In this paper, a multi-encoding approach using wavelet based subband coding is proposed to accomplish error free calculations from exact representation of Daubechies 4-tap wavelet filter coefficients using the algebraic integer (AI) representation. By mapping the irrational coefficients to a convenient AI basis, the proposed architecture is designed employing a parallel channel model having two data paths carrying integer sequences. The computations done in the AI architecture are exactly accurate and are done entirely in a multiplier-free circuit. The design is implemented on a Xilinx Virtex-6 device at 172 MHz and hardware co-simulated with an ML605 board at 100 MHz. AI mapping facilitates simplicity and error-free calculations. The proposed architecture has a single final reconstruction step (FRS). Booth encoding has been adopted at the FRS to minimize the error which can be incurred at this point. This paper provides a hardware and power analysis for different bit lengths. An example output image sequence for the mandrill image is also provided.

This paper describes a novel method for the computation of the Discrete Fourier Transform (DFT). The development of a truly centered DFT is coupled with a method for computing the Centered DFT to provide an FFT that requires no complex multiplications and which allows a highly parallel implementation.

This paper concerns linear prediction of the value of a bandpass signal containing one or more passbands from a finite set of its past samples. The method of choosing prediction coefficients involves the eigenvector corresponding to the smallest eigenvalue of a matrix dependent on a function which is the Fourier transform of the set of intervals making up the passband. The method is developed for a set of arbitrary past samples and applied here to a set of "interlaced" samples that are nonuniform but periodic. The method applies to finite energy signals as well as to bandpass signals of polynomial growth, which connects to the theory of generalized functions. Computational examples are given of prediction coefficient values and of signal predictions.

Formulas for linear prediction of a band-limited signal are developed, where the signal may be either deterministic or wide-sense stationary. The prediction formulas are based on finite differences modified by two or more parameters, and finite differences allow the formulas to be easily adapted to changes in order of the prediction. It is shown that a formula to predict the next signal value from a set of past, equally spaced values is a formula that can be extended to provide prediction at points even beyond that. In addition, the formula is extended to a difference scheme involving an arbitrary number of parameters as well as to a formula that includes samples of the derivative of the signal. This approach differs from that of solving the normal (or Yule-Walker) equations, but it has the advantage that the (suboptimal) prediction coefficients are independent of the particular signal spectrum or autocorrelation function.>

Some formulas for the prediction of the values of a band-limited function based on its samples from the past are generalized by including past samples of its first derivative. The new sums, developed by an approach based on Newton series, make it possible to double the distance between the sample points. The resulting formulas are shown to apply to the prediction problem for a large class of entire functions of exponential type. In addition, a related prediction formula which uses past samples of successively higher derivatives is shown to behave similarly to the Taylor series approximation, again for a class of functions that includes the band-limited functions.