Wide-band time varying digital signals are extensively used by GSM, TV relays or radars. Analyzing those signals requires building a time frequency representation (TFR) in real-time. Most of TFRs are derived from the Wigner-Ville TFR; unfortunately they are computationally too intensive for real time processing. In this paper we propose an alternative approach to design an ASIC which computes a particular TFR of an input signal in real-time that we named F-TFR. Our approach is based on gradual signal channelizing using modulation, FIR filtering and time-interleaving of the channelized signals. After a brief introduction, we describe in detail the F-TFR algorithm. Then, we study the corresponding hardware architecture introducing signal interleaving and equations adaptations which are necessary for hardware implementation. Finally, we present some typical signals analysis by F-TFR along with an hardware prototype.