Efficient rational sampling rate alteration using IIR filters

2000 ◽  
Vol 7 (1) ◽  
pp. 6-7 ◽  
Author(s):  
A.I. Russell
Keyword(s):  
Sampling Rate ◽  
Iir Filters ◽  
Rational Sampling

Filters in Multirate Systems

2009 ◽  
pp. 64-102
Author(s):  
Ljiljana Milic
Keyword(s):  
Digital Filter ◽  
High Performance ◽  
Spectral Characteristics ◽  
Sampling Rate ◽  
Signal Distortion ◽  
Iir Filters ◽  
Sampling Rate Conversion ◽  
Low Complexity Implementation ◽  
Rate Conversion

The role of filtering in sampling-rate conversion has been considered in Chapter II. The importance of filtering arises from the fact that the sampling theorem should be respected for all the sampling rates of the system at hand. Filters are required to bandlimit the spectrum of the signal to the prescribed bandwidth in accordance with the actual sampling rate. In sampling rate conversion systems, filters are used in decimation to suppress aliasing and in interpolation to remove imaging. Since an ideal frequency response cannot be achieved, the performance of the system for sampling rate conversion is mainly determined by filter characteristics. Obviously, an appropriate filter should enable the sampling rate conversion with minimal signal distortion. The main advantage of a multirate system is the computational efficiency, and therefore, a decimator (interpolator) that implements a high-order digital filter could not be tolerated. The specific role of a digital filter in sampling rate conversion demands high-performance filtering with the lowest possible complexity. To reach this goal one has to concentrate first on the choice of the appropriate design specifications in order to provide minimal signal distortion. Secondly, the multirate filter is to be designed in a manner to satisfy the prescribed characteristics and to provide a low-complexity implementation structure. In this chapter, we discus first the spectral characteristics of decimators and interpolators and introduce three commonly used types of filter specifications. In the sequel, we review the MATLAB functions that are appropriate for the design of FIR and IIR filters to satisfy the specifications. An approach to computation of aliasing characteristics of decimators is given and illustrated by examples. This chapter considers also the analysis of sampling rate conversion for band-pass signals. Chapter concludes with MATLAB exercises for individual study.

Spatial-Temporal Non-Uniform Subband Broadband Beamforming

2010 ◽  
Vol 108-111 ◽  
pp. 1223-1228
Author(s):  
Long Yang Huang ◽  
Jun Luo ◽  
Wei Jun Pan
Keyword(s):  
Delay Line ◽  
Filter Banks ◽  
Sampling Rate ◽  
Infinite Impulse Response ◽  
Iir Filters ◽  
Broadband Beamforming ◽  
Broadband Signal ◽  
General Parameter ◽  
Aperture Array ◽  
Processing Architecture

A spatial-temporal scheme based on non-uniform subband general parameter filter banks for broadband beamforming of scaled aperture array is proposed in this paper. The scaled aperture array is composed of several uniformly-spaced linear subarrays, each of which processes an octave subband signal respectively. The non-uniform subband signal is implemented by tree-structure general parameter filter banks. Each subarray broadband beamforming is carried out by a kind of tapped-delay-line (TDL) infinite-impulse-response (IIR) filters beamformer, and four subarrays share the same weights. This processing architecture based beamformer splits the broadband signal into several narrower subband ones which are processed in parallel, and subarray is operating with lower sampling rate, which contributes to decreasing the computational load significantly and improving the speed and performances as well. Simulations show that computation complexity and load of this beamformer are much lower relative to the conventional TDL broadband beamfomer.

Lth-Band Digital Filters

2009 ◽  
pp. 206-241
Author(s):  
Ljiljana Milic
Keyword(s):  
Transfer Function ◽  
Digital Filters ◽  
Intersymbol Interference ◽  
Transfer Functions ◽  
Sampling Rate ◽  
Angular Frequency ◽  
Efficient Implementation ◽  
Fir Filters ◽  
Linear Phase ◽  
Iir Filters

Digital Lth-band FIR and IIR filters are the special classes of digital filters, which are of particular interest both in single-rate and multirate signal processing. The common characteristic of Lth-band lowpass filters is that the 6 dB (or 3 dB) cutoff angular frequency is located at p/L, and the transition band is approximately symmetric around this frequency. In time domain, the impulse response of an Lth-band digital filter has zero valued samples at the multiples of L samples counted away from the central sample to the right and left directions. Actually, an Lth-band filter has the zero crossings at the regular distance of L samples thus satisfying the so-called zero intersymbol interference property. Sometimes the Lthband filters are called the Nyquist filters. The important benefit in applying Lth band FIR and IIR filters is the efficient implementation, particularly in the case L = 2 when every second coefficient in the transfer function is zero valued. Due to the zero intersymbol interference property, the Lth-band filters are very important for digital communication transmission systems. Another application is the construction of Hilbert transformers, which are used to generate the analytical signals. The Lth-band filters are also used as prototypes in constructing critically sampled multichannel filter banks. They are very popular in the sampling rate alteration systems as well, where they are used as decimation and interpolation filters in single-stage and multistage systems. This chapter starts with the linear-phase Lth-band FIR filters. We introduce the main definitions and present by means of examples the efficient polyphase implementation of the Lth-band FIR filters. We discuss the properties of the separable (factorizable) linear-phase FIR filter transfer function, and construct the minimum-phase and the maximum-phase FIR transfer functions. In sequel, we present the design and efficient implementation of the halfband FIR filters (L = 2). The class of IIR Lth-band and halfband filters is presented next. Particular attention is addressed to the design and implementation of IIR halfband filters. Chapter concludes with several MATLAB exercises for self study.

Design and Implementation of Multirate Digital Filters

2002 ◽  
pp. 257-292 ◽  
Author(s):  
Hakan Johansson ◽  
Lars Wanhammar
Keyword(s):  
Power Consumption ◽  
Digital Filters ◽  
Sampling Rate ◽  
Design Flow ◽  
Low Power Consumption ◽  
Iir Filters ◽  
Lattice Wave ◽  
Wave Digital Filters ◽  
Filter Structures ◽  
Algorithm Level

In this chapter we discuss techniques to design and implement multirate digital filters with low power consumption which also allow a reduction in the design effort, since the resulting circuits are highly modular and regular and can relatively easily be incorporated in the normal design flow of commercial tools. First we briefly review techniques that can be applied at various design levels, i.e., from algorithm level down to layout, to reduce the power consumption in CMOS implementations of both digital FIR and IIR filters and are useful in many other DSP algorithms. Second, we discuss the properties of lattice wave digital filters and various techniques to design efficient multirate digital filters for changing the sampling rate by a factor of two. Third, we discuss the design of multistage multirate digital FIR filter structures for arbitrary bandwidths. Finally, we provide some design examples.

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