This paper presents the design and implementation of an eight order efficient FIR filter for wireless communication system. In this work, factored canonical signed digit representation (FCSD) is used for representing the filter coefficients in order to reduce the design complexity, area and delay of the FIR filter. Complexity of the system has been reduced by replacing binary coefficients with FCSD representation. Further area and delay has been improved by replacing multiplication operation with add and shift method where carry save adder (CSA) is used for addition of two numbers and barrel shifter is used for shifting the data words. Representation of coefficient in the FCSD format along with fastest adder and shifter improves the performance of the system. FIR filter has been designed using an equiripple method in MATLAB and further synthesized on Spartan 3E XC3S500E target FPGA device. Simulation results show that optimized FCSD based FIR filter offers a less number of slices, look up tables (LUTs) and flip-flops as compared to CSD and conventional FCSD based FIR filter, in addition to enhanced performance.

1. Neha Goel Ashutosh Nandi
Dept. of Electronics and Comm. Engg. National Institute of Technology Kurukshetra, India
nehagoel0392@gmail.com, ashutosh.chl@gmail.com
Design of Optimized FIR Filter Using FCSD
Representation
Keywords— FIR Filter, CSA, Barrel shifter, FCSD.
Abstract—This paper presents the design and implementation
of an eight order efficient FIR filter for wireless communication
system. In this work, factored canonical signed digit
representation (FCSD) is used for representing the filter
coefficients in order to reduce the design complexity, area and
delay of the FIR filter. Complexity of the system has been
reduced by replacing binary coefficients with FCSD
representation. Further area and delay has been improved by
replacing multiplication operation with add and shift method
where carry save adder (CSA) is used for addition of two
numbers and barrel shifter is used for shifting the data words.
Representation of coefficient in the FCSD format along with
fastest adder and shifter improves the performance of the system.
FIR filter has been designed using an equiripple method in
MATLAB and further synthesized on Spartan 3E XC3S500E
target FPGA device. Simulation results show that optimized
FCSD based FIR filter offers a less number of slices, look up
tables (LUTs) and flip-flops as compared to CSD and
conventional FCSD based FIR filter, in addition to enhanced
performance.
I. INTRODUCTION
Digital FIR filter is one of the essential components in
Digital Signal Processing (DSP) and communication
system. With an explosive growth in mobile
computing and multimedia applications, demand for low
power and high speed DSP system has seen a tremendous
growth [1]. Digital filters are used to modify the attributes of
signal by removing noise from the original signal and
shape the spectral characteristics of the resulting signal
[2]. Digital filters are very superior in level of performance as
they are highly stable, accurate and versatile as compared
to analog filter [3]. Moreover, Portable applications
require digital filter which operates at high data rate and low
power consumption as high power consumption reduces
battery lifetime, affecting device reliability and increasing
cool cost [4]. Due to this reason, the requirement of a digital
filter with optimized area, power and
delay is a challenging task.
DSP applications require a large order FIR filter. However,
the complexity increases with increase in filter order because of
requirements of larger mathematical computations [5].
Therefore, real time implementation of this filter with
precise value is posing as a serious challenge. In order to
achieve efficient digital filter, order of FIR filter must be as
small as possible. This paper focuses mainly on the FIR filter due to
its absolute stability and linear phase response [6]. On the
basis of hardware implementation, digital filter can be
classified into two categories: multipliers based and
memory based [7].
The main components of digital filter consist of registers to
save the samples of signals, adders to carry out sum operations
and multiplier for multiplication of the filter coefficients with
signal samples [8]. Despite the fact that designing of digital
filter seems simple, but the design bottleneck is its multiplier
block for speed, area and power consumption [9]. Complexity
is mainly dominated by coefficient multiplication operation
[10,11]. In order to reduce complexity, the filter
coefficients are represented in FCSD representation which
requires the least number of adders [12]. The filter can
be further optimized by using CSA and a barrel shifter
to achieve the operation of multiplication [13].
The rest of the paper is organized as follows: an overview of
FIR filter is given in section II. Section III consists of modules
for FIR filter. Section IV describes the proposed work for
filter optimization. In section V, simulation results
are discussed. Finally, section VI concludes the paper
by summarizing the main contributes.
Multipliers based design includes multiple constant
multiplication (MCM) with add and shift
operations.MCM based FIR filter uses
transposed structure which increases the speed of the
system.The area can be further saved by optimizing
coefficient with quantization technique. Memory based
design are divided into two approaches: distributed
arithmetic (DA) and Look Up table (LUT) method. The
DA based approach computes the inner product by
accumulating bit level partial results in the FIR
filter. The LUT based approach stores odd multiple
of input signal in ROM to realize constant
multiplications in MCM [7].
II. FIR FILTER
FIR filter is also known as non-recursive digital filters as they
don’t have feedback [6]. Output of the FIR filter can
be described by the following difference equation
FIR filters are digital filter with finite impulse response
which involves convolution operation given by equation [2]:
Y[n] = X[n]*H [n] (1)
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Int. Journal of Electrical & Electronics Engg. Vol. 2, Spl. Issue 1 (2015) e-ISSN: 1694-2310 | p-ISSN: 1694-2426

2. Fig.1. Transposed form of FIR filter
Digital filter can be designed by calculating the filter
coefficient on the basis of filter order, sampling frequency,
pass band and stop band frequencies etc.[5]. Generally, power
consumption and the amount of computation are directly
proportional to filter order. Filter coefficient can be found with
the MATLAB FDA tool. Further, the filter can be designed by
different method including window functions, frequency
sampling and equiripple method [9]. Table I lists the
parameters of the low pass FIR filter and the corresponding
magnitude response is shown in Fig. 2.
TABLE I. FIR Filter Design Parameter
Filter Parameter Value
Design method Equiripple
Order 8
Density factor 20
Sampling frequency FS = 48000 Hz
Passband frequency Fpass = 9600Hz
Stopband frequency Fstop = 12000Hz
Passband weight Wpass = 1
Stopband weight Wstop = 1
The calculated coefficients of the proposed FIR filter are [9,
16, 17, 32, 33, 32, 17, 16, 9]. Coefficients are symmetric in
nature which further reduces area and power consumption [5].
Order for FIR filter is N while the length of the filter is N+1
which is similar to the number of the filter coefficients [10].
As the filter order increases, complexity of the system
increases by consuming more amount of time for signal
processing.
Where N and Hk represents the length and coefficients of the
FIR filter respectively [10].Basically FIR filter consists of two
structures, i.e., direct form and transposed form. In direct
form, signal samples are multiplied by filter coefficients and
combined together in adder block [7]. A modification over
direct form is transposed structure as shown in fig 1. In
transposed form, the same input signal is multiplied by several
coefficients. In the present work, transposed form is used
which reduces area and delay as compared to direct form [6].
(2)
k
K knxHnY
N
)()(
0
1




Fig.2. Lowpass FIR filter magnitude response
Three modules are needed for implementation of optimized
FIR filter, i.e., delay, addition and multiplication. Barrel
shifter is used to provide shift operation and CSA is used to
carry out a sum operation. The modules used for
implementation are:
Barrel shifter is an integral component in several
computing devices which is mainly used for shifting and
rotating multiple bits in a single clock. It can be designed with
the help of combinational logic circuits such as logic gates,
multiplexers and decoders. However, the MUX based barrel
shifter provides less delay and power when compared to other
circuits [13]. Therefore, in the present work, BS is designed
using multiplexers architecture. Shifting a data word by a
specific amount of shift is performed in one clock cycle.
Sequences of multiplexers are used to implement the barrel
shifter and the output of one mux is connected to the input of
the next mux that depends on the shift distance [7]. The data
word can be shifted up to 8 bits either in left or right direction.
If the input pin is zero, then the observed output remains same,
i.e., without applying shifting operation. On the other hand,
Int. Journal of Electrical & Electronics Engg. Vol. 2, Spl. Issue 1 (2015) e-ISSN: 1694-2310 | p-ISSN: 1694-2426
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B. Barrel Shiifter
CSA is mainly used for fast arithmetic in a DSP system for
addition of three or more binary numbers. In CSA, there is no
propagation delay as compared to the ripple carry adder and
carry look ahead adder [4]. For sufficient large value of n, it
provides results very quickly and relatively occupies less area
in comparison to normal adders. CSA includes full adders but
the carry output is taken out from each bit to form second
result vector instead of passing it to the next most significant
bit [8]. It consists of three numbers (x, y, z) as the input which
is added together and provides sum (s) and carry (c) as an
output. Hence, this adder is called as 3:2 compressor, where
the operation is performed in one time unit duration. In carry
save operation, the carry is passed until last step whereas
ordinary addition is done in the last step only. When CSA is
implemented on FPGA, then two LUTs are required for
generation of carry and sum bit where as single LUT is
required for the carry propagation adder [11]. Fig.3 represents
CSA that consists of 17 half adders and 15 full adders.
A. Carry Save Adder
III. MODULES FOR FIR FILTER

3. Fig.3. Block diagram for 16-bit Carry Save Adder
C. Conventional FCSD
Factored Canonical Signed Digit representation is a slight
modification over CSD. It replaces multiplier operation with
add and shift operations on the basis of prime factors of the
coefficients [9]. A combination of effective factorization and
CSD representation of filter coefficient leads to a reduction in
the number of adders which further hardware cost. It provides
a relatively greater reduction in filter area, but at the cost of
decreased clock speed [9].Increase in delay is the major
drawback of this algorithm. The Factored CSD algorithm
provides a trade-off between calculated complexity and
convergence [12]. Following example compares CSD and
FCSD algorithm.
y = 217*x
= (11011001)*x % 217 in binary form
= (1001’001’1’1’) *x % 217 in signed digit
= (256- 32-4-2-1) * x
= (x << 8) –(x << 5) – (x << 2) – (x << 1) – x
Cost of CSD = 4 adders
y = 217*x
= (7*31)* x
= (x << 3– x) *(x << 5 – x)
Cost of FCSD = 2 adders
It is concluded that, the number of adders has been reduced by
using FCSD instead of CSD technique. Therefore, we have
used FCSD formulation for reducing filter complexity.
IV. PROPOSED WORK FOR OPTIMIZED FIR FILTER
FIR filter based on FCSD technique is proposed that use carry
save adder and barrel shifter for addition and shifting
operations. FCSD technique used for coefficient
V. SIMULATION RESULTS
This section presents the simulation results of the proposed
FIR filter. A Low pass FIR Filter is designed using equiripple
method in MATLAB FDA tool box for calculation of
coefficients. The filter can be designed in two structures, i.e.
direct form and transposed form. We have used transposed
form structure which reduces the implementation cost in terms
of area and delay. FIR filter architecture has been designed
and implemented on Xilinx Spartan3E XC3S500E using
VHDL. This results in realizing an FIR filter which can be
operated at maximum frequency of 238.322 MHz by
consuming 79 slices. The characteristics of proposed FPGA
based FIR filter are summarized in table II along with the
comparison of the proposed filter with CSD and FCSD
technique.
TABLE II: Performance Comparison between different approaches
Parameter CSD FCSD Proposed
work
No. of slices 808 789 79
No. of flip-flops 510 512 126
No. of 4 input
LUT’s
1349 1290 146
Frequency (MHz) 43.814 44.911 238.322
Min. Period (ns) 22.824 22.266 4.196
As shown in table II, Number of slices has been reduced
from 789 to 79 in FCSD technique by consuming 126
numbers of flipflops. Proposed FCSD based FIR filter
occupies 146 number of look up tables as compared to FCSD
technique. In comparison to FCSD, this result shows the
enhanced performance in terms of speed and area due to
efficient utilization of embedded multiplier and LUTs inside
the device. Fig. 4 compares the proposed FCSD technique
with CSD and FCSD method in the form of bar graph. The
proposed work offers very less number of slices, LUTs and
flipflops as compared to other two techniques generated by
MATLAB. Simulation results shows that proposed filter
consumes 89.98% less number of slices, 88.682% less number
of LUTs and 75.39 % less number of flipflops as compared to
FCSD technique to provide cost effective filter. Time delay of
if the input is non zero, then output is shifted in either
specified direction. After shifting operation, all the partial
products (PP) are added together to achieve multiplication
operation. Thus, Performance of FIR filter is improved by use
of barrel shifter in terms of area and delay [13].
representation reduces the area of the filter as compared to the
CSD technique, but with the disadvantage of increased delay.
This propagation delay can be improved by using CSA and a
barrel shifter. For multiplication of filter coefficients with the
input signal add and shift method is used. Therefore, the
multiplier consists of one adder unit (CSA) and one shifter
unit (barrel shifter). The filter is processed step by step in
which coefficients are first factored and subsequently
represented in CSD format. CSA is used, when the input
signal is multiplied with filter coefficients and added together
in the last step. Optimization of FIR Filter considering area
and delay constraints has been achieved using FCSD
representation, CSA and barrel shifter. These combinations of
FCSD technique with CSA and BS can target significant
reduction in circuit complexity, area and delay.
Int. Journal of Electrical & Electronics Engg. Vol. 2, Spl. Issue 1 (2015) e-ISSN: 1694-2310 | p-ISSN: 1694-2426
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4. the proposed filter has been improved considerably which in
turn increases the operational speed of the system. This
reduction in design complexity, area and delay of proposed
FCSD based filter can be viewed as a possible alternative for
circuit designer.
Fig.4. Bar graph representing CSD, FCSD and proposed work comparison
VI. CONCLUSION
The proposed FIR filter has been designed for 8 tap using
FCSD representation of filter coefficients. An optimized FIR
filter has been designed using barrel shifter and CSA in
VHDL which is further simulated on Xilinx Spartan3E based
XC3S500E target FPGA device. The results show that
optimized FCSD based FIR filter can be operated at a
maximum frequency of 238.322 MHz by consuming 79 slices,
126 flip-flops and 146 LUTs. Simulation results shows that
optimized filter occupies 89.98% less number of slices,
88.682% less number of LUTs and 75.39 % less number of
flipflops as compared to FCSD technique. Delay of the
optimized FIR filter has been reduced by 18.071 ns. It is
concluded that, use of FCSD representation in FIR filters
along with fastest adder and shifter can target significant
reduction in design complexity, area and delay when
compared to other approaches.
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0
400
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slices flip-flops LUT’s Frequency
(MHz)
CSD FCSD Proposed work
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