential delay is a filter

design parameter used to control the filter’s frequency response. M is restricted to be either 1 or 2. The transfer

function for a single comb stage, referenced to the high

input sample rate is

Hc(z)=1-zRM

(2)

There is a rate change switch (indicated in the

figure as the decimation function) between the two

filter sections. The decimator subsamples the output of

the last integrator stage, reducing the sample rate from

fs to fs/R. The system transfer function for the

composite CIC filter, referenced to the high sampling

rate, is

H(z)= Hi(z) Hc(z)

=(1-zRM

)N/(1-z

-1)

N

=[ 𝑧𝑅𝑀−1𝑘=0

-k]N

From the last form of the CIC transfer

function, we observe that the CIC filter is equivalent to

a cascade of N uniform FIR (finite impulse response)

filter stages with unit coefficients; that is, the filter is

equivalent to a cascade of N box-car filters. The CIC

decimator is actually implemented using the pipelined

architecture The pipeline registers P0, P1, P2 and P3

shorten the critical path through the differentiator

cascade

V.CIC INTERPOLATOR Exchanging the integrator cascade with the

differentiator cascade, as shown in Figure 3, produces a

CIC interpolator. Data is presented to the filter at the

rate fs/R where it is processed by the differentiators.

The rate expander in the figure causes a rate increase by

a factor R by inserting R-1 zero valued samples between consecutive samples of the comb section

output. The up-sampled and filtered data stream is

presented to the output at the sample rate fs. Just like

the CIC decimator, the Core implementation uses a

pipelined structure.

Fig 4:CIC Interpolator

VI.SIMULATION RESULT Analysis and Synthesis prototype filters with

length 16 taps is choosen. For filter design we use a

method from [3]. The decimation factor L is 2. All

calculation are based on a sampling rate of 8 kHz.

The echo-path is modeled by FIR-filter. The

FIR impulse response has a reverberation time of 72 ms

and was measured in a large car. As excitation signal

we use colored noise, which is generated by first order

IIR filtering of white noise, and speech.

Here five stage decimator and interpolator is

used. It Supports decimation and interpolation rate

changes between 8 and 16,383. Number of CIC stages

programmable between 1 and 8.Multiplierless filter

architecture is ideal for systems. Output of the decimator is given in fig 6.output is nothing but the

o/p

I I I C C C R

i/p

o/p

C C C I I I R

i/p



1234

ISSN:2229-6093

two’s complement of the filter output.fig 7 discuss the

output of the interpolator which is nothing but zero

padding and shiffting right by 2.fig 8 gives the output

of the synthesis filter which is nothing but the

reconstructed output 80 percent of the input is obtained

using the bit error ratio.power is calculated using

synopsys tool and is shown in fig 9.

Fig 5: vhdl output analysis filter (length=16, direct form

fir filter)

Fig 6: vhdl output for decimator(decimation factor=5)

Fig 7:vhdl output for interpolator(interpolation

factor=5)

Fig 8: vhdl output for synthesis filter

Types of adaptive

algorithm

Power consumption(µw)

Full band 728.5519

subband 455.3215

Tabel 1: comparison of power

Fig 9:synopsys output

VI CONCLUSION There are number of adaptive algorithms

available in literature and every algorithm has its own

properties, but aim of every algorithm is to achieve

minimum mean square error at a higher rate of

convergence with lesser complexity.

In this paper , we focused on power consumption using

synopsys EDA tool.power consumped by full band is

728.5519µw and the power consumed by subband is

455.3215µw.

REFERENCES

[1] M. M. Sondhi, ―The history of echo cancellation,‖

IEEE Signal Process. Mag., vol. 23, no. 5, pp. 95–98,

Sep. 2006.

[2] J. Benesty, T. Gaensler, D. R. Morgan, M. M.

Sondhi, and S. L. Gay, Advances in Network and



1235

ISSN:2229-6093

Acoustic Echo Cancellation. Berlin, Germany:

Springer-Verlag, 2001.

[3] C. C. Kao, ―Design of echo cancellation and noise

elimination for speech enhancement,‖ IEEE Trans.

Consumer Electronics, vol. 49, no. 4, pp.1468–1473,

Nov. 2003.

[4] H. Ding, ―Fast affine projection adaptation

algorithms with stable and robust symmetric linear

system slovers,‖ IEEE Trans. Signal Process., vol. 55, no. 5, pp. 1730–1740, May 2007.

[5] W. S. Gan, S. Mitra, and S. M. Kuo, ―Adaptive

feedback active noise control headset: implementation,

evaluation and its extensions,‖ IEEE Trans. Consumer

Electronics, vol. 51, no. 3, pp.975–982, Aug. 2005.

[6] A. H. Sayed, Adaptive Filters. New York: Wiley,

2008.

[7] K. A. Lee, W. S. Gan, and S. M. Kuo, Subband

Adaptive Filtering: Theory and Implementation.

Hoboken, NJ: Wiley, 2009.

[8] M. D. Courville and P. Duhamel, ―Adaptive

filtering in subbands using a weighted criterion,‖ IEEE

Trans. Signal Process., vol. 46, no. 9, pp. 2359–2371,

Sep. 1998.

[9] S. S. Pradhan and V. U. Reddy, ―A new approach to

subband adaptive filtering,‖ IEEE Trans. Signal

Process., vol. 47, no. 3, pp. 655–664, Mar. 1999.

[10] K. A. Lee and W. S. Gan, ―Improving convergence

of the NLMS algorithm using constrained subband

updates,‖ IEEE Signal Process. Lett., vol. 11, no. 9, pp.

736–739 , Sep. 2004.

[11] K. A. Lee and W. S. Gan, ― Inherent decorrelating

and least perturbation properties of the normalized

subband adaptive filter,‖ IEEE Trans. Signal Process.,

vol. 54, no. 11, pp. 4475–4480, Nov. 2006.

[12] M. S. E. Abadi and J. H. Husøy, ―Selective partial

update and setmembership subband adaptive filters,‖

Signal Processing, vol. 88, no. 10, pp. 2463–2471, Oct. 2008.

[13] J. Ni and F. Li, ―A variable regularization matrix

normalized subband adaptive filter,‖ IEEE Signal

Process. Lett., vol. 16, no. 2, pp. 105–108, Feb. 2009.

[14] J. Ni and F. Li, ―A variable step-size matrix

normalized subband adaptive filter,‖ IEEE Trans.

Audio, Speech, Lang. Process., to be published, DOI:

10.1109/TASL.2009.2032948.

[15] J. Arenas-García, M. Martínez-Ramón, A. Navia-

Vázquez, and A. R. Figueiras-Vidal, ―Plant

identification via adaptive combination of transversal

filters,‖ Signal Process., vol. 86, pp. 2430–2438, 2006.

[16] J. Arenas-Garcia, A. R. Figueiras-Vidal, and A. H.

Sayed, ―Mean-square performance of a convex

combination of two adaptive filters,‖ IEEE Trans.

Signal Process., vol. 54, no. 3, pp. 1078–1090, Mar.

2006.

[17] L. A. Azpicueta-Ruiz, A. R. Figueiras-Vidal, and

J. Arenas-García, ―Acoustic echo cancellation in

frequency domain using combinations of filters,‖ in

19th Int. Congress on Acoustics (ICA), Madrid, Sep.

2007.

[18] N. J. Bershad, J. C. M. Bermudez and J.-Y.

Tourneret, ―An affine combination of two LMS

adaptive filters —Transient mean-square analysis,‖

IEEE Trans. Signal Process., vol. 56, no. 5, pp. 1853–

1864, May 2008.

[19] M. R. Petraglia, P. B. Batalheiro, ―Nonuniform

subband adaptive filtering with critical sampling,‖

IEEE Trans. Signal Process., vol. 56, no. 2, pp. 565–

575, 2008.

[20] J. Arenas-Garcia and A. R. Figueiras-Vidal,

―Adaptive combination of proportionate filters for

sparse echo cancellation,‖ IEEE Trans. Audio, Speech,

Lang. Process., vol. 17, no. 6, pp. 1087–1098, Aug.

2009.

[21] P. P. Vaidyanathan, Multirate Systems and Filter

Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.

BIOGRAPHIES

Pavya.s, is final year ME-VLSI

Design student in K.S.Rangasamy

college of technology, Tiruchengode,

Tamil nadu. Her area of interest is

Digital signal processing and VLSI

design techniques.

Babu.P, M.E,(P.hD)., is working as

Associate Professor in

K.S.Rangasamy college of

Technology, Tiruchengode, Tamil

Nadu. His area of interest is Digital signal processing.



1236

ISSN:2229-6093

design of normalized subband adaptive filter for … · design of normalized subband adaptive...

Documents