The Basic Concept Of Cic Filter Accounting Essay

This paper presents a design and execution of CIC based decimation filter for WCDMA Applications. This construction consists three phases. The comb decimation filter at the first phase operates at the input trying rate and nothing rotated sharpened 2nd phase operates at lower trying rate as compared to first subdivision lesser than M1 decimation factor and compensation subdivision is operates at lesser than M decimation factor. This multistage construction reduces the sampling rate at every phase of the CIC decimation filter. The sharpened 2nd phase produces the wider passband sag and better halt set alias rejection. This wider passband sag will be compensated with the aid of compensation subdivision. This filter construction is designed with MATLAB Simulink environment and implemented with aid of Virtex-V XC5VLX110T-3ff1136. Device use and simulation consequences are generated and tabulated. The developed construction improves the passband sag and stopband aliasing rejection.


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CIC Filter, Filter sharpening, Zero rotary motion, Decimator, Compensation filter, MATLAB Simulink, Xilinx Virtex-V


WiMAX is a wireless information communicating engineering based around the IEEE 802.16 criterion supplying high velocity informations over a broad country. The WiMAX stands for World Wide Interoperability for Microwave Access and it is a engineering for point to multipoint radio networking. WiMAX engineering expected to run into the demands of a big assortment of users from those in developed states desiring to put in a new high velocity informations web really stingily without the cost and clip required to put in a broad web, to those in rural countries necessitating fast entree where wired solutions may non be feasible because of distance and cost involved. Additionally it is being used for nomadic applications, supplying high velocity informations to users on the move. In this paper we are planing the decimation filter for WiMAX criterion as per the specification mentioned in the tabular array 1. The trying rate decrease is required in WiMAX is 8, which is realized with multi phase realisation techniques which improves the passband and stopband fading efficaciously and reduces the complexness, device use and power ingestion as compared to individual phase realisation.

Table 1: WCDMA Specifications and Filter Design Parameters

Frequency scope ( GHz )

Deciliter: 2.11 – 2.17

UL: 1.92 – 1.98A

Channel Spacing ( MHz )


Data Rate

8.34 M chips/sec



Input trying frequence Fs ( MHz )


Pass set Edge ( MHz )


Stop set Edge ( MHz )


Pass set rippling ( dubnium )

A 0.5

Stop set fading ( dubnium )


The design and execution of different decimation filter construction of CIC ( Cascaded-integrator comb ) filter with assorted techniques has been reported in the past few decennaries by many research workers [ 1-13 ] . In 1981, Eugene Hogenauer [ 1 ] proposed a category of digital filter for insertion and decimation the advantages compared to other type of filters is it requires no multipliers and usage limited storage hereby taking to more economical hardware executions. They are designated as cascaded integrator-comb ( CIC ) filter, because construction consists of an equal figure of planimeter subdivision runing at the high sampling rate and a comb subdivision runing at the low sampling rate. J. F. Kaiser and R.W. Hamming [ 2 ] describes the filter sharpening technique based on the thought of amplitude alteration map ( ACF ) which is restricted to symmetric non-recursive ( FIR ) filters with piecewise changeless passband and stopband.

A. Kwentus [ 3 ] designed and implemented a programmable CIC multirate decimation filter construction with filter sharpening techniques to better the filters passband response. This allows the first phase CIC decimation filter to be followed by a fixed-coefficient second-stage filter instead than a programmable filter thereby accomplishing a important hardware decrease over bing attacks. A low power fifth order decimation comb filter with programmable decimation ratio ( 16 and 8 ) and trying rate ( 128 MHz and 44.8 GHz ) for GSM and DECT application have been proposed by Y.Gao et al [ 4 ] . The low power ingestion is achieved by following attacks. First the non-recursive architecture for comb filter is employed, 2nd unneeded calculations eliminated with multiphase execution of each phase and 3rd each polyphase constituents implemented with data-broadcast construction.

Several strategies have been proposed by G. J. Dolecek and S.K.Mitra [ 5-7 ] to plan CIC filters with improved magnitude response. The writers proposed a different construction that consists of a comb subdivision and a sharpening comb subdivision with the latter subdivision runing at a lower rate than the high input rate for the realisation of comb-decimation filter with a sharpened magnitude response. Using sharpening with zero rotary motion to the decimation filter in the last phase provides really good consequences, salvaging in figure of operations comparing to the instance of sharpening of complete filter. M.Laddomada, [ 8 & A ; 9 ] has presented the mathematical model to optimise the decimation filters by presenting a category of sharpened modified comb filter aimed at increasing the rejection of quantisation noise around the folding set and cut downing the passband sags of the decimation filters.

The model for zero rotary motion in the multistage CIC filter construction has been proposed by Marko Nikolic and MiroslavLutovac [ 12 ] . It was reported that the sharpening in the last phase of decimation filter enhances the public presentation and salvaging in figure of operations comparing to the instance of sharpening of complete filter. Shahana T.K et Al [ 13 ] designed multistandard architecture as a solution for the hereafter radio transceivers to achieve higher system capacities and informations rates. An efficient reconfigurable execution is a cardinal to accomplish low power ingestion. They designed a double manner RNS ( Residue Number System ) based decimation filter which can be programmed for WCDMA and WiMAX applications. Area utilised is increased by 24 % to include WiMAX compared to Single Mode WCDMA Standards. Ioan lie et Al [ 14 ] presented a synthesis and execution of digital decimating filter for an Ultrasonic beam former, which uses delta sigma modulators to get the standard supersonic signals. This design is implemented by a FPGA engineering ( Altera 10K series ) and the simulation consequences are analyzed.

Ze Tao and Svante Signell [ 15 ] presented a delta sigma ADCs comprise the modulator and decimating filter for multistandard radio applications viz. . GSM, WCDMA, 802.11a, 802.11b, 802.11g and WiMAX. Shahana T.K et Al [ 12 ] , proposed a GUI based design tool for multistandard decimation filter for 6 wireless communicating criterions, dwelling of GSM, WCDMA, 802.11a, 802.11b, 802.11g and WiMAX. The decimation is done in two or three phases to cut down the complexness and power dissipation. The chief thought of this paper is to plan and implement the multistage CIC decimation filter construction for WiMAX application by decimation factor 8, with the advantages presented earlier to obtain the construction which can run at a lower sampling rate to accomplish better public presentations than the original comb filter based construction.


Cascaded planimeter comb [ 1 ] or Hogenauer filter, are multirate filters used for recognizing big sample rate alterations in digital systems. CIC filters are multiplierless constructions, dwelling of lone adders and hold elements which is a great advantage when taking at low power ingestion. So the CIC filters are often used in digital down convertor and digital up convertors.

The CIC filter is a category of hardware efficient additive stage FIR digital filter consists of an equal figure of phases of ideal planimeter and comb filter brace. The extremely symmetric construction of this filter allows efficient execution in hardware. However the disadvantage of a CIC filter is that is passband is non level, which is unwanted in many applications. This job can be overcome through the usage of compensation filter. CIC filter achieve trying rate lessening ( decimation ) without utilizing generation. The CIC filter foremost performs the averaging operation so follows it with the decimation.

2.1 CIC filter for sample rate Conversion

The CIC filters are utilized in multirate systems for building digital up convertor and down convertor. The ability of comb filter to execute filtrating without generation is really attractive to be applied to high rate signals ; furthermore CIC filters are convenient for big transition factor, since the low base on balls bandwidth is really little. In multistage decimators with big transition factor, the comb filter is the best solution for first decimation phase, whereas in insertion, the comb filter is convenient for the last phase.

2.2 CIC filter for decimation

The basic construct of CIC filter is given in Figure 1 ( a ) , which consists of factor of M down sampler and K-stage CIC filter. Using 3rd individuality, the factor of M down sampling station is moved and placed behind the planimeter subdivision and before the comb subdivision as shown in Figure 1 ( B ) . Finally the CIC decimator is implemented as a cascade of K planimeter, factor of M down sampling station and the cascade of K discriminator subdivisions. The planimeter part operates at the input informations rate, whereas the comb part operates at M clip ‘s lower sampling rate.

( a ) Cascade of CIC Filter and Down Sampler

( B ) Cascade of Integrator Section, Down Sampler and Comb Section

( degree Celsius ) Implementation Structure of Single Stage CIC Filter

( vitamin D ) Implementation Structure of CIC Filter with K Stages

Figure 1: Block Diagram representation of CIC Filter

The transportation map of the CIC filter in z-domain is given as [ 1 ] .

( 1 )

Where, M is the decimation factor

In equation ( 1 ) the numerator ( 1-z-M ) represents the transportation map of comb subdivision and the denominator 1/ ( 1-z-1 ) indicates the transportation map of planimeter subdivision.

Figure 1 ( degree Celsius ) shows the first order CIC filter ; here the clock splitter circuit divides the oversampling clock signal by the oversampling ratio M after the planimeter phase. The planimeter operates at the input trying frequence, while the discriminator operates at down sampled clock frequence degree Fahrenheit /M. By runing discriminator at the lower sampling rate the power ingestion is reduced.

A magnitude feature of the comb filter is improved by cascading [ 3 ] several indistinguishable comb filters which is shown in Figure 1 ( vitamin D ) . The transportation map of multistage comb filter composed of indistinguishable individual phase comb filter is given by,

( 2 )

Figure 2: Response of CIC filter with different K values

Figure 2 shows the frequence response of CIC filter for different phases, while increasing the K values passband sag lessenings and stopband fading additions.


The construction proposed in this paper is shown in figure 4 which consists of two phases, the first phase H1L ( omega ) is responsible for stopband assumed name rejection and the 2nd phase { 3 [ H1 ( zM1 ) ] 2K – 2 [ H1 ( zM1 ) ] 3K } is responsible for passband sag public presentation. By using nothings rotary motion with sharpening technique in the 2nd phase is expected to better the stopband assumed name rejection compared to bing CIC filter constructions. However it is expected to cut down the passband sag. This decrease can be minimized by cascading the sine compensator as a last phase.

Filter sharpening [ 2 ] is the technique to better the passband sag and stopband fading utilizing multiple realisation of a low order BASIC filter holding the signifier.

( 3 )

where, Hp ( degree Fahrenheit ) is a low order basic filter, N and m are non-negative whole numbers represent the figure of non-zero derived functions of Hnm ( degree Fahrenheit ) at points Hnm ( degree Fahrenheit ) = 0 and Hnm ( degree Fahrenheit ) = 1 severally.

The Kaiser-Hamming sharpening technique applied to linear-phase FIR filters with group hold of D samples has the transportation map of H11 ( omega ) , for n=1 ; m=1 can be written as

( 4 )

The term [ 3z-D – 2 Hp ( omega ) ] is responsible for passband sag decrease and Hp ( omega ) is responsible for stopband rejection.

Generalized comb filter ( GCF ) with rotated zero [ 8, 9 & A ; 12 ] has better distribution of nothings than multistage sharpened CIC filter in the stopband fading in the aliasing set. The 3rd order generalized comb filter ( GCF3 ) [ 12 ] can be obtained from 3rd order CIC filter by revolving the nothing both sides with the angle. This can be denoted as GCF3 of ( M, I± ) as modified comb filter of the 3rd order used for decimation with factor M.

The transportation map of GCF3 ( M, I± ) can be represented by,

( 5 )


( 6 )

( 7 )

From equation ( 14 ) and ( 15 ) the zero rotary motion map can be written in

( 8 )

Where, I± is rotary motion angle,

is a filter quality parametric quantity and,

is the highest frequence of the input signal [ 8 ]

The generalised transportation map of two phase CIC filter can be written as

( 9 )

Decimation factor M=M1 * M2

The transportation map of two phase sharpened CIC filter can be written as

( 10 )

Using zero rotary motion in the 2nd phase of modified sharpened subdivision of the filter, which distributes the nothings in the sharpened subdivision. This improves the stopband alias rejection but somewhat cut down the passband sag. This passband sag can be improved by presenting the sine compensator as 3rd phases. The block diagram of the CIC filter with compensator is shown in figure 4.

The input of the 2nd phase is obtained from the decimated end product of the first phase. This is expected to cut down the computational complexness by M1 times. Then the sharpened zero rotary motion is applied to the 2nd phase along with decimation factor M2. The revolved and decimated end product obtained from the 2nd phase is given to the compensator to better the passband sag.

By and large sine compensation is found to be one of the methods to better the passband public presentation of the filter. See the filter with transportation map given [ 6 ] .

( 11 )

Here, A = ; B =

The compensation filter parametric quantity ‘b ‘ depends on the value of K, non on the decimation factor M. For the given value of B and K, the value of decimation factors non expected to impact the worst instance alias rejection.

The transportation map of the nothing rotated CIC filter with compensator can be written as,

( 12 )

The developed CIC filter with compensator is realized and shown in figure 4. The first phase is comb decimator with decimation factor M1 which can be realized in either recursive or non-recursive strategy. As a consequence 2nd phase ( sharpened zero rotated ) is moved to a lower rate which is M1 times lower than the input rate. The compensation filter plays an of import function for compensation of the passband sag introduced by the 2nd phase.

Figure 3: Modified Sharpened CIC Filter Structure

Figure 4: Proposed CIC Filter Structure


The recent promotion in the VLSI engineering peculiarly in FPGA as made possible, the realisation of advanced Digital Signal Processing algorithm in high frequence sphere. With this development a individual bit solution is possible for complex DSP based applications like, ADC, Decimation and Interpolation in the communicating system.

A digital execution twosome with signal processing algorithms greatly enhances the system public presentation, reduces the cost and increase the dependability of the system. Low power DSP systems are implemented by altering the trying clock for each subsystem depending on the existent demands. The sampling rate alteration consequences in aliasing ; this necessitates the usage of filters to get the better of it. So in this subdivision we discuss the execution of sharpened CIC filter construction.

The initial theoretical account was designed and tested in Simulink. Simulink is a package bundle from Mathworks for mold, imitating the dynamic systems. This Simulink theoretical account is used as the mention theoretical account for synthesis of the design in FPGA. To aim the faculty for FPGA, we choose to utilize Xilinx System Generator, which provide a Simulink blockset that is so converted to VHDL for synthesis and execution. This VHDL coevals flow is shown in figure 5. The figure 7, 8 and 9 shows the theoretical account of the Basic CIC, Modified CIC and Proposed CIC Filter Implementation Structures severally.

Each filter construction is designed in MATLAB Simulink environment utilizing FDA Tool and tested the Decimation filter architecture with different input signal. The same will be implemented utilizing Xilinx tool boxes, the VHDL codification and Testbench for the designed Simulink theoretical account was generated utilizing System Generator HDL Coder. This method is efficient and it takes less clip to prove and implement a design as compared to the undertaking of composing HDL Code for single constituent.

Figure 5: FPGA Synthesis Flow

Figure 6: Realization of CIC Filter Structure with K=1

Figure 7: Realization of Modified Sharpened CIC Filter Structure with K=1and L=2

Figure 8: Realization of Proposed CIC Filter Structure with K=1and L=2


The CIC filter with sharpening, zero rotary motion and compensation is developed and the frequence response for the decimation factor M = 16 with different phases are obtained. Assorted parametric quantities considered for analysis is given in table 1.

The magnitude response for the decimation filter with and without compensator have been computed and shown in figure 9 for M=16 with K=2 and L=4. Figure 9 ( a ) shows the overall magnitude response of CIC filter with and without compensator for M1 = 4 and M2 = 4. It is clear from the figure that passband sag is improved and the stopband alias rejection is reduced compared to the constructions reported earlier. The expanded part of the passband sag and stopband assumed names rejection is shown in figure 9 ( B ) and 9 ( degree Celsius ) severally for clear apprehension. Figure 10, 11 and 12 shows the basic CIC filter, modified sharpened CIC filter and the proposed CIC filter construction simulated end product wave forms.

( a ) Overall magnitude responses

( B ) Passband rapid climbs

( degree Celsius ) Detailed position of the magnitude response around the first nothing

Figure 9: Magnitude responses plots for M=8, M1=2, M2=4 with K=1 and L=2

Figure 10: Output wave form of Proposed CIC Filter Structure with K=1and L=2 utilizing Wave range

Figure 11: Output wave form of Proposed CIC Filter Structure with K=1and L=2 utilizing Scope

Figure 12: Output wave form of Proposed CIC Filter Structure with K=1and L=2 utilizing Scope

Table 2 shows the device use sum-up, passband, stopband public presentation of basic CIC, modified CIC and Proposed CIC construction. Compared to basic CIC and modified CIC filter construction, proposed CIC filter with and without compensator but the proposed construction gives 47 % betterment in passband sag public presentation and 8 % betterment in stopband fading.


The proposed CIC filter construction with and without compensator was designed and implemented with aid of FPGA kit Virtex-V and simulation consequences are graphed and tabulated for a decimation factor of 16. The rating shows that betterment in the passband sag and stopband fading public presentation of the designed CIC filter as compared to bing filter constructions. The execution consequence shows the device use sum-up of the designed filter construction. This decimation filter is best suited for WCDMA and DSP related application. The same filter construction with decimation factor 8 is suited for WiMAX decimation filtering.

Table -2 Overall Comparison of Proposed CIC Performance with bing

















to the full






in Watts



( dubnium )



( dubnium )

CIC [ 1 ]









Modified Sharpened CIC [ 5 ]












Proposed CIC without Compensator












Proposed CIC with Compensator












Passband Droop and Stopband Improvement in Percentage

47 %

8 %


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