Tight Wavelet Frame Using Complex wavelet Designed in Free Shape on Frequency Domain

In this paper, we propose a construction method of a tight wavelet frame using a complex wavelet designed in a free shape on the frequency domain. This method is divided into two parts. First, based on the designed complex wavelet, we construct an approximate tight wavelet frame. Next, based on it, we construct a tight wavelet frame with minor modification. Additionally, for example, we show the construction process of the tight wavelet frame using the approximate Gabor wavelet.