EFFICIENT DIGITAL FREQUENCY DOWN CONVERTER

STRUCTURE USING CIC FILTERS AND INTERPOLATED

FOURTH-ORDER POLYNOMIALS

Youngbeom Jang, Do-Han Kim

Sangmyung University, San 98-20, Anseo-dong, Cheonan-Si, Chungnam-Do, Korea

Won-Sang Lee

TamulMultimedia, Anyang Trade Center, Bisan-dong, Anyang-Si, Gyeonggi-Do, Korea

Keywords: DFDC, CIC, ISOP, IFOP.

Abstract: In this paper, we propose an efficient digital frequency down converter (DFDC) structure using CIC

(Cascaded Integrator-Comb) decimation filters and interpolated fourth-order polynomials (IFOP). Typical

DFDC with high decimation factors consist of a CIC filter and a halfband filter. By inserting the proposed

IFOP between the CIC and halfband filters, it is shown that passband droop and aliasing band attenuation

characteristics are simultaneously improved. Since the IFOP requires only three multiplications, the

proposed DFDC can be used in intermediate frequency blocks of the high-speed communication systems.

1 INTRODUCTION

Since DFDCs (Digital Frequency Down Converters)

with narrow bandwidth require high orders, power

consumption and implementation area should be

considered. To save on implementation cost,

conventional VLSI chips for DFDCs utilize CIC

filters followed by halfband filters and a

Programmable Finite Impulse Response (PFIR) filter.

For example, a DFDC chip with a 16384 decimation

ratio consists of CIC, halfband, and PFIR stages,

where the decimation factors of the CIC, halfband

and PFIR stages are 32, 32 and 16, respectively. CIC

filters are widely used in the first stage of the DFDC

since they do not require multiplications(Hogenauer,

1981). Studies to improve CIC filter characteristics

have been undertaken(Yang, 1996)(Gao, 1999). In

(Kwentus, 1997), a sharpening technique using a

combination of three filters(Kaiser, 1977) is applied

to a CIC filter. By using this method, the ripple in

the passband and attenuation in the aliasing band can

be mitigated, but the implementation cost is quite

high. In (Oh, 1999), ISOP(Interpolated Second

Order Polynomial) is inserted between CIC and

halfband filters. This method reduces the ripple in

the passband, but attenuation in the aliasing band is

worsened. In this paper, we propose an efficient

IFOP technique to reduce ripple in the passband and

attenuation in the aliasing band simultaneously.

2 PROPOSED METHOD USING

IFOP

The system function of the CIC filters, which do not

require multiplications, is expressed as

⎭

⎬

⎫

⎩

⎨

⎧

−

)(

(1)

where M, L, and R represent the decimation factor,

filter order, and differential delay, respectively.

When L is increased in equation (1), the stopband

attenuation is improved but passband ripple is

exacerbated, as shown in Fig. 1. In general, L should

be determined to satisfy the desired stopband

attenuation specification.

165

Jang Y., Kim D. and Lee W. (2007).

EFFICIENT DIGITAL FREQUENCY DOWN CONVERTER STRUCTURE USING CIC FILTERS AND INTERPOLATED FOURTH-ORDER POLYNOMI-

ALS.

In Proceedings of the Second International Conference on Signal Processing and Multimedia Applications, pages 161-164

DOI: 10.5220/0002135301610164

 SciTePress

(a)

(b)

Figure 1: Frequency response and aliasing band of CIC

filter (M=8, R=1, one halfband filter).

Figure 2: Zeros location of the proposed IFOP filter in z-

plane.

After the stopband attenuation specification is

satisfied, methods for dealing with the passband

ripple can be applied. In a DFDC using CIC filters,

halfband filters usually follow the CIC section, and

therefore aliasing bands are considered instead of a

stopband. When a halfband filter is used, the aliasing

band is determined, as shown in Fig. 1. When two

halfband filters are used, the aliasing band and

passband become narrower by half. To reduce ripple

in the passband and attenuation in the aliasing bands,

we propose the following IFOP

)(

zzpzpzp

IIII

++++

−−−−

(2)

In equation (2), the absolute value of the

denominator is for DC increase proportionally to 1,

and I is the interpolation factor. Excluding scaling

and interpolation factors, the basic equation is

represented as

1)(

−−−−

++++= zzpzpzpzP

(3)

To design an optimal IFOP filter, the above basic

equation is factored as

)1)(1(

)()()(

−−−−

++++=

zzqzzq

zQzQzP

(4)

As shown in Fig. 2, the IFOP filter is controlled

for two zeros to place on the real axis, and is used to

improve the passband ripple of the CIC filter. The

filter is determined for two zeros to place on the unit

circle, and used to improve aliasing band attenuation

of the CIC filter. The overall proposed DFDC

structure is shown in Fig. 3.

Figure 3: Overall proposed DFDC structure.

To examine the effect of the proposed IFOP, the

DFDC structure using one or two halfband filters

was investigated. Passband ripple and aliasing band

attenuation of the proposed DFDC with IFOP are

compared with three other structures which are ISOP

structure [4], CIC only structure[1], and Sharpened

structure[2], respectively. Results are summarized in

Table 1. As shown in Table 1, ripple in the passband

and attenuation in the aliasing band of the proposed

IFOP are improved simultaneously. In the case of

L=4, R=1, and one halfband filter, the passband

ripple and aliasing band attenuation of the CIC-only

structure are 3.593dB and 41.314dB, respectively.

And those of the ISOP structure are 0.416dB and

38.138dB, respectively, where it is shown that the

passband ripple is improved, but aliasing band

attenuation is worsened. However, those of the

proposed IFOP structure are improved to 0.308dB

and 62.256dB, representing better results than those

of the ISOP method. In a two-halfband case

simulation, Table 1 shows that the proposed

structure provides better performance. The proposed

structure shows better passband ripple and aliasing

band attenuation results. From the given

specifications, the proposed DFDC design procedure

can be summarized as

(1) CIC and halfband filters specification decision

1-1 M, R, L decision for CIC filter

1-2 Number and specification decision for halfband

filters

(2) CIC and halfband filters design

2-1 Observation of frequency responses

2-2 Target frequency decision of stopband or

aliasing band

(3) IFOP design

3-1 Value of I decision

3-2 Minimization of aliasing band attenuation

through adjusting the

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166

3-3 Minimization of passband ripple through

adjusting the

3-4 From the and

q ,

q IFOP decision

Table 1: Passband droop and aliasing attenuation of the

CIC-only, Sharpened, ISOP, and IFOP(one halfband:

1/(4M), two half band: 1/(8M)).

3 DESIGN EXAMPLES

3.1 Example 1

Using the proposed method, we demonstrate an

example of a DFDC design with a decimation factor

of 36. Overall specifications of the passband

frequency and ripple are 0.00525 and 0.2dB,

respectively. The specifications of the stopband

frequency and attenuation are 0.0105 and 70dB,

respectively. Since the decimation factor is 36, we

choose a factor of 18 for the CIC and a factor of 2

for the halfband filter to satisfy these specifications.

Desired parameters of the CIC filter are R=1, M=18

and L=5. The halfband filter used in this design

example is typical. The combined frequency

response of the CIC and halfband section is shown

in Fig. 4. As shown, the passband ripple and

stopband attenuation are 1.07dB and 55.42dB,

respectively. Since the weak points of the stopband

attenuation are

=0.02 and

=0.035, parameter I

of the IFOP is determined with 18. Adjusting value

of the

q , zeros of

)(

are placed in

=0.02

and

=0.035. We then adjust

q to minimize the

passband ripple. Overall improved passband ripple

and stopband attenuation are 0.1995dB and 74.71dB,

respectively, as shown in Fig. 4. From the obtained

and

, system function of the IFOP in this

example is expressed as

72543618

2053.04367.05374.04367.02053.0)(

−−−−

+−−−= zzzzzP

(5)

(a)

(b)

DFDCs

passband

ripple(dB)

stopband

attenuation(dB)

CIC+HBF 1.07 55.42

CIC+IFOP+HBF 0.1995 74.71

(c)

Figure 4: Frequency response improved by proposed IFOP

in the design example 1.

3.2 Example 2

The second example is a design for a DFDC with a

decimation factor of 10. Overall specifications of the

passband frequency and ripple are 0.01875 and

0.3dB, respectively. And the specifications of the

stopband frequency and attenuation are 0.0375 and

70dB, respectively. Since the decimation factor is 10,

we choose a factor of 10 for the CIC and a factor of

fc = 1/(4M) fc = 1/(8M)

passband

ripple

aliasing

attenuation

passband

ripple

aliasing

attenuation

L=4,

R=1

0.3081 62.2555 0.0234 102.09

L=4,

R=2

2.2805 56.7509 0.1682 94.416

L=6,

R=1

0.5417 82.9282 0.0316 136.85

Pro-

posed

IFOP

L=6,

R=2

6.3643 80.2976 0.339 128.61

L=4,

R=1

0.4162 38.138 0.04 67.04

L=4,

R=2

4.5393 42.26 0.2615 67.27

L=6,

R=1

0.752 57.334 0.0652 100.56

ISOP

L=6,

R=2

8.7786 65.361 0.555 101.07

L=4,

R=1

3.5926 41.314 0.8751 67.758

L=4,

R=2

15.634 53.355 3.5988 70.518

L=6,

R=1

5.3889 61.971 1.3127 101.63

CIC-

only

L=6,

R=2

23.450 80.033 5.3983 105.78

L=2,

R=1

0.84 32.33 0.062 58.40

Sharpen

L=4,

R=1

2.692 73.14 0.231 126.10

EFFICIENT DIGITAL FREQUENCY DOWN CONVERTER STRUCTURE USING CIC FILTERS AND

INTERPOLATED FOURTH-ORDER POLYNOMIALS

167

1 for the halfband filter to satisfy these

specifications. Chosen parameters of the CIC filter

are R=1, M=10 and L=5. The halfband filter used in

this design example is also the typical one as in the

previous example. The combined frequency

response of the CIC and halfband section is shown

in Fig. 5. Fig. 5 shows that the passband ripple and

stopband attenuation of the CIC and halfband filter

are 2.94dB and 57.86dB, respectively.

Since the weak points of the stopband attenuation

are

=0.075 and

=0.125, parameter I of the

IFOP is determined with 5. Adjusting the value of

the

q , zeros

)(

are placed in

=0.075 and

=0.125.

(a)

(b)

DFDCs

passband

ripple(dB)

stopband

attenuation(dB)

CIC + HBF 2.94 57.86

CIC+IFOP+HBF 0.289 71.27

(c)

Figure 5: Frequency response improved by proposed IFOP

in the design example 2.

We then adjust

q to minimize the passband ripple.

Overall improved passband ripple and stopband

attenuation are 0.289dB and 71.27dB, respectively,

as shown in Fig. 5. System function of the IFOP in

this example is expressed as:

2015105

4418.05571.07695.05571.04418.0)(

−−−−

+−−−= zzzzzP

(6)

4 CONCLUSIONS

We propose a DFDC structure that can improve the

passband ripple and aliasing band attenuation

simultaneously. By adjusting the zero position of the

two polynomials repeatedly, the overall frequency

response in the passband and aliasing band is

improved, and the coefficients of the IFOP can be

obtained. The implementation cost of the structure is

competitive. Since the proposed DFDC satisfies

linear phase characteristics and needs only three

more multiplications, it can be widely used in

IF(Intermediate Frequency) blocks of the high-speed

communication systems.

REFERENCES

Hogenauer, EB, 1981, ‘An economical class of digital

filters for decimation and interpolation’, IEEE Trans.

Acoust., Speech, Signal Processing, vol. ASSP-29, No.

2, April, pp. 155-162.

Kwentus, AY, Jiang, Z, Willson Jr., AN, 1997,

‘Application of filter sharpening to cascaded integer-

comb decimation filters’, IEEE Trans. Signal

Processing, vol. 45, Feb. pp. 457-467.

Kaiser, J, Hamming, R, 1977, ‘Sharpening the response of

a symmetric nonrecursive filter by multiple use of the

same filter’, IEEE Trans. Acoust., Speech, Signal

Processing, vol. ASSP-25, Oct. pp. 415-422.

Oh, HJ, Kim, S, Choi, G, Lee, YH, 1999, ‘On the use of

interpolated second-order polynomials for efficient

filter design in programmable downconversion’, IEEE

Journal on selected areas in communications, vol. 17,

April, pp. 551-560.

Yang, HK and Snelgrove, WM, 1996, ‘High speed

polyphase CIC decimation filters’, In International

Symposium on Circuits and Systems, Volume 2, pp.

229-232.

Gao, Y, Jia, L, Tenhunen, H, 1999, ‘An improved

architecture and implementation of cascaded

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ASIC / SOC Conference, pp. 391-395.

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