The fast time frequency transform (F.T.F.T.): A novel on-line approach to the instantaneous spectrum

This paper describes a concept for fast on-line transformation of signals into the combined time-frequency domain. Assuming a limited number of narrow-band signal components equidistantly spaced on the frequency axis, the number of computations required is minimized and an optimal time and frequency resolution is accomplished at the same time. Typically, for a postulated N-number of components, N being a power of 2, instantaneous amplitudes and frequencies are presented at each Nth input sample. From the fluctuations of the frequency over time, a measure for instantaneous bandwidth is derived that can be interpreted as the reciprocal of instantaneous signal-to-noise ratio. Instantaneous output of the FTFT may allow improved recognition of short transient patterns in noisy signals such as the Electro-Encephalo-Gram (EEG) and optimized feature coding and data compression compared to techniques, that average over a period of time. Using integer arithmetic and a high level programming language, the throughput rate on a single 20 MHz microprocessor is better than 1.5 KHz.