NOVEL SIGNAL SEPARATION PRINCIPLE BASED ON DFT WITH EXTENDED FRAME FOURIER-ANALYSIS

In general, a time-limited signal such as a single sinusoidal waveform framed by a frame period T can be utilized for conveying a multi-leve l symbol in data transmission. If such a signal is analyzed by the con ventional DFT (Discrete Fourier Transform) analysis, the infinite numb er of frequency components with frequency spacing f(D) = T-1 is needed . This limits the accuracy with which the original frequency of the un framed sinusoidal waverform can be identified. It is especially diffic ult to identify two similar framed sinusoids whose frequency spacing i s narrower than f(D). An analytical principle for time-limited signals is therefore proposed by introducing the concept of an Extended Frame into DFT. Waveform analysis more accurate than DFT is achieved by tak ing into account multiple correlations between extended frames made of an input frame signal and the element frequency components correspond ing to the length of each extended frame. In this approach, it is poss ible to use arbitrary element frequency spacing less than f(D). It als o allows an element frequency to be selected as a real number limes of f(D), rather than as an integer times of f(D) that is used for DFT. W ith this analyzing mechanism, it is verified that an input frame signa l with only the frequency components which coincide with any of the el ement frequencies can be exactly analyzed. The disturbance caused by t he input white noise is examined. As a result, it is found that the su perior noise suppression function is achieved by this method over a co nventional matched filter. In addition, the error caused by using a fi nite number of element frequencies and the A/D conversion accuracy req uired for sampling an input signal are examined, and it is shown that these factors need not impede practical implementation. For this reaso n, this principle is useful for multi-ary transmission systems, noise tolerant receivers, or systems requiring precise filtering of time lim ited waveforms.