1.  Field of the Invention
The present invention relates generally to a decimation filtering apparatus and method, and more particularly to a decimation filtering apparatus and method using interpolated second order polynomials (ISOPs). 
2.  Description of the Related Art
With the development of wideband analog-to-digital conversion (ADC) technology and fast digital signal processing (DSP) technology, it has become possible to perform sampling and digital signal processing at an Intermediate Frequency (IF) band as well as at baseband.  The term "software radio system", as used herein, refers to a system which starts the digital signal processing at the IF or Radio Frequency (RF) levels. 
A software radio system can effectively support multi-band, multi-mode and multi-function communications by virtue of the programmability of the digital signal processing software.  For example, a base station of an AMPS (Advanced Mobile Phone Service) mobile communication system, having a structure illustrated in FIG.  1, provides 30 KHz channels to respective users, and employs RF and IF stage receivers for the respective channels.  As shown in FIG.  2, a software radio system can perform a channel separating operation by using one wideband RF stage, one wideband ADC and N digital filters (where N is the number of the channels). 
When such a software radio technique is applied to both a communication terminal (mobile station) and the base station in a mobile communication system, it is possible to accommodate the entire national and regional standards and provide a roaming service between different service areas.  This software radio concept may be widely applied to the base stations and communication terminals of future mobile communication systems such as a PCS (Personal Communication System) and IMT-2000 (International Mobile Telecommunication) systems. 
A software radio system should include a decimation filter, a rate converter, a fast multiplier and a trigonometrical function generator.  A baseband stage of a software radio receiver should isolate a signal of interest, which is usually a very narrowband signal, from a wideband input signal.  To this end, it is important to effectively design a fast decimation filter. 
At present, known digital downconverters for a digital interface include model GC4014 manufactured by Gray Corporation, and models HSP50016 and HSP50214 manufactured by the Harris Corporation.  A digital downconverter is also disclosed in a paper by Alan Y. Kwentus, Zhognong Jiang, and Alan N. Willson, Jr., "Application of Filter Sharpening to Cascaded Integrator-Comb Decimation Filters", IEEE Trans.  Signal Processing, vol.  45, pp.  457-467, February 1997. 
Among the above devices, model HSP50214 may be an improvement over models GC4014 and HSP50016.  The device HSP50214 (hereafter referred to interchangeably as the '214 device or first prior art) has a three-stage structure of a Cascaded Integrator-Comb (CIC) filter, a halfband filter and a programmable Finite Impulse Response (FIR) filter.  In the '214 device, the CIC filter is an Recursive Running Sum (RRS) filter used for decimation, which is relatively simple to implement.  The halfband filter is a power-of-two decimating filter and half of the filter coefficients are "0", making it relatively simple to implement the hardware.  That is, the '214 device primarily performs decimation by using the CIC filter, and then performs decimation at multiples of 2 using the halfband filter.  In addition, the programmable FIR filter is used for compensating for a droop in the passband caused by the CIC filter. 
Another prior art method (hereafter referred to interchangeably as the Willson method or second prior art) proposed in the paper by Willson Jr. uses a frequency response sharpening technique of Kaiser Hamming.  The sharpening filter can remove the programmable FIR filter at the final stage in '214 device by decreasing attenuation of the passband in use.  That is, the Willson method employs a two-stage structure of a sharpening filter and a halfband filter.  When a CIC transfer function is H(z), a transfer function of the sharpening filter becomes H.sup.2 (z)(3-2H(z)). 
A downconverter of the '214 device is composed of a CIC filter, a halfband filter and a programmable FIR filter.  The CIC filter employed performs 4-to-32 decimation; the halfband filter performs 1-to-5 decimation; and the programmable FIR filter performs 1-to-16 decimation, so that the overall filter may perform 4-to-16384 decimation.  However, since the halfband filter and the programmable FIR filter perform operations using one adder and one multiplier, an increase in the filtering operations may undesirably restrict the bandwidth of the signal for decimation.  Moreover, since the passband droop of the CIC filter depends upon the programmable FIR filter at the final stage, the programmable FIR filter may be relatively complicated in structure. 
In addition, the downconverter realized in accordance with the Willson method minimizes passband attenuation by applying the frequency response sharpening technique of Kaiser Hamming to the CIC filter, so as to remove the programmable FIR filter.  However, for certain applications, the downconverter should still use a programmable FIR filter at the final stage for the overall device to perform satisfactorily.  Furthermore, since the sharpening filter has the transfer function of H.sup.2 (z)(3-2H(z)), the downconverter may be as complicated as for the case in which three CIC filters are used. 
The above-described prior art devices use a CIC filter with an RRS structure, which is most generally used in decimation applications and is generally simple to implement; but, the use of the CIC filter may cause the droop in the passband.  To compensate for the droop, the '214 device uses only the programmable FIR filter at the final stage.  As a result, the FIR filter may need a large number of taps, which makes it difficult to implement the filter.  Moreover, the Willson device includes several CIC filters, as can be appreciated from the transfer function of the sharpening filter.  Thus, it appears to be difficult to implement the Willson device.  Further, for application to various systems, the Willson device also requires the programmable FIR filter at the final stage.