Multiplicative Finite Impulse Response Research Articles

Reconfigurable filter bank structures for low complexity digital channelizer using fractional interpolation and MFIR filters with cosine modulation

A low complexity digital reconfigurable filter bank structure which is suitable for digital channelizers in software defined radio is proposed in this paper. In order to get a sharp transition width with low hardware complexity, multiplicative finite impulse response (MFIR) filter is used as the prototype filter in the proposed structure. A masking stage and a channel generation stage constitute the two stages of the proposed structure. In the masking stage, 5 sub-bands are generated by performing cosine modulation technique on the prototype filter. In the channel generation stage, different channels are generated by doing spectral addition/subtraction operations on the interpolated versions of the MFIR filter. Hence, the basic techniques used in the proposed structure are, cosine modulation and fractional interpolation technique. By adjusting a 3-bit control signal, different regions and channels, generated by the two stages, can be obtained. The proposed structure has a hardware complexity, which is much lesser than that of the state-of-the art techniques used for SDR channelizers. The number of channels generated using the proposed structure is also more. The main advantage of the proposed structure is that the hardware complexity of the proposed structure remains the same even if the number of channels is increased.

Multiplicative finite impulse response filters: implementations and applications using field programmable gate arrays

This paper describes how modern field programmable gate array (FPGA) technology can be used to build practical and efficient multiplicative finite impulse response (MFIR) filters with low-pass, high-pass, band-pass and band-stop characteristics. This paper explains how MFIR structures can be built with or without linear phase characteristics and implemented efficiently on modern FPGA architectures using fixed-point arithmetic without incurring stability problems or limit cycles which commonly occur when using equivalent infinite impulse response structures. These properties have a particular importance for applications such as tunable resonators, narrow band rejectors and linear phase filters which have demanding, narrow transition band requirements. The results presented in this paper indicate that MFIR filters are, for some applications, a viable alternative to existing filter structures when implemented on an FPGA.

Round-Off Noise of Multiplicative FIR Filters Implemented on an FPGA Platform

The paper analyzes the effects of round-off noise on Multiplicative Finite Impulse Response (MFIR) filters used to approximate the behavior of pole filters. General expressions to calculate the signal to round-off noise ratio of a cascade structure of Finite Impulse Response (FIR) filters are obtained and applied on the special case of MFIR filters. The analysis is based on fixed-point implementations, which are most common in digital signal processing algorithms implemented in Field-Programmable Gate-Array (FPGA) technology. Three well known scaling methods, i.e., L2 bound; infinity bound and absolute bound scaling are considered and compared. The paper shows that the ordering of the MFIR stages, in combination with the scaling methods, have an important impact on the round-off noise. An optimal ordering of the stages for a chosen scaling method can improve the round-off noise performance by 20 dB.

On the coefficient quantization of Multiplicative FIR filters

This paper analyzes the effects of coefficient quantization of Multiplicative Finite Impulse Response (MFIR) filters used to approximate the behavior of pole filters. Statistical analysis, zero displacement sensitivity and frequency domain analysis are used as measures of the filter performance for different coefficient lengths. A practical expression for determining the required number of bits for the coefficient quantization as a function of a predefined maximum deviation in the magnitude response is proposed in combination with an alternative method based on a time domain analysis. The time domain analysis allows, for a specific pole approximation, to investigate the sensitivity of the MFIR structure to coefficient variations. The paper concludes that, statistically, the MFIR pole approximation filter does not require a larger number of quantization bits for its coefficients than the corresponding Infinite Impulse Response (IIR) filter.

2-D generalized MFIR filters

An efficient structure for 2-D linear phase FIR (finite-impulse response) filters is introduced. The structure is the 2-D counterpart of the 1-D MFIR (multiplicative FIR) filters. It is shown that this structure is capable of satisfying tight specifications with a significantly reduced number of coefficients. The performance improves for tighter specifications with centered transition bands. The filter coefficients are obtained by minimizing an l/sub p/ error function. It is shown that the optimization problem is readily broken up into a set of simpler subproblems. For the special case of p=2, these subproblems reduce to simple matrix inversions. Increasing the filter order does not affect the problem complexity since it only requires an increase in the number of matrix inversions needed. Examples illustrating the capabilities of this structure and comparisons with other approaches are given. >