Approximations of the inverse wavelet transform for analogue circuits

Abstract

We propose two approximations of the inverse wavelet transform implemented with a voltage adder and two analog filters. They work together with a set of scaled band-pass analog filters that perform the wavelet transform of a continuous time signal. With this approach an integrated circuit has been fabricated. On-chip measurements demonstrate signal to reconstruction error ratios up to 25.8 dB.

On‐chip wavelet denoising system implemented with analogue circuits

“…1 a . An exact reconstruction could be achieved if had a unitary gain (and zero phase) all along L , but the actual obtained gain of this summation is on L , for the selected [3]. Then we can expect an error of about 3.7% in the gain of the spectrum of the reconstructed output signal.…”

“…However, [2] shows the feasibility of implementing the WT of a continuous‐time signal with a set of frequency‐scaled analogue biaquadratic bandpass filters, where the set of outputs is the WT of the input signal. Moreover, an approximation of the IWT can be achieved if we add all these filter outputs, as shown in [3]. In this Letter we present an adaptation of the hard‐thresholding denoising method for analogue circuits.…”

“…Wavelet transform for analogue circuits: In [2] and [3] it is shown that the WT that is continuous in translation and discrete in scale is very suitable for analogue circuits. Such transform is sometimes called dyadic WT [4].…”

Design and fabrication of low loss and high suppression monolithic inverse wavelet transform processor

“…Generally, signal processing systems require the inverse wavelet transform processor (IWTP) has small size, low loss, high suppression and low cost in flaw detection, image processing, wireless communication and other fields. Many methods, such as analog circuits, digital circuits and surface acoustic wave (SAW) devices, have been proposed to implement the inverse wavelet transform (IWT) in hardware [1,2,3,4,5,6].…”