An embedding approach to frequency-domain and subband adaptive filtering

• Published in: IEEE transactions on signal processing Vol. 48; no. 9; pp. 2607 - 2619
• Main Authors: Merched, R., Sayed, A.H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2000; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive filters; Adaptive structures; Applied sciences; Arithmetic; Blocking; Computational efficiency; Convergence; Derivation; Detection, estimation, filtering, equalization, prediction; Discrete cosine transforms; Discrete transforms; Echo cancellers; Exact sciences and technology; Frequency domain analysis; Information, signal and communications theory; MDF; Signal and communications theory; Signal processing; Signal processing algorithms; Signal, noise; Telecommunications and information theory; Transforms; Subband decomposition; Time domain method; Circulant matrix; Discrete Fourier transformation; Discrete transformation; Adaptive filtering; Signal processing; Toeplitz matrix; Cosine transform; Hartley transformation
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/78.863066

Frequency-domain and subband implementations improve the computational efficiency and the convergence rate of adaptive schemes. The well-known multidelay adaptive filter (MDF) belongs to this class of block adaptive structures and is a DFT-based algorithm. We develop adaptive structures that are based on the trigonometric transforms, discrete cosine transform (DCT) and discrete sine transform (DST), and on the discrete Hartley transform (DHT). As a result, these structures involve only real arithmetic and are attractive alternatives in cases where the traditional DFT-based scheme exhibits poor performance. The filters are derived by first presenting a derivation for the classical DFT based filter that allows us to pursue these extensions immediately. The approach used in this paper also provides further insights into subband adaptive filtering.