Orthogonal frequency-division multiplexing (OFDM) has been selected as a baseline waveform for long-term evolution (LTE) and fifth-generation new radio (5G NR). Fast-convolution (FC)-based frequency-domain signal processing has been considered recently as an effective tool for spectrum enhancement of OFDM-based waveforms. FC-based filtering approximates linear convolution by effective fast Fourier transform (FFT)-based circular convolutions using partly overlapping processing blocks. In earlier work, we have shown that FC-based filtering is a very flexible and efficient tool for filtered-OFDM signal generation and receiver side subband filtering. In this paper, we present a symbol-synchronous FC-processing scheme flexibly allowing filter re-configuration time resolution equal to one OFDM symbol while supporting tight carrier-wise filtering for 5G NR in mixed-numerology scenarios with adjustable subcarrier spacings, center frequencies, and subband bandwidths as well as providing co-exitence with LTE. The proposed scheme is demonstrated to support envisioned use cases of 5G NR and provide flexible starting point for sixth generation development.