外文翻譯_外文文獻_英文文獻_iir數(shù)字濾波器的設(shè)計-展示頁
2024-12-16 04:21本頁面
【正文】 e passband and stopband, p? and s? , are usually called the peak ripple values. Note that the frequency response )( ?jeG of a digital filter is a periodic function of ? ,and the magnitude response of a realcoefficient digital filter is an even function of ? . As a result, the digital filter specifications are given only for the range ????0 . Digital filter specifications are often given in terms of the loss function, )(lo g20)( 10 ??? jeG?? , in dB. Here the peak passband ripple p? and the minimum stopband attenuation s? are given in dB,., the loss specifications of a digital filter are given by dBpp )1(lo g20 10 ?? ??? , dBss )(lo g20 10 ?? ?? . Preliminary Considerations As in the case of an analog lowpass filter, the specifications for a digital lowpass filter may alternatively be given in terms of its magnitude response, as in Figure . Here the maximum value of the magnitude in the passband is assumed to be unity, and the maximum passband deviation, denoted as 1/ 21 ?? ,is given by the minimum value of the magnitude in the passband. The maximum stopband magnitude is denoted by 1/A. For the normalized specification, the maximum value of the gain function or the minimum value of the loss function is therefore 0 dB. The quantity max? given by dB)1(lo g20 210m a x ?? ?? Is called the maximum passband attenuation. For p? ?? 1, as is typically the case, it can be shown that pp ??? 2)21(lo g20 10m a x ???? The passband and stopband edge frequencies, in most applications, are specified in Hz, along with the sampling rate of the digital filter. Since all filter design techniques are developed in terms of normalized angular frequencies p? and s? ,the sepcified critical frequencies need to be normalized before a specific filter design algorithm can be applied. Let TF denote the sampling frequency in Hz, and FP and Fs denote, respectively,the passband and stopband edge frequencies in Hz. Then the normalized angular edge frequencies in radians are given by TFFFF pT pTpp ??? 22 ???? TFFFF sT sTss ??? 22 ???? Selection of the Filter Type The second issue of interest is the selection of the digital filter type,.,whether an IIR or an FIR digital filter is to be employed. The objective of digital filter design is to develop a causal transfer function H(z) meeting the frequency response specifications. For IIR digital filter design, the IIR transfer function is a real rational function of 1?z . H(z)=NMdNzzdzdd pMzzpzpp ?????????? ???? ......2211022110 Moreover, H(z) must be a stable transfer function, and for reduced putational plexity, it must be of lowest order N. On the other hand, for FIR filter design, the FIR transfer function is a polynomial in 1?z : ???? NnnznhzH0 ][)( For reduced putational plexity, the degree N of H(z) must be as small as possible. In addition, if a linear phase is desired, then the FIR filter coefficients must satisfy the constraint: ][][ Nnhnh
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