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An all-pass filter is a signal processing filter that passes all frequencies equally in gain, but changes the phase relationship between various frequencies. It does this by varying its phase shift as a function of frequency. Generally, the filter is described by the frequency at which the phase shift crosses 90° (i.e., when the input and output signals go into quadrature – when there is a quarter wavelength of delay between them). They are generally used to compensate for other undesired phase shifts that arise in the system, or for mixing with an unshifted version of the original to implement a notch comb filter. They may also be used to convert a mixed phase filter into a minimum phase filter with an equivalent magnitude response or an unstable filter into a stable filter with an equivalent magnitude response. == Active analog implementation == The operational amplifier circuit shown in Figure 1 implements an active all-pass filter with the transfer function : which has one pole at -1/RC and one zero at 1/RC (i.e., they are ''reflections'' of each other across the imaginary axis of the complex plane). The magnitude and phase of H(iω) for some angular frequency ω are : As expected, the filter has unity-gain magnitude for all ω. The filter introduces a different delay at each frequency and reaches input-to-output ''quadrature'' at ω=1/RC (i.e., phase shift is 90 degrees). This implementation uses a high-pass filter at the non-inverting input to generate the phase shift and negative feedback to compensate for the filter's attenuation. * At high frequencies, the capacitor is a short circuit, thereby creating a unity-gain voltage buffer (i.e., no phase shift). * At low frequencies and DC, the capacitor is an open circuit and the circuit is an inverting amplifier (i.e., 180 degree phase shift) with unity gain. * At the corner frequency ω=1/RC of the high-pass filter (i.e., when input frequency is 1/(2πRC)), the circuit introduces a 90 degree shift (i.e., output is in quadrature with input; it is delayed by a quarter wavelength). In fact, the phase shift of the all-pass filter is double the phase shift of the high-pass filter at its non-inverting input. === Interpretation as a Padé approximation to a pure delay === The Laplace transform of a pure delay is given by : where is the delay (in seconds) and is complex frequency. This can be approximated using a Padé approximant, as follows: : where the last step was achieved via a first-order Taylor series expansion of the numerator and denominator. By setting we recover from above. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「All-pass filter」の詳細全文を読む スポンサード リンク
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