Frequency Convolution for Implementing Window Functions in Spectral Analysis
Windowing is a common method to reduce spectral leakage in Fourier analysis. Based on the principle that time domain multiplication corresponds to frequency domain convolution, this paper suggests frequency convolution to implement windowing functions by FIR filter structure. The proposed digital filter has full compatibility for variable length of window and is capable of implementing the three most popular windows, viz. Hanning, Hamming and Blackman. Numerical simulation indicates that the method consumes \(78\,\%\) less area, \(11\,\%\) higher throughput rate than the CORDIC-based (co-ordinate rotation digital computer) method, and achieves \(33\,\%\) lower quantization error for fixed point than the time domain multiplication method. Furthermore, an example of stretch processing in HF radar is shown to reduce the \(99\,\%\) computational complexity because of the segmental frequency points windowing.
KeywordsFourier analysis Spectral leakage Windowing Frequency domain convolution FIR filter
- 2.S. Aggarwal, K. Khare, Efficient window-architecture design using completely scaling-free CORDIC pipeline. in 2013 26th International Conference on VLSI Design and 2013 12th International Conference on Embedded Systems, pp. 60–65 (2013)Google Scholar
- 5.S.K. Mitra, Digital Signal Processing a Computer-based Approach, 2nd edn. (McGraw-Hill, New York, 2001)Google Scholar
- 9.J. Tan, B.Y. Wen, Y.W. Tian et al., Design and FPGA implementation of time-frequency transforming for stretch processing. IEICE Electron. Expr. 11, 1–6 (2013)Google Scholar
- 10.Xilinx: ’Xilinx logic core product specifications CORDIC v4.0 DS249’, (Xilinx 2011)Google Scholar