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INTRODUCTION
In the last decade, there has been an enormous increase in the
applications of wavelets in various scientific disciplines to
relate the discrete-time filter bank with the theory of
continuous time function space [1]. Wavelet techniques
represents real life non stationary signal which is powerful
technique for achieving compression. Wavelet based
techniques has efficient parallel VLSI implementation low
computational complexity, flexibility in representing non
stationary image signals. In order to meet the real time
requirements in many applications, design and implementation
of DWT is required [2], [3].
Typical applications of wavelets include signal processing,
image processing, numerical analysis, statistics, biomedicine,
etc. [4], [5].Redundancies in video sequence can be removed
by using Discrete Cosine Transform (DCT). DCT suffers from
the negative effects of blackness and mosquito noise resulting
in poor subjective quality of reconstructed images at high
compression [5],[8].In order to meet the real time
requirements in many applications, design and implementation
of DWT is required [6], [7].
II. DISCRETE WAVELET TRANSFORM
DWT is based on sub band coding, is fast computation
wavelet transform. The resolution of the signal, which is a
measure of the amount of detail information in the signal, is
determined by the filtering operations, and the scale is
determined by up sampling and down sampling (subsampling)
operations [2],[13].A schematic of three stage
In Figure 1, the signal is denoted by the sequence a[n], where
n is an integer. The low pass filter is denoted by L1 while the
high pass filter is denoted by H1. At each level, the high pass
filter produces detail information b[n], while the low pass
filter associated with scaling function produces coarse
approximation, c[n].
Here the input signal a[n] has N samples. At the first
decomposition level, the signal is passed through the high pass
and low pass filters, followed by sub sampling by 2.The
output of the high pass filter has N/2 samples and b[n].These
N/2 samples constitute the first level of DWT coefficients.
The output of the low pass filter also has N/2 samples and
c[n]. The signal is then passed through low pass and high pass
filters for further decomposition. The output of the second low
pass filter followed by sub sampling has N/4 samples and
e[n].The output of the second high pass filter followed by
subsampling has N/4 samples and d[n].The second high pass
filter constitutes the second level of DWT coefficients. The
low pass filter output is then filtered once again for further
decomposition and produces g[n], f[n] with N/8 samples. The
filtering and decimation process is continued until the desired
level is reached. The maximum number of levels depends on
the length of the signal.
III. DATA DEPENDANCIES WITHIN DWT
The wavelet decomposition of a 1-D input signal for three
stages is shown in Figure 1. [9], [12]. The transfer functions of
the sixth order high pass (g(n)) and low pass h(n)) filter can be
expressed as follows:
DWT-SA ARCHITECTURE
The proposed architecture is shown in Figure 11. It is obtained
by systematic analysis of the FRA register allocation in
conjunction with the filter equations 1a and 1b .Delay of the
DWT-SA architecture consists of the latency period necessary
to fill up the filter for the first time, plus the delay through the
registers as described in Table 1. The output coefficients are
obtained from the final filter stage.
The architecture is optimized in hardware by using only a
single multiplier and adder set in each filter cell to generate all
high pass and low pass coefficient. The coefficients which are
present at the output of filter are stored in register.The control
logic controls the switching action of switch. The data which
are coming from delay input and register bank is controlled by
switch. According to the position of switch, one of the data is
select and performs filtering operations. This process is
continued up to the 53 clock cycle.
SIMULATION RESULTS OF DWT-SA
ARCHITECTURE FOR DAUBECHIES3, HAAR
AND COIFLETS1 WAVELET
MATLAB is the software which is used in this project to
verify the result with VHDL simulation. The high pass and
low pass coefficients are calculated from MATLAB which are
in decimal form. We convert these into binary and padding
some zeroes in it. Because the filter cell and multiplexer is
designed for31 bit, 13 bit respectively. Out of this13 bit, 12
bits are data bits and 1 MSB bit is signed bit. The signed bit
represents the positive or negative number.
All the implementation and simulation is done in Active
HDL7.1. Simulated waveform gives result for different band
select. When band select is ‘1’ the low pass coifficients are
selected and gives Approximation coefficients. When band
select is ‘0’ the high pass coifficients are selected and gives
Details coefficients. The result of DWT-SA is in hexadecimal
format. For the verification of VLSI results, MATLAB is
used. The approximation and detail coefficient are obtained
from MATLAB.
TABLE III, TABLE IV and TABLE V show the result in
terms of approximation coefficient in hexadecimal form of
daubechies3, haar and coiflets1 wavelet.