A Calculation Method of Optimal Exponential Power Polynomial Interpolation Filter Coefficients

Abstract

The invention relates to a calculation method of an optimal exponent power polynomial interpolation filter coefficient. The method comprises the following steps: determining normalization bandwidth of baseband signals and a normalization frequency spectrum scope of a first mirror image, determining a passband scope and a stopband scope of an image-rejection low pass filter, determining the number and order of exponent power polynomials and constructing optimization variables including coefficients of the exponent power polynomials based on this, defining one ideal low pass filter, calculating a weight approximation error, constructing constraint conditions, establishing a constraint optimization problem about the coefficients of the exponent power polynomials and calculating a coefficient of an optimal exponent power polynomial. The calculation method provided by the invention enables the fitted image-rejection low pass filter to reserve the advantages of having linear phases and not introducing sample crosstalk and also have a good stopband inhibition feature.

Description

technical field [0001] The invention relates to the technical field of digital signal processing, in particular to a method for calculating optimal exponential power polynomial interpolation filter coefficients. Background technique [0002] In a digital communication system, both the fractional digital up-down conversion function and the symbol synchronization function need to perform fractional delay sampling on the known sample sequence, that is, from a certain position between two adjacent known samples (by the fractional delay amount) decision) to collect a new sample. However, such samples do not exist in the known sample sequence, so interpolation is required to obtain such samples. [0003] From the perspective of signal processing, the interpolation operation is equivalent to figure 1 The hybrid digital-to-analog / analog-to-digital conversion process shown: first, the original continuous signal is reconstructed according to the known sample sequence; then, the reco...

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Problems solved by technology

However, the de-imaging low-pass filter fitted with Lagrangian polynomials has a poor ability to suppress broadband image components

like Figure 4 As shown, the anti-image low-pass filter fitted by four 3rd-order Lagrangian polynomials can only suppress the image component of the normalized bandwidth around f=0.8 to the level of -35dB; as Figure 5 As shown, the de-imaging filter fitted by six 5th-order Lagrange polynomials can only suppress the image component with a normalized bandwidth around f=0.8 to a level of -45dB

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