Digital signal processing techniques and methods are widely used in modern computers and communication systems. The basic idea is to express signals with a series of numbers, and then perform various fast mathematical operations on these digital signals. The purpose is diverse, some are for encryption, and some are for removing noise and other irrelevant information, called filtering; sometimes some types of digital signal processing operations are transformed into transforms, such as discrete Fourier transform (DFT), Wavelet transform (Wavelet T), etc. VerilogHDL is currently the most widely used hardware description language for the design of digital electronic systems. It can be used for logic design at various levels, and for simulation verification, timing analysis, and logic synthesis of digital logic systems. The design of the wavelet filter belongs to the circuit design of a complex algorithm. Therefore, it is an ideal method to use Veril-ogHDL to model and simulate the biorthogonal wavelet filter and realize the automatic design of the circuit.
1 Design of wavelet filter
For the wavelet function, it is required to have orthogonality, compact support, symmetry and smoothness. Orthogonality can make the transformation non-redundant; compact support brings excellent spatial resolution; symmetry ensures that the phase of its corresponding filter is linear; smoothness can produce less distortion. In this way, the discrete binary wavelet transform is greatly restricted. For this reason, a biorthogonal wavelet transform is proposed. The wavelet filter designed in this paper is a kind of dual-channel complete reconstruction filter based on the biorthogonal wavelet transform, so the signal can be decomposed to achieve accurate reconstruction, so it has a good effect on the signal filtering. Because it has the characteristics of forward transform binary up-sampling sampling and inverse transform binary down-sampling sampling, the biorthogonal wavelet filter can be designed as a dual-channel fully reconstructed filter with a polyphase structure when performing filter design. Biorthogonal wavelet transform can be regarded as the result of filtering the original signal through a series of high and low pass filters and sampling, and the reconstruction process is the opposite. In order for the transformed signal to be completely reconstructed, Y (n) = x-kX (n) must be satisfied, where k = 1. The process of decomposition and reconstruction of the biorthogonal wavelet filter is shown in Figure 1.
Let G (z) and H (z) be the decomposition low-pass and high-pass filters, respectively. H (z) filtering after downsampling is equivalent to filtering with H (z2) first and then downsampling, so:
Among them: Ge and Go are the even and odd terms of G (z), He and H, respectively. These are the even and odd terms of H (z), respectively. According to equation (1), equation (2) can establish a multi-phase structure model of the biorthogonal wavelet filter as shown in FIG. 2.
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