Real-time Fourier transformation (RTFT) of signals is a fundamental concept, enabling to perform Fourier analysis at speeds beyond the limitations of conventional digital signal processing engines. In the optical domain, RTFT is commonly performed by inducing large amounts of group-velocity dispersion on the signal (time-varying light wave) of interest so that to map the signal's frequency spectrum along the time domain. However, the optical frequency resolution of this method is typically restricted above the GHz range, which represents a critical limitation for applications in real-time spectroscopy, ultrafast detection , imaging and sensing, and more especially, for photonic-assisted generation and processing of radio-frequency signals. Here we propose a new concept for realization of RTFT, which involves super-position of multiple signal replicas that are shifted simultaneously along the temporal and frequency domains, leading to an output temporal waveform that effectively maps the input optical spectrum. This configuration overcomes the frequency-resolution limitations of dispersion-based RTFT schemes, while providing the desired signal's spectrum with minimal latency, equal to the inverse of the frequency resolution. We experimentally demonstrate a practical implementation of the concept on optical signals using a frequency shifted feedback (FSF) laser, achieving a frequency resolution of ≃ 30 kHz and a time-bandwidth product exceeding 400, while the predicted linearity of the frequency-to-time mapping process is shown over a 20 GHz bandwidth. The introduced concept should be of general interest for high-speed, real-time Fourier analysis, beyond the optical-domain implementation reported here; moreover, this work also paves the way for novel applications of FSF lasers in several areas, including high-precision metrol-ogy and optical or RF waveform synthesis and processing.