Djordje Babic

Implementation of the transposed Farrow structure

The Farrow structure provides an efficient way to implement sampling rate increase between arbitrary sampling rates. However, in the case of sampling rate decrease the Farrow structure can only implement filters with poor anti-aliasing properties because the transfer zeros are clustered around the integer multiples of the input sampling rate and not around the multiples of the output sampling rate where aliasing components appear. This problem can be overcome by using the transposed Farrow structure with the transfer zeros clustered around the integer multiples of the output sampling rate. The aliasing components are attenuated using the same polynomial function as for the Farrow structure. The main difference is that this polynomial is determined using the output sampling period as the basic interval, instead of the input sampling period. This paper gives overview and compares two alternative implementation forms for the transposed Farrow structure.

Decimation by irrational factor using CIC filter and linear interpolation

This paper presents an efficient way to implement flexible multirate signal processing systems with high oversampling ratio and adjustable fractional or irrational sampling rate conversion ratio. One application area is a multi-standard communication receiver which should be adjustable for different symbol rates utilized in different systems. The proposed decimation filter consists of parallel CIC (cascaded integrator-comb) filters followed by a linear interpolation filter. The idea is to use two parallel CIC filters to calculate the two needed sample values for linear interpolation. These samples occur just before and after the final output sample. This corresponds to a system where the linear interpolation is done at the higher input sampling rate.

Power efficient structure for conversion between arbitrary sampling rates

This work presents a novel efficient method for conversion between arbitrary sampling rates. The method allows arbitrary number of zeros at multiples of both input and output sampling rates, thus it has both good anti-imaging and good anti-aliasing properties. Further, two equivalent efficient implementation structures are presented. The implementation is done either by using the modified Farrow or transposed modified Farrow structure. By choosing one of these two alternatives appropriately, it is possible to shift most of the operations to lower sampling rate.

Discrete-time modeling of polynomial-based interpolation filters in rational sampling rate conversion

If sampling rate conversion (SRC) is performed between arbitrary sampling rates, then the SRC factor can be a ratio of two very large integers or even an irrational number. An efficient way to reduce the implementation complexity of a SRC system in those cases is to use polynomial-based interpolation filters that mimic digitally the hybrid analogue/digital system. In practice, the sampling rate conversion is approximated with a rational factor. In this case, the hybrid analogue/digital model used to represent the SRC process may be represented by an equivalent discrete-time model. The discrete-time modeling of the rational SRC has been used earlier for the zeroth order interpolation. This paper extends this idea to arbitrary polynomial-based interpolation. Furthermore, this paper derives the relation between various polynomial-based interpolation filters (Farrow structure and its modifications) and polyphase FIR model filters. This paper observes possible applications of these relations, such as filter design, implementation complexity reduction, and response distortion analysis.

Reconstruction of non-uniformly sampled signal using transposed Farrow structure

The non-uniform sampling of the signal can be product of an intentional or unintentional process. For example jitter sampling is an unintentional process which is a consequence of time error of sampling circuits. In many DSP applications it is very important to reconstruct the signal from its non-uniformity distributed samples, especially to obtain a uniformly sampled sequence. This paper presents an efficient and accurate technique to obtain an uniform sequence from the non-uniform input. The reconstruction is done by using the transposed Farrow structure. The reconstruction can also be done in a decimating way, reducing the number of samples. The transposed Farrow structure can be designed to satisfy given frequency or time domain requirement according to the application at hand.

Decimation by non-integer factor in multistandard radio receivers

In many applications it is required to have a system for non-integer sampling rate conversion (SRC), which supports any decimation factor, and provides enough attenuation for aliasing and imaging signal components. A good example case is a software radio receiver, where the ratio of sampling rate just after A/D converter and symbol rate for a supported standard may be a ratio of two large mutually prime numbers. In a digital mobile receiver, it is very important to reduce the power consumption. The power consumption in context of SRC can be reduced by designing a system that has low rate of multiplication and addition operations.This paper introduces a novel non-integer decimation method. The proposed structure is a combination of an FIR filter and a polynomial-based interpolation filter. For the special case based on a cascaded integrator-comb (CIC) filter and simple polynomial-based interpolation filter, the proposed combination has a very efficient implementation structure. The results shown in this paper indicate that the computational complexity and multiplication rate can be reduced compared to the earlier solutions.

Polynomial-based filters with odd number of polynomial segments for interpolation

In many signal processing applications, it is beneficial to use polynomial-based interpolation filters. Actual implementations of these filters can be performed effectively by using the Farrow structure or its modifications. In the literature only polynomial-based filters having even number of polynomial pieces N have been considered. This letter presents a modification of the implementation form which allows realizing polynomial-based filters having an odd number of polynomial pieces. The condition that N must be even integer is not required any more. Further, a frequency-domain filter optimization method is developed, based on the methods for even-length filters. We illustrate through examples the performance of the odd-length polynomial-based filters.

Prolonged transposed polynomial-based filters for decimation

If sample rate conversion (SRC) is performed between arbitrary sample rates, then the SRC factor can be a ratio of two very large integers or even an irrational number. An efficient way to reduce the implementation complexity of a SRC system in those cases is to use polynomial-based interpolation filters. The impulse response of these filters is of a finite duration and piecewise polynomial so that it is expressible in each subinterval of the same length T by means of a polynomial of a low order. Here, T can be equal to, a multiple of, or a fraction of either the input or output sample period. The actual implementation of the polynomial-based filters can be performed directly in the digital domain effectively by using the Farrow structure or its modifications. This paper introduces for an arbitrary sampling rate reduction a novel implementation form referred to as the prolonged transposed modified Farrow structure. For this structure, T is an integer multiple of the output sampling period. Compared with the modified transposed Farrow structure, it has a narrowed pass-band region with almost the same complexity. In addition, a decimator structure consisting of a cascade of the prolonged transposed Farrow structure and a fixed linear-phase finite-impulse response decimator is introduced in order to reduce the overall computational complexity.

On impulse response symmetry of Farrow interpolators in rational sample rate conversion

In this paper, the impulse response symmetry of Farrow interpolation filters and its significance in rational sample rate conversion is addressed. Four methods for ensuring impulse response symmetry are proposed. Comparison of different symmetrization schemes is made, with filters optimized based on the discrete-time impulse response model. The results indicate that optimization based on the discrete-time model often results in better performance than optimization based on the continuous-time model, and that there are significant performance differences between symmetrization schemes.

Implementation of Farrow structure based interpolators with subfilters of odd length

Interpolation filters are used to interpolate new sample values at arbitrary points between existing discrete-time samples. An interesting class of such filters is polynomial-based interpolation filter. These filters can be efficiently implemented using the Farrow structure and its modifications. Traditionally, the polynomial based interpolation filters have been implemented by using Farrow structure with finite impulse response (FIR) subfilters of even length. This paper presents the modification of the Farrow structure, which can have FIR subfilters of odd length. Applying the proposed modification of this paper will result in a natural implementation form for even order Lagrange and spline based interpolators. The obtained results provides more freedom in designing Farrow structure based filters, as structures with odd and even length FIR subfilters may be equally applied. These results are extended to a modified Farrow structure case as well, in which the number of multipliers is nearly halved.