Disclosed techniques for improving computational efficiency can be applied to synthesis and analysis in digital signal processing. A base discrete-time Orthogonal Frequency Division Multiplexing (OFDM) signal is generated by performing at least one linear transform, including an inverse discrete Fourier transform (IDFT), on a first matrix of data symbols. A sparse data matrix is provided as an update to the first matrix of data symbols. The at least one linear transform is performed on the sparse data matrix to generate an update discrete-time OFDM signal. The update discrete-time OFDM signal and the base discrete-time OFDM signal are summed to produce an updated discrete-time OFDM signal.