Novel Signal Separation Principle Based on DFT with Extended Frame Fourier Analysis

Noriyoshi KUROYANAGI  Lili GUO  Naoki SUEHIRO  

IEICE TRANSACTIONS on Communications   Vol.E79-B   No.2   pp.182-190
Publication Date: 1996/02/25
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Communication Theory
frequency analysis,  sinusoid estimation,  matched filter,  cross-correlation analysis,  

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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-level symbol in data transmission. If such a signal is analyzed by the conventional DFT (Discrete Fourier Transform) analysis, the infinite number of frequency components with frequency spacing fD = T1 is needed. This limits the accuracy with which the original frequency of the unframed sinusoidal waverform can be identified. It is especially difficult to identify two similar framed sinusoids whose frequency spacing is narrower than fD. 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 taking into account multiple correlations between extended frames made of an input frame signal and the element frequency components corresponding to the length of each extended frame. In this approach, it is possible to use arbitrary element frequency spacing less than fD. It also allows an element frequency to be selected as a real number times of fD, rather than as an integer times of fD that is used for DFT. With this analyzing mechanism, it is verified that an input frame signal with only the frequency components which coincide with any of the element frequencies can be exactly analyzed. The disturbance caused by the input white noise is examined. As a result, it is found that the superior noise suppression function is achieved by this method over a conventional matched filter. In addition, the error caused by using a finite number of element frequencies and the A/D conversion accuracy required for sampling an input signal are examined, and it is shown that these factors need not impede practical implementation. For this reason, this principle is useful for multi-ary transmission systems, noise tolerant receivers, or systems requiring precise filtering of time limited waveforms.