Summary: We obtain symmetric \(C^\infty\) real-valued tight wavelet frames in \(L_2(\mathbb{R})\) with compact support and the spectral frame approximation order. Furthermore, we present a family of symmetric compactly supported \(C^\infty\) orthonormal complex wavelets in \(L_2(\mathbb{R})\). A complete analysis of nonstationary tight wavelet frames and orthonormal wavelet bases in \(L_2(\mathbb{R})\) is given.