Multirate Signal Processing
Iyappan Crazy
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Abstract
In single-rate systems, only one sampling rate is used throughout a digital signal processing system, whereas in multirate systems the sampling rate is changed at least once. This laboratory deals with the realization and analysis of multirate systems. In the first experiment we will examine the effects of decimation and interpolation. Next, a tree structure filter bank with quadrature mirror filters (QMFs) will be built and the quality of the reconstructed output signal will be discussed. Finally, we will analyze an example where the short-time Fourier transform (STFT) is used as a filter bank.
Key takeaways
- The output signal is at a lower sampling rate, and thus has a lower bandwidth (f s /2) than the input signal (f s /2).
- The resulting signal has a sampling rate f s = Lf s , and a spectrum that includes periodic images of the original signals spectrum.
- After m stages, a filter bank with 2 m outputs is built and the output signals are decimated by a factor of 2 m with respect to the input signal.
- In each stage of the synthesis filter bank the sampling rate of the signals has to be increased again.
- For H = 1 the bandpass output signals have the same sampling rate as the input signal.
Related papers
Review on Multirate Signal Processing
International Journal of Advance Research in Computer Science and Management Studies [IJARCSMS] ijarcsms.com, 2020
"Multirate" simply means "multiple sampling rates". A multirate DSP system simply uses more than one sampling rate within the system. In many systems, multirate DSP increases processing efficiency, which reduces DSP hardware requirements. During the last decade, however, they have increasingly found applications in new and emerging areas of signal processing, as well as in digital communications.
Multirate Systems and Applications
EURASIP Journal on Advances in Signal Processing, 2007
Filterbanks for the application of subband coding of speech were introduced in the 1970s. Since then, filterbanks and multirate systems have been studied extensively. There has been great success in applying multirate systems to many applications. Most notable of these applications include subband coding, signal analysis, and representation using wavelets, subband denoising, and so forth. Different applications also call for different filterbank designs and the topic of designing one-dimensional and multidimensional filterbanks for specific applications has been of great interest. Recently there has also been a lot of interest in applying multirate theories to the area of communication systems such as transmultiplexers, filterbank transceivers, and precoded systems. There are strikingly many dualities and similarities between multirate systems and multicarrier communication systems. Many problems in multicarrier transmission can be studied by extending results from multirate systems and filterbanks. This exciting research area is one that is of increasing importance. The aim of this special issue is to bring forward recent developments on filterbanks and the ever expanding area of applications of multirate systems. In this special issue, there are a total of 13 papers, which are roughly grouped into 3 categories.
Multirate Filters: An Overview
APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems, 2006
Multirate filtering techniques are widely used in both sampling rate conversion systems and in constructing filters with equal input and output rates in the case where the use of a conventional method becomes extremely costly. The purpose of this paper is twofold. First, this paper gives a short review on designing proper digital filters that are useful in providing the desired sampling-rate conversion between the output and input signals. Second, this paper shortly reviews on how to apply multirate technigies as well as complementary filters for constructing digital filters in cases where the implementation of a conventional filter becomes, due to a too huge arithmetic complexity and the effects of finite word length effect, so large that this filter is not possible to construct in practice. In the second case, when using both multirate filtering and complementary filters enable one to share the overall filtering task between several simplified low-order sub-filters that operate at the lowest possible sampling rates and have significantly relaxed design constraints. Due to these facts, the resulting filter has significant reductions in the overall complexity as well in finite word-length effects.
Multirate DSP and its technique to reduce the cost of the analog signal conditioning filters
International Journal of …, 2010
There are many reasons to change the sample rate of a sampled data signal. Here we discuss the two basic operations in a multirate system ie decreasing (decimation) and (increasing) the sampling rate of a signal. Also the use of multirate filters at the interfaces ...
The spectral theory of multirate filter banks
Time-Frequency and Time-Scale Analysis, IEEE-SP International Symposium, 1992
One of the open questions for multirate systems is the requirement for a nonexistence unified analytic technique that can be used to characterize any system. The problem can be solved by means of the spectral analysis technique presented by the authors. This unified characterization technique helps to simplify any investigation of multirate systems by providing an analytic technique. As a
Time-invariant and time-varying multirate filter banks : application to image coding
Annales Des Télécommunications
This paper reviews various concepts and solutions of time-invariant and time-varying multirate filter banks. It discusses their performance for image and video coding at low bit rates, and their applicability in the MPEo-4 framework. ~me-invariant multirate filter banks, and methods of design with different criteria appropriate for signal compression are first presented. Several procedures of quantization, namely scalar and lattice vector quantization, with bit allocation optimized in the rate-distortion sense, are used for the encoding of the subband signals. A technique of rate-constrained lattice vector quantization (Rc-LvQ), combined with a three components entropy coding, allow, together with distortion psychovisual weighting mechanisms to obtain significant visual improvements versus scalar quantization or the zerotree technique. However, time-invariant multirate filter banks, although efficient in terms of compression, are not well suited for content-based fimctionalities. Content-based features may require the ability to manipulate and thus encode a given region in the scene independently of the neighbouring regions, hence the use of transformations that can be adapted to arbitrary size bounded supports. Also, to increase the compression efficiency, one nuty want to adapt the transformation to the region characteristics, and thus use transform switching mechanisms, with soft or hard transitions. Three main classes of transformations can address these problems: shape-adaptive block transforms, transforms relying on signal extensions and transforms relying on time-vauing multirate filter banks. These various solutions, with their methods of design, are reviewed. Emphasis is put on an extension of the SDF (symmetric delay factorization) technique which opens new perspectives in the design of time-bounded and time-yawing .filter banks. A region-adapted rate-distortion quantization algorithm has been used in the evaluation of the transformations compression efficiency. The coding results illustrate the interest of these techniques for compression but also for features such as quali~, scalabilio' applied to selected regions of the image.
Theory of Multirate Signal Processing with Application to Signal and Image Reconstruction
2005
General single-channel, multirate optimal filtering problem. Note that the estimate and observation signals may be at different rates.. .. .. 4.4 An illustration of ordinary causal FIR Wiener filtering and the relationship between samples of sequencesd[n] and x[n], P = 3.. .. .. . 4.5 An illustration of single-channel, multirate causal FIR Wiener filtering and the relationship between samples of sequencesd[n] and x[m], P = 2.
Design and Implementation of Digital Filter Bank to Reduce Noise and Reconstruct the Input Signals
Signal & Image Processing : An International Journal, 2015
Digital Signal Processing
Lecture – 29 IIR Realizations This is the 29 th lecture on DSP and our topic today is IIR Realizations. In the previous lecture, we talked about the process of transposition and then FIR realization. We discussed the direct form structure, its transposed structure, the cascade structure and the parallel structure. The parallel is obtained by polyphase decomposition and parallel in FIR does not lead to a higher speed. Even if it is parallel processing, the speed cannot be increased but the realization can be made canonic by sharing delays. We took an example to illustrate this. Polyphase decomposition is not normally resorted to because it does not speed up processing, but it is very useful in multi rate signal processing where decimation and interpolation do reduce the computational complexity. Then we said that in the linear phase realizations, because of symmetry or anti-symmetry, the number of multipliers can be reduced approximately a factor of half, exactly half if the length is even or order length + 1 divided by 2 if the order is odd. Today we will discuss about IIR Realizations.
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Multirate Signal Processing: Some Useful Graphical Results
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Multirate signal processing is a phenomenon in which the sampling rate of the signal is changed in order to increase the efficiency of the various signal processing operations. Undersampling, reduces the sampling rate, whereas oversampling, followed by interpolation, increases the sampling rate. The ability to process signals at multiple sampling rates has made it possible to reduce the costs and improve performance. In this paper a basic overview of sampling is presented. Then different possibilities have been explored in terms of undersampling and oversampling. Graphical interpretations have led to some interesting results.
Multirate signal reconstruction and filter design via sampled-data
This paper studies the problem of digital signal reconstruction in the multirate framework. In contrast to the typical digital domain formulation in the current digital signal processing, we present a solution that optimizes an ¤ ¦ ¥ analog performance, via the modern sampled-data control. While the standard technique often indicates that an ideal digital low-pass filter is preferred, we show that the optimal solution need not be an ideal low-pass when the signal is not completely band-limited. The present method also suggests a new filter design method without recourse to analog filter designs. A design example is presented to show the advantages of the present method.
Design and implementation of linear-phase and/or pairwise-symmetric perfect-reconstruction FIR multirate filter banks
2005
This thesis studies the structures, design procedures and implementations of FIR perfect-reconstruction digital filter banks. The first part of the thesis deals with the structures and the design procedures of the perfect-reconstruction filter banks where the polyphase transfer matrices are lossless. These structures are parameterized by a set of rotation angles [37]. The usual procedure is to blindly optimize these angles to minimize an objective function where the objective function consists of all the stopband energies of the filters which we would like to design. This procedure is very time-consuming because of the nonlinear objective function and the large number of parameters to be optimized. The pairwise-symmetry property is imposed on these perfect reconstruction systems as a means of decreasing the number of parameters (rotation angles). The pairwise-symmetric property together with a method to initialize these rotation angles gives a very efficient design procedure. Design...
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ISRN Signal Processing, 2013
During the last two decades, there has been substantial progress in multirate digital filters and filter banks. This includes the design of quadrature mirror filters (QMF). A two-channel QMF bank is extensively used in many signal processing fields such as subband coding of speech signal, image processing, antenna systems, design of wavelet bases, and biomedical engineering and in digital audio industry. Therefore, new efficient design techniques are being proposed by several authors in this area. This paper presents an overview of analysis and design techniques of the two-channel QMF bank. Application in the area of subband coding and future research trends are also discussed.
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2000
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Configurable Multirate Filter Banks
American Journal of Applied Sciences, 2008
Multimedia communications require efficient and real-time implementations of multirate digital signal processing systems. The backbone structures of multirate systems are digital multirate filter banks. Therefore, efficient multimedia communications rely, in the first place, on real-time implementations of multirate filter banks. In this paper, we describe a Field Programmable Gate Array (FPGA) implementation of the analysis and synthesis filter banks which are the fundamental components of multirate systems. The implementation utilizes the parallel form of the distributed arithmetic technique which enables maximum exploitation of the parallelism inherent in the multirate filtering operation. Performance results demonstrate the effectiveness of the implementation and suggest that the FPGA platform is indeed attractive for implementing multirate filter banks..
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Review: Design of Highly Efficient Multirate Digital Filters
In this paper we propose the literature review related to design the multirate digital filters for audio application. One of the main objectives of this survey paper is to find the comparison between various multirate digital filters used in audio applications and communications. Another objective is to provide novel approach in order to help the reader with choosing the most appropriate digital filter for the multirate digital signal processing.
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