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ARPN Journal of Science and Technology2011-2012. All rights reserved.

http://www.ejournalofscience.org

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Multirate Filtering For Digital Signal Processing and

Its Applications

1 Suverna Sengar and 2 Partha Pratim Bhattacharya

Department of Electronics and Communication Engineering

Faculty of Engineering and Technology

Mody Institute of Technology & Science (Deemed University)

Lakshmangarh, Dist. Sikar, Rajasthan,

Pin 332311, [email protected], [email protected]

ABSTRACT

Multirate Filtering techniques are used when conventional method becomes extremely costly and this technique is widely

used in both sampling rate conversion system and in constructing filters with equal input and output rates. The basicconcepts and building blocks in multirate digital signal processing are discussed here which includes down-sampler, up-

sampler and analysis/synthesis representation. Applications of multirate digital filters in DS/CDMA code acquisition,Kalman filtering for optimal signal reconstruction from noisy subband system and lossy compression approach totransmultiplexed images are also reviewed.

Keywords:Multirate filters, Decimation, Interpolation, Multistage system and Analysis/Synthesis filter.

1. INTRODUCTION

A multirate filter is a digital filter that changesthe sampling rate of the input signal into another desired

one. These filters are of essential importance incommunications, image processing, digital audio, andmultimedia. Unlike the singlerate system, the samplespacing in the multirate system can vary from point topoint [1]-[2]. This often result in more efficient

processing of signals because the sampling rates atvarious internal points can be kept as small as possible,but this also results in the introduction of a new type oferror, i.e., aliasing.

1.1 TIME-DOMAIN

REPRESENTATION OF DOWN-

SAMPLING AND UP-SAMPLING

Two discrete signals with different samplingrates can be used to convey the same information. For

example, a band limited continuous signal xc(t) might berepresented by two different discrete signals {x[n]} and{y[n]} obtained by the uniform sampling of the original

signal xc(t) with two different sampling frequencies F tand Ft.

x[n]=xc(nT) and y[n]=xc(nT') (1)

where T= 1/Ft and T=1/ Ft are the corresponding

sampling intervals. When the sampling frequencies Ftand Ft are chosen in such a way that each of them

exceeds at least two times the highest frequency in thespectrum of xc(t), the original signal xc(t) can be

reconstructed from either {x[n]} or {y[n]}. Hence, thetwo signals operating at two different sampling rates arecarrying the same information. By using the discrete-time operations, signal {x[n]} can be converted to{y[n]}, or vice versa, with minimal signal distortions.

The two basic operations in sampling ratealteration process are the down-sampler and up-sampler.These two operators can perform the sampling rate

alteration: a down-sampler used for decreasing thesampling rate, and an up-sampler used for increasing thesampling rate.

1.2 DOWN-SAMPLING OPERATION

The down-sampling operation with a down-

sampling factor M, where M is a positive integer, isimplemented by discharging M1 consecutive samplesand retaining every M

th sample. Applying the down-

sampling operation to the discrete signal {x[n]},

produces the down-sampled signal

y[m]= x[ mM] (2).

The down-sampling can be imagined as a two-step operation. In the first step, the original signal {x[n]}is multiplied with the sampling function {sM[n]} definedby,

sM[n]= (3).


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Multiplying the sequence {x[n]} by thesampling function {sM[n]} results in the intermediate

signal {ys[m]},

ys[m]=x[n]sM[n]= (4).

This operation is called a discrete sampling. Inthe second step, the zero valued samples in {ys[m]} areomitted resulting in the down-sampled sequence {y[m]},

y[m]=ys[mM]=x[ mM] (5).

The down-sampling operation is sometimescalled the signal compression, and the down-sampler is

also known as a compressor. A block diagram

representing the down-sampling operation is shown inFigure 1 [3].

Figure 1:Block diagram representation of a

down-sampler

1.3 UP-SAMPLING OPERATION

The up-sampling by an integer factor L is

performed by inserting L-1 zeros between twoconsecutive samples. Applying the up-samplingoperation to the discrete signal {x[n]}, produces the up-

sampled signal {y[m]} is defined as,

y[m]= (6).

A block diagram presentation of equation-6 isgiven in Figure 2 [3].

Figure 2:Converting the sampling rate with an up-sampler

The up-sampling is sometimes called the

sequence expansion, and the term expander is sometimesused for the device.

1.4 DECIMATION AND

INTERPOLATION

The process of sampling rate decrease is calleddecimation, and the process of sampling rate increase is

called interpolation. Two devices, the down-sampler andthe up-sampler, are elements that change the sampling

rate of the signal. The drawback of the down-sampling isthe aliasing effect, where as the up-sampling produces

the unwanted spectra in the frequency band. Decimationhas used to avoid the effects of aliasing, which occurs

when the highest frequency in the spectrum of a down-sampled signal H exceeds the value /M. Ininterpolation, the L-1 images caused by inserting L-1zeros between the samples should be removed.

1.4.1 DECIMATION

Decimation requires that aliasing should be

prevented. So before, down sampling with the factor ofM, the original signal has to be band limited to /M. Thismeans that the factor-of-M decimation has to be

implemented in two steps:-

i) Band limiting of the original signal to /M

ii) Down-sampling by the factor-of-M.

Figure 3 [4] shows the block diagram of adecimator implemented as a cascade of the decimation

Filter H(z), also called the anti-aliasing filter, and thefactor-of-M down-sampler. The performance of adecimator is mainly determined by the filtercharacteristics.

Figure 3:Block diagram representation ofdecimator

1.4.2

INTERPOLATION

Interpolation requires the removal of theimages. This means that the factor-of-L interpolation hasto be implemented in two steps:

i) Up-sampling of the original signal by inserting

L-1 zero-valued samples between twoconsecutive samples.

ii) Removal of the L-1 images from the spectrumof the up-sampled signal.

Figure 4 [4] shows the block diagram of aninterpolator implemented as a cascade of a factor-of-Lup-sampler and a lowpass filter, frequently called the

anti-imaging filter. The cut-off frequency of the filter is/L. The anti-imaging (interpolation [5]) filter H (z) isused to remove images from the spectrum of the up-sampled signal. Removal of images from the spectrum of

the signal causes the interpolation of the sample values

in time domain. The zero-valued samples in the up-sampled signal {xu[m]} are filled with the interpolatedvalues.


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Figure 4:Block diagram representation of aninterpolator

2. APPLICATIONS OF MULTIRATE

FILTERS

A multirate filter is used to change the samplingrate of the input signal into another desired one andmultirate filtering [6] can be used in various fields, like itis used in multirate adaptive filtering for DS/CDMAcode acquisition, Multirate kalman filtering for optimal

signal reconstruction from noisy subband system,multirate filters use in lossy compression approach totransmultiplexed image and many more. Different

applications of multirate filters are described in thesubsequent sections.

2.1 MULTIRATE ADAPTIVE FILTERING

FOR DS/CDMA CODE ACQUISITION

In direct sequence code division multiple access(DS/CDMA) system [7], to recover the transmitted

information, the received signal should first despreadedusing a locally generated pseudo noise (PN) codesequence. The code acquisition performs initial code

timing alignment between the locally generated andreceived signals. Code acquisition method is usuallyconducted using a correlator to serially search the code

phase, which is related to the channel propagation delay.This approach performs well for the adaptive filteringapproaches [8] have high acquisition-based capacityanddrawback of these schemes is high computational

complexity. Due to down-sampling operations, thecomputational complexity of the adaptive filters can beeffectively reduced.

Code synchronization is a very essential and

important part of any spread spectrum (SS)

system inorder to remove the spreading effect induced by thetransmitter and to exploit the processing gain of the

spread signal. The receiver must be able to estimate thedelay offset between the spreading code in the received

signal and the locally generated replica of the codebefore data demodulation is started. Codesynchronization is usually developed over two steps,namely acquisition and tracking [9]-[10].In this

application of multirate processing, not only thecomputational complexity, but also the mean acquisitiontime can be effectively reduced. Here the basic idea ofthe scheme used in multirate adaptive filtering for

DS/CDMA code acquisition is discussed.

2.1.1 SCHEME USED FOR MULTIRATEFILTER SYSTEM MODEL

There are K active users and each user is

specified with a pseudo-noise (PN) sequence with lengthL, where L is the processing gain. Consider an additivewhite Gaussian noise (AWGN) channel. The user-ktransmitted signal is given by

Xk(n)= (7)

where dk(j) {1, -1} is the j-th BPSK(binary phase

shifting keying) symbol of user- k, Ck(l) is the

l-th chip of user-ks PN sequence, and p(n) is therectangular pulse having a unit amplitude and a chip-duration, Tc . Now, assume that user-1 is the desireduser. The received signal can be written as

r(n) =

= (8)

where w(n) is AWGN (additive white Gaussian noise)and i(n)is the summation of interference and noise. Let

the mean of i(n)be zero and the variance be . Assume

that , k = 1, ... , K are integer multiples of Tc, and

uniformly distributed over {0, 1. . . L - l}, The carriersynchronization is established before code acquisition

and no data are transmitted during acquisition (i.e. d1(j)= 1). The main objective is to estimate the delay of the

desired user, from the composite received signal,

{r(n)}. Here proposed to use an adaptive filter (AF) toestimate the delay of the desired user from the tap-

weight vector of the filter. The block diagram of the AFbased DS/SS code acquisition system is shown in Figure5 [8].

Figure 5:Block diagram for the adaptive acquisitionsystem


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THE SCHEME

Figure 6 [11] shows the Structure of theproposed scheme, which consists of two adaptive filters.

The input of the first filter (wc(.)) is the down-sampledlocally generated PN sequence; the down-samplingfactor is D. The reference signal is the down-sampledreceived signal. Here, the lowpass filter is an averaging

filter with length D. Let where is an

integer, and is a fractional

delay, -D/2 < . To determine the fractional

delay, then need the second filter (wf(.)). The filterappearing in front of wf(.) is named the delay tuningfilter (DTF); its output is just a delay version of theinput. If copy the delay identified by the first filter to theDTF, the second filter can identify the fractional delay.Feedback the peak position of wf(.) to the filter in frontof wc(.), which is namely the phase tuning filter (PTF).

The fractional delay will vanish. The convergentweights of the first filter only have a non-zero weight. Innoisy environment, this will greatly reduce acquisitionerror. The cross adaptation of these two filters will

effectively determine the code phase.

Figure 6:The Proposed Scheme

2.1.2 PERFORMANCE ANALYSIS

Here, first consider the computational

complexity. Now, only consider the requiredmultiplications per chip duration. The second filter has2D-1 taps and each tap needs two multiplications for

LMS weight-updating. The first filter has Mptaps and itstap-weights updating rate is D times slower than thesecond filter. Thus, its computational complexity perchip duration, Cp, is given by

where N is the number of chips for tap-weightconverging. Then consider the probability of acquisitionerror. An acquisition error may occur due to the first

filter, the second filter, or both. The probability ofacquisition error is then

(10)

where and are the correct taps of the first and

the second filters, respectively; and denote the

probabilities of correct acquisition of the first and the

second filters, respectively. Finally, consider the meanacquisition time. The propose scheme gives an estimate

after N chips elapses. Figure 7 [11] shows the state

transition diagram, whose transfer function is

where TP is the penalty time,z is a delay operator and Peis the probability of acquisition error.

Figure 7:The state transition diagram of the

proposed acquisition system

2.1.3 EXISTING SIMULATION RESULTS

The simulation results are demonstrating theeffectiveness of the proposed scheme. Here, K = 20

(SINR = -13dB), L = 128, D = 4, Mp= 32, and Tp=

(chips) are considered. Both filters use a same step sizep. For a 32-tap conventional adaptive acquisitionmethod, it needs 64 multiplications per chip, but theproposed scheme only requires 30 multiplications per

chip. Figure 8 shows the theoretical and simulatedacquisition error probabilities Pe in various step sizes.


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Figure 8: Theoretical and simulated probabilities of

acquisition errorP, versus step sizesp for the proposedscheme

The probability Pewas evaluated after N chips

using samples. For P = 2 samples were

observed. Now, N is selected to be four times of the time

constant of the first filter . These results are

substituted into equation (13) for theoretical andsimulated mean acquisition time calculation. The resultsare shown in Figure 9.

As shown in Figure 8, as step size increases theprobability of error also increases and from Figure 9 itcan be seen that as step size increases the meanacquisition time decreases. So, not only the

computational complexity is low, but also the meanacquisition time is low.

Figure 9: Theoretical and simulated mean acquisitiontime versus step sizesof the proposed scheme

2.2 MULTIRATE KALMAN

FILTERING FOR OPTIMAL SIGNAL

RECONSTRUCTION FROM NOISY

SUBBAND SYSTEM

The multirate signal processing is to decomposethe original signal into complementary frequency bands

and then process them separately in each subband. Inthis application use decimation and interpolation filtersor analysis/synthesis filter banks that allow perfect

reconstruction [12]. The perfect reconstruction (PR)filter bank systems are based on the assumption that thesubband components are free of noise. While, in

practical systems, the subband components are alwayscontaminated by noises due to the effect of quantization[13], round-off [14] and other distortion, therefore, the

perfect reconstruction is no longer possible. Forimproving the applicability of filter bank systems use themultirate kalman synthesis filter [15] in place ofconventional synthesis filters to achieve optimalreconstruction of the input signal in noisy filter bank

systems Figure 11 [16].

The input signal embedded in the state vector,the multichannel representation of subband signals is

combined with the statistical model of input signal toderive the multirate state-space model for the filter banksystems and the subband noises are assumed to beadditive ones. The multirate Kalman filter can be

constructed to provide the minimum variance estimationof the input signal based on observations of noisy

subband components. Here going to discuss first thebasics idea of multirate kalman synthesis filtering and toexplain the state-space model and also mention themultirate state-space model for 2-D kalman filtering.

Figure10:Noisy M-band filter bank system equippedwith a multirate Kalman synthesis filter

2.2.1 FILTER BANK SYSTEMS AND

PROBLEM FORMULATION

a.

FILTER BANK SYSTEMS

Let {Hk(Z), Gk(Z): k = 0,1,... , M - 1} denotesthe M band filter bank systems. The bank of filters {Hk(Z)} constitutes the analysis filters. Each filter output is


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down-sampled and transmitted to the receiver. Wherethey are up-sampled and fed into the bank of synthesis

filters {Gk(Z)} for signal reconstruction Figure 11 [16].

Figure 11:M-band filter bank system with cleansubband paths

b. MULTICHANNEL REPRESENTATIONOF SUBBAND SIGNALS

Let { hi , gi ; i=0,1} denote the impulseresponse of 2-band analysis/synthesis filter bank, the

equivalent multichannel representation of subband

signals .

y(n) = (14)

where f(n) = = , y(n) =

and H(k) is the multichannel impulse response matrix ofthe form

H(k) = (15)

The above are the so-called

polyphase components of respectively.

If additive noisy corruption are included in the subbandcomponents, the received subband signal r(n) can beexpressed as follows:

r(n) = y(n)+ v(n) (16)

v(n) = in (16) is the additive-noise

disturbance vector.

2.2.2 MULTIRATE STATE-SPACE MODEL

FOR 1-D SIGNAL

a. THE BASIC SIGNAL MODEL

Let p = , where are chosen such

that .

By substituting k = k-, we can rewrite equation (14) asa causal form

y(n)= (17).

Now, can write the state vector as

x(n)= ,

then

X(n+1)=A x(n)+B (18).

Here further denote

and , the subband output is

y(n) = C x(n)+D (19).

Considering the effect of noisy disturbancevector v(n), now formulate the problem as the form of

state-space model

X(n+1)=A x(n)+B x(-1)=x-1

r(n)=C x(n)+D + v(n) (20).

b. THE STATISTICAL MODEL

The state space model describing the statistical

characteristic of the input signal, which has the form

z(k+1)= f(k) = H z(k)(21)

where z(k) and u(k) are the state vector and drivingsource, respectively. Let z(n) = z[2(n+)], theequivalent block generation model is given below

z(n+1)=

f(n+)=

f[2(n+)]= H z(n)(22)

c. THE MULTIRATE STATE-SPACE

MODEL

The multirate state space model will be givenbeloww(n+1) =

r(n)= (23)

where w(n) = , is the state vector of the

system model. Similarly, the multirate state-space modelfor 2-D signal [15] can also be written.

2.2.3 NUMERICAL RESULTS

Simulation is carried out to show the feasibility

and effectiveness of the proposed 2-D Kalman filteringfor optimal 2-D signal reconstruction from noisy


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subband systems. Here compared the performance of theproposed 2-D multirate Kalman filter versus the

conventional perfect reconstruction (PR) filters for 2-Dsignal reconstruction under different noise levels. The

simulation was implemented with Matlab. Now adopteda set of 2-band quadrature mirror filter (QMF) PR filter

bank {h (n)}of length 8 in the simulation [17]. The 2x2subband decomposition of test image is implementedthrough two 1-D separate analysis filter bank

{ i=0,1.with

Two quantitative measures, SNRim,n

and SNRr,are input noise level and reconstruction performance,

respectively. The test image Hillside is of size 160 160

8 (Figure 12 (a) [15]). The image is converted to zero

mean prior to 2 x 2 subband decomposition and itsautocorrelation function. White additive noise atdifferent SNR levels was added to all the four subband

images. Figure 13 [15] demonstrates the reconstructionperformance comparison with both the proposedmultirate Kalman filtering and the conventional PR

synthesis filters under different SNR level. It is observedthat the improvement in reconstruction SNR with theproposed 2-D multirate Kalman filtering is considerable.

Figure 12: (a)Original image Hillside of size 160

160;(b) 2 2 subband decomposition of Hillside;

(c) noise-corrupted subband image at SNRi= 0dB;(d) reconstructed image with conventional PRfilter banks at SNRi= 0 dB;(e) reconstructed image with 2-D Kalmanfiltering at SNRi= 0 dB;

(f) Reconstructed image with conventional PRfilter banks at SNRi= 8 dB;(g) reconstructed image with 2-D Kalmanfiltering at SNRi= 8 dB

Figure 13:Reconstruction SNRversus additive noise

SNR level

Figure 12(e) [15] show that, even in the

extremely low SNR, case, the main structure of the

original image is still distinguishable on thereconstructed image with 2-D multirate Kalman filtering.

2.3 LOSSY COMPRESSION

APPROACH TO TRANSMULTIPLEXED

IMAGES

Multimedia content is more and more popularin many different types of telecommunications. Thatswhy use a new and efficient method for sending several

images through a single transmission line is needed. Thetransmultiplexer is a structure that combines up-sampled

and filtered signals for the transmission over a singletransmission line. Transmultiplexing [18] is easy toapply because it needs only simple digital processing:up-sampling, filtering and summing. All these operationsused in transmultiplexer are linear and time-invariant.

Figure 14 [20] shows the structure of 4-channel (M=4)transmultiplexer.

Figure 14:Scheme of 4-channel image transmultiplexer

The main problem in transmultiplexers ispreventing image distortion caused by the change of

amplitude and phase as well as image leakage from onechannel into another. The main motivation of thisapplication, lossy compression is to achieve a perfect

image reconstruction in the receiver by using appropriate

filters [19].

In compression algorithm the number of bits

needed to represent the signal (image) or its spectrum is


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minimized. The fundamental concept of compression isto split up the frequency band of a signal (image) and the

quantized each subband using a bit rate accuratelymatched to compromise between the two opposite

criteria: minimize distortions and maximize thecompression rate.

Over the past several years, the waveletmethods have gained widespread acceptance in signalprocessing and in the signal compression. Multirate

processing is related to signal transformation usingwavelets. Wavelet packets are a way to analyze a signalusing base functions which are well localized both intime and in frequency. The properties of wavelet

transform make it useful in compression. The mainadvantage of the wavelet transform is used in lossycompression which reduces the signal (image) spectrum

by eliminating redundant information. Lossycompression is generally used where a loss of a certainamount of information will not be detected by the users.

2.3.1 IMAGE TRANSMULTIPLEXING

Figure 14 [20] shows the structure of the four-

channel (M=4) image transmultiplexer. The input imagesare up-sampled and filtered vertically and summed toobtain two combined images. These combined imagesare then up-sampled and filtered horizontally and

summed to obtain the final version of combined image[19]. In presented system the combined image consists

of four times more pixels than each input image. At thereceiver end, the signal is relayed first two channels of

the detransmultiplexing, where the signals are filteredand down-sampled horizontally. Then these signals arerelayed to four channels where images are filtered and

down-sampled vertically to recover the original image.

2.3.2COMPRESSION

Wavelet packet algorithm generates a set of

orthogonal sub-images that are derived from a singlecombined image. The wavelet spectra are produced bycascading filtering and down-sampling operations in a

tree-structure. Wavelet packets were introduced forsplitting images into its frequency components so that tocompress the image by non-uniform quantization.

The 2-D wavelet packet transform (WPT) canbe viewed as a decomposition system in Figure 15 [20]for three levels. The basis data are the coefficients of

wavelet series of the original image. The next levelresults of one step of the 2-D wavelet discrete transform(WDT). Subsequent levels are constructed by recursivelyapplying the 2-D wavelet transform to the low and high

frequency sub-bands of the previous wavelet transform.The higher level component has two times narrower

frequency bands when compare with the subsequentlower frequency components. Multirate processinginvolves the application of filtering and down-sampling.The main objective is the design of lowpass and

highpass filters which gives useful transformations andallow recovering the transmitted images.

Figure 15: 2-D wavelet packet transforms structure

2.3.3 EXAMPLE

Four test images (boats, F-16, Lena andbaboon) with 512 512 pixels resolution in 256

grayscale levels were selected for the analysis. The

combined image has 1024 1024 pixel resolution. Its

luminance values are integer numbers from -1088 to

1884. The combining filters and the separation

filters were designed by algorithm presented in [21].

Linearity property of the transmultiplexer

system enables to split the combined image into itsfrequencycomponents. The periodicity of spectrum of the

combined image is shown in Figure 16 [20]. Thesampling densities in the frequency domain for all levelsare the same but the amounts of samples are different.The spectrum of the up-sampled signal consists of theoriginal spectrum and its components.

The three level 2-D wavelet packetdecomposition was provided by the discrete Meyer

wavelets. The absolute values of coefficients of waveletpacket decomposition are shown in Figure 17 [20]. Themain part of energy (96.6%) of the signal is localized inlast four sub-bands of the network AAA (2.5%), HAA

(13.3%), VAA (10.4%) and DAA (70.4%). The

compression with factor 16 was obtained by omittinginformation from other bands. The reconstructed output

images are shown in Figure 18 [20]. The large part of thesignal energy was sent and the compression was not very


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high, some distortions are visible. In the presentedexample data from bands with the energy higher than

0.2% of the whole energy was transmitted.

Another possible solution is the preliminarycompression of the input images, e.g. using JPEG

algorithm [22], and Figure of JPEG for lossycompression in transmultipexer system [20] andapplying the 1-D transmultiplexer after converting of thebit streams into integer 1-D signal. The compression

with factor 16 using the JPEG algorithm on the each ofinput images allows to gain the better quality of imagesthan in case of the compression of the combined image.

Figure 16: Amplitude [dB] of spectrum ofcombined image

Figure 17:2-D wavelet packet transform coefficients

Figure 18: Comparison of input and output images

3. CONCLUSION

The fundamentals of multirate filters and itsapplications in various fields like multirate adaptivefiltering for DS/CDMA code acquisition, Kalman

filtering for optimal signal reconstruction from noisysub-band system and lossy compression approach totransmultiplexed images are discussed in this paper. InDS/CDMA code acquisition, it is proposed that a low

complexity is achieved using fast acquisition adaptivefiltering using the multirate signal processing technique.Unlike the conventional methods, the proposed schemedoes not divide the uncertainty region into cells andsearch the code phase cell by cell. Instead, it uses a two-step procedure for searching. Firstly, it searches the codephase in the whole region with a lower resolution.

Secondly, it searches the code phase in a small regionwith a high resolution. Due to this multirate processingand searching strategy the computational complexity and

mean acquisition time can be effectively reduced.Multirate Kalman filtering combines the multichannelrepresentation of sub-band signal with the statistical

model of input signal to derive the multirate state-spacemodel for noisy filter bank systems. The signalreconstruction can be formulated as the optimal stateestimation with multirate Kalman filtering. Lastly lossycompression approach to transmultiplexed images uses

the transmultiplexer for sending the several images overa single transmission line. The transmultiplexer is astructure that combines suitably up-sampled and filtered

signals for the transmission by a single channel that usesdifferent algorithms to reduce the high frequencycomponents which causes major error in output images

of the transmultiplexer.


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REFERENCES

[1] R.W.Schafer and L.R.Rabiner, A digital signalprocessing approach to interpolation,

Proc,IEEE,vol.61, pp. 692-702, June 1973.

[2] G.Oetken, T.W.Parks,and H.W.Schussler, Newresults in the design of digital interpolators,

IEEE Trans. Acoust. Speech signal Proc.,vol.23,pp. 301-309,June 1975.

[3] Ljiljana Mili, University of Belgrade, Serbia,

Multirate Filtering For Digital SignalProcessing: MATLAB Applications, 2009.

[4] Ljiljana Mili and Tapio Saramki and RobertBregovic, Multirate Filters: An Overview.

[5] Nkwachukwu Chukwuchekwa, InterpolationTechniques in Multirate Digital Signal Processingfor efficient communicationsystem,vol.3.no.2.March, 2011.

[6] L. D., Milic and M.D. Lutovac, "Efficientmultirate filtering," in Gordana Jovanovi &-Dolecek, (ed.), Multirate Systems: Design &Applications, Hershey, PA: Idea GroupPublishing, pp. 105-142, 2002.

[7] Seokho Yoon, Lickho Song, So Ryoung Park,Sun Youg Kim and Jooshik Lee, A Code

Acquisition Scheme for DS/CDMA systems,Hallym University, 1998.

[8] Mohamed G. El-Tarhuni and Asrar U. Sheikh,

"An Adaptive Filtering PN Code AcquisitionScheme with Improved Acquisition BasedCapacity in DS/CDMA," IEEE Ninth

International Symposium on PIMRC, vol.3, pp.1486-1490, 1998.

[9] M.Simon et at, Spread Spectrum

Communications, vol.3, Computer SciencePress, Rockville, Maryland, 1985.

[10] R.Dixon, Spread Spectrum System, John Wilayand Sons, New York, 1984.

[11] Hua-Lung Yang, Wen-Rong Wu, MultirateAdaptive Filtering for DS/CDMA CodeAcquisition, 2003.

[12] P.P. Vaidyanathan, Multirate Digital Filters,Filter Banks, Polyphase Networks, andApplications: A Tutorial, Proc. of The IEEE,

vo1.78, pp.56-93, Jan. 1990.

[13] R. A. Haddad and N. Uzun, Modeling, analysisand compensation of quantization effects in M-

band subband codes, in Proc. ICASSP 93, pp.III-173-176.

[14] P. P. Vaidyanathan, On coefficient-quantization

and computational roundoff effects in losslessmultirate filter banks, IEEE Trans. SignalProcessing, vol. 39, no. 4, pp. 1006-1008, Apr.1991.

[15] J.Q.Ni, K.L. Ho, K.W. Tse, and M.H.Shen,Multirate Kalman Filtering Approach forOptimal Two-Dimensional Signal Reconstructionfrom Noisy Subband Systems, IEEE, vol.1, 06August 2002.

[16] B. Chen, Optimal Signal Reconstruction inNoisy Filter Bank Systems: Multirate KalmanSynthesis Filtering Approach, IEEE Trans.

Signal Processing, vo1.43, pp.2496-2504, Nov.,1995.

[17] A.Delopoulos, Optimal Filter Banks for SignalReconstruction from Noisy SubbandComponents, IEEE Trans. signal processing, vol.

44, pp212-224, Feb., 1996.

[18] A. N. Akansu, P. Duhamel, X. Lin, & M.Courville, Orthogonal Transmultiplexers in

Communications: A Review, IEEE Trans. on

Signal Processing, vol. 46(4), pp. 979-995, 2001.

[19] P. Sypka, B. Ziolko, and M. Ziolko, "Integer-to-integer filters in image transmultiplexers", IEEEInternational Symposium on Communications,Control and Signals, Marrakech, Morocco, March13-15. 2006.

[20] Przemyslaw Sypka , Mariusz Ziolko and Bartosz

Ziolko, Lossy Compression Approach toTransmultiplexed Images, AGH University ofScience and Technology al. Mickiewicza 30, 30-059 Krakow, Poland, 07-09 June 2006.

[21] P. Sypka, M. Zio6ko, and B. Zio6ko, LosslessJPEG-Base Compression of TransmultiplexedImages, IEEE 14-th European Signal ProcessingConference, Florence 2006.

[22] ISO/JEC IS 10918-1 / ITU-T Rec. T.81,Information technology- digital compression andcoding of continuous still images, Requirementsand guideline.

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