Abstract
This paper outlines the development of a multiple-clock-cycle implementation (MCI) of a signal adaptive two-dimensional (2D) system for space/spatial-frequency (S/SF) signal analysis. The design is based on a method for improved S/SF representation of the analyzed 2D signals, also proposed here. The proposed MCI design optimizes critical design performances related to hardware complexity, making it a suitable system for real time implementation on an integrated chip. Additionally, the design allows the implemented system to take a variable number of clock cycles (CLKs) (the only necessary ones regarding desirable—2D Wigner distribution-presentation of autoterms) in different frequency-frequency points during the execution. This ability represents a major advantage of the proposed design which helps to optimize the time required for execution and produce an improved, cross-terms-free S/SF signal representation. The design has been verified by a field-programmable gate array (FPGA) circuit design, capable of performing S/SF analysis of 2D signals in real time.
Highlights
The short-time Fourier transform (STFT), its energetic version-spectrogram (SPEC), and the Wigner distribution (WD) are the conventional mathematical tools commonly used in nonstationary signal analysis, [1,2,3,4,5, 8,9,10, 20]
The proposed method will be compared, regarding the calculation complexity, with the conventional S/SF distributions (S/SFDs) (2D SPEC and 2D WD) and calculation, (3) Proposed method with the 2D STFT calculation based on the FFT routines, (4) Proposed method using the recursive
The proposed method significantly improves calculation complexity of the 2D SM and 2D WD, note that it is quite numerically intensive, Table 2
Summary
Systems used in nonstationary 1D and 2D signals processing are based on the developed mathematical methods (distributions), defined in their 1D, [1,2,3,4,5,6,7], and 2D, [8,9,10,11,12,13,14,15,16,17,18,19], forms, respectively. The reduced interference method proposed in [5], named the S-method (SM), extended to the 2D form in [12] and frequently used, [26,27,28], reduces cross-terms with preservation of the WD autoterms It is defined in a computationally simple way that requires calculation of the 1D convolution in the 1D signals case, [5], and the 2D convolution in the 2D signal case, [12]. The proposed hardware design allows the implemented system to take a variable number of CLKs in different frequency-frequency points within the execution and, to produce a pure cross-terms-free S/SF signal representation that retains the desirable autoterms presentation of the 2D WD In this way, the design optimizes the execution time, overcoming the main drawback of the MCI designs in comparison to the parallel ones.
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