An orthogonal function‐type adaptive digital filter applying a modified discrete fourier transform
Yoshio Itoh, Masaki Kobayashi, Toshiyuki Morkawa, Hiroji Kusaka · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1991
Abstract An orthogonal function‐type adaptive digital filter (orthogonal function type ADF) is known as a means of improving the convergence speed of a tap coefficient in the case in which input is a colored signal such as a voice. Two different methods have been used for pole location of a transfer function of this ADF. One is the pole location of equal interval of 2π/N(rad). (N: tap number of ADF) starting at the phase 0 (rad) on the circle whose radius is very close to 1 within the unit circle of the z‐plane. The other is the one resulting from rotating the above location by π/N(rad). In the case of the former pole location, it has been shown that it is equivalent to a frequency sampling type ADF such that input is a periodic process of period N. Why improvement in convergence speed of the latter is the case is not clear at this date. In this paper we first derive an equivalent circuit of an orthogonal function type ADF using the latter pole location. In this circuit a modified discrete Fourier transform (MDFT) appears in which phase of a pole of a resonator of frequency sampling filter is shifted by π/N(rad). Next, we present a condition for expansion coefficients of the MDFT circuit to be orthogonal to one another. Moreover, we clarify that this equivalent circuit is of a construction that satisfies the orthogonal condition of the MDFT circuit. Finally, we verify these results of investigation by several computer simulations.