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 recently considered as an effective tool for transmitter and receiver side subband filtering of OFDM-based waveforms. However, for the original continuous FC-based model, the filtering can, in general, be configured in time-direction only with the granularity of half subframe, corresponding to 7, 14, or 28 symbols with 15 kHz, 30 kHz, or 60 kHz subcarrier spacing, respectively. In this paper, we present a symbol-synchronous FC-processing scheme flexibly allowing filter re-configuration with the time resolution equal to one OFDM symbol while supporting tight carrier-wise filtering for 5G NR in mixednumerology scenarios with adjustable subcarrier spacings, center frequencies, and subband bandwidths, as well as providing co-existence with LTE. Proposed approach segments each stream of time-domain OFDM symbols into overlapping processing blocks of fixed size. Symbol synchronous processing is achieved by dynamically adjusting the overlap between the processing blocks while aligning the payload part of the processing block with the boundaries of the OFDM symbols. The proposed scheme is demonstrated to support the envisioned use cases of 5G NR and provide a flexible starting point for sixth generation (6G) development.