DFT-based complex harmonic wavelet (CHW) is being used to directly compute frequency content with respect to time by employing discrete Fourier transform and inverse discrete Fourier transform. However, DFT coefficients suffer severe leakage of energy from one band to another band of frequency. To minimize the leakage between bands, a new basis function for harmonic wavelet transform using discrete cosine transform (DCTHWT) is proposed, which leads to a better representation of the time-frequency spectrum. The proposed DCTHWT bases are formulated by multiplying DCT-II matrix with a block diagonal matrix in which blocks are phase multiplied DCT-II matrices. The time-frequency analysis using the proposed DCTHWT is studied for different non-stationary input signals, and observed that leakages are minimized compared to the spectrogram, computed using DFT-based CHW. In addition to the aforesaid advantage, the proposed wavelet transform has features like admissibility, orthogonality, multiresolution and band-limited nature in the frequency domain. Further, the computational complexity of the proposed DCT-based harmonic wavelet transform is studied and observed that it has asymptotic gain of \(50 \%\) compared to CHW and \(33 \%\) compared to the modified CHW. Hence, the proposed DCT-based HWT is efficient in terms of computational complexity and have better time-frequency representation compared to DFT-based complex harmonic wavelet transform.

基于 DFT 的复谐波小波 (CHW) 通过采用离散傅里叶变换和离散傅里叶逆变换来直接计算相对于时间的频率成分。然而，DFT 系数会遭受从一个频带到另一频带的严重能量泄漏。为了最小化频带之间的泄漏，提出了一种使用离散余弦变换（DCTHWT）的谐波小波变换的新基函数，它可以更好地表示时频频谱。提出的 DCTHWT 基是通过将 DCT-II 矩阵与块对角矩阵相乘来制定的，其中块是相位相乘的 DCT-II 矩阵。针对不同的非平稳输入信号研究了使用所提出的 DCTHWT 的时频分析，并观察到与频谱图相比泄漏最小化，使用基于 DFT 的 CHW 计算。除了上述优点外，所提出的小波变换在频域还具有可接纳性、正交性、多分辨率和带限性等特点。此外，对所提出的基于 DCT 的谐波小波变换的计算复杂性进行了研究，并观察到它的渐近增益为\(50 \%\)与 CHW 相比，\(33 \%\)与修改后的 CHW 相比。因此，所提出的基于 DCT 的 HWT 在计算复杂度方面是有效的，并且与基于 DFT 的复谐波小波变换相比具有更好的时频表示。