Pushkar Patwardhan

Eigenfilter Approach to the Design of One-Dimensional and Multidimensional Two-Channel Linear-Phase FIR Perfect Reconstruction Filter Banks

We present an eigenfilter-based approach for the design of two-channel linear-phase FIR perfect-reconstruction (PR) filter banks. This approach can be used to design 1-D two-channel filter banks, as well as multidimensional nonseparable two-channel filter banks. Our method consists of first designing the low-pass analysis filter. Given the low-pass analysis filter, the PR conditions can be expressed as a set of linear constraints on the complementary-synthesis low-pass filter. We design the complementary-synthesis filter by using the eigenfilter design method with linear constraints. We show that, by an appropriate choice of the length of the filters, we can ensure the existence of a solution to the constrained eigenfilter design problem for the complementary-synthesis filter. Thus, our approach gives an eigenfilter-based method of designing the complementary filter, given a ldquopredesignedrdquo analysis filter, with the filter lengths satisfying certain conditions. We present several design examples to demonstrate the effectiveness of the method.

Time-frequency localization optimized biorthogonal wavelets

The time-frequency product of any function in L2 (R) is bounded by the uncertainty principle. This paper presents a method to design linear phase biorthogonal wavelets with the time-frequency localization as the optimality criterion, improving on the previous designs on the same theme. The design philosophy is to optimize the time-frequency product of the wavelet, after fixing the number of vanishing moments of the analysis and synthesis lowpass filters of the corresponding filter bank. The regularity of the discrete filters has also been evaluated.

Effect of voice quality on frequency-warped modeling of vowel spectra

The perceptual accuracy of an all-pole representation of the spectral envelope of voiced sounds may be enhanced by the use of frequency-scale warping prior to LP modeling. For the representation of harmonic amplitudes in the sinusoidal coding of voiced sounds, the effectiveness of frequency warping was shown to depend on the underlying signal spectral shape as determined by phoneme quality. In this paper, the previous work is extended to the other important dimension of spectral shape variation, namely voice quality. The influence of voice quality attributes on the perceived modeling error in frequency-warped LP modeling of the spectral envelope is investigated through subjective and objective measures applied to synthetic and natural steady sounds. Experimental results are presented that demonstrate the feasibility and advantage of adapting the warping function to the signal spectral envelope in the context of a sinusoidal speech coding scheme.

Polyphase Conditions and Structures for 2-D Quincunx FIR Filter Banks Having Quadrantal or Diagonal Symmetries

In this brief, we derive conditions on the polyphase matrix of 2-D finite-impulse response (FIR) quincunx filter banks, for the filters in the filter bank to have quadrantal or diagonal symmetry. These conditions provide a framework for synthesizing polyphase structures which structurally enforce the symmetry. This is demonstrated by constructing examples of small parameterized matrix structures which satisfy the above conditions, thus giving perfect reconstruction FIR quincunx filter banks with quadrantal or diagonally symmetric short-kernel (i.e., short-support) filters. It is also shown that cascades of the above constructed small structures can be used to construct filters of higher order.

Preservation of 2-D Signal Symmetries in Quincunx Filter-Banks

An important problem in the analysis of symmetric extension methods is to determine the conditions under which signal symmetries are preserved by the filtering (convolution) and downsampling operations. In this letter, we provide a complete characterization of four-fold two-dimensional signal symmetries viz. quadrantal symmetry, diagonal symmetry, and 90deg rotational symmetry. We then consider Quincunx filter-banks and determine the conditions under which the four-fold signal symmetries are preserved by the filtering and downsampling operations

A class of time-frequency product optimized biorthogonal wavelet filter banks

The time-frequency product of any function in L2 (R) is bounded by the uncertainty principle. This paper presents a method to design linear phase biorthogonal filter banks with the time-frequency localization as the optimality criterion. The design philosophy is to optimize the time-frequency product of the iterated wavelet, after fixing the number of vanishing moments of the analysis and synthesis lowpass filters, by adjusting a single parameter.

Tree structures and algorithms for hybrid transforms

Zerotree based image coding techniques use a standard multiresolution representation of images obtained by a repeated 2-band Discrete Wavelet Transform of images. A lot more modularity and flexibility can be achieved by use of hybrid transforms of images. In this paper we explore the advantages, issues and tree structures for hybrid transforms of images. A few new algorithms for embedded image coding using hybrid transforms have been drafted. The results, interpretations and scenarios where hybrid transforms might find better application than existing methods have been discussed.

Design of 2-D

In this letter, we extend the eigenfllter filter design method for the design of two-dimensional Mth band lowpass filters, with the filter impulse response having quadrantal or diagonal symmetry. We show that imposing the Mth band and symmetry constraints puts restrictions on the possible choices of the matrix M. We identify sufficient conditions on M, and show a class of matrices satisfying those conditions, so that Mth band lowpass filters with quadrantal or diagonal symmetry can be designed.

M

Filter bank optimization for coding gain maximization for given input statistics has been well studied before. Principal Component Filter Banks (PCFB) have proven to be optimal whenever the minimization objective is a concave function of the subband variances produced by the filter bank. However PCFBs are known to exist for only three special classes of orthonormal filter banks(FBs): Any class of two channel FBs, the transform coder class and the unconstrained order subband coder class. This paper explores the design of FIR Paraunitary(PU) FBs for special case of uniform 3-band subband coder class, giving a detailed analysis of the design method. This method directly maximizes the coding gain. Results have been compared to the PCFB approximation algorithm by Peter Vouras and Trac D. Tran which uses complete parameterization of FIR PU FBs in terms of Givens rotation building blocks.

th Band Lowpass FIR Eigenfilters With Symmetries

In one-dimensional (1-D) filter-banks (FBs), symmetries (or anti-symmetries) in the filter impulse-responses (which implies linear-phase filters) are required for symmetric signal extension schemes for finite-extent signals. In two-dimensional (2-D) separable FBs, essentially, 1-D processing is done independently along each dimension. When 2-D nonseparable FBs are considered, the 2-D filters (2-D signals in general) can have a much larger variety of symmetries (anti-symmetries) than the 1-D case. Some examples of 2-D symmetries possible are quadrantal, diagonal, centro, 4-fold rotational, etc. In this letter, we analyze the filter symmetries in a subclass of tree-structured 2-D nonseparable FBs, whose sampling matrices can be factored as a product of Quincunx sampling matrix and a diagonal matrix. Within this subclass, we distinguish between two types and show that we can have diagonally symmetric filters in Type-I FBs and quadrantally symmetric filters in Type-II FBs. We then discuss how these FBs with quadrantally and diagonally symmetric filters can be used with a symmetric signal extension scheme on finite-extent signals