外文翻譯_外文文獻_英文文獻_iir數(shù)字濾波器的設(shè)計-文庫吧
2024-11-14 04:21 本頁面
【正文】 able approximation to these filter would be to truncate the impulse response as indicated in Eq.() for a lowpass filter. The magnitude response of the FIR lowpass filter obtained by truncating the impulse response of the ideal lowpass filter does not have a sharp transition from passband to stopband but, rather, exhibits a gradual rolloff. Thus, as in the case of the analog filter design problem outlined in section , the magnitude response specifications of a digital filter in the passband and in the stopband are given with some acceptable tolerances. In addition, a transition band is specified between the passband and the stopband to permit the magnitude to drop off smoothly. For example, the magnitude )( ?jeG of a lowpass filter may be given as shown in Figure . As indicated in the figure, in the passband defined by 0 p???? , we require that the magnitude approximates unity with an error of p?? ,., ppjp fo reG ???? ? ????? ,1)(1. In the stopband, defined by ??? ??s ,we require that the magnitude approximates zero with an error of is,? .e., ,)(sjeG ?? ? for ??? ??s . The frequencies p? and s? are , respectively, called the passband edge frequency and the stopband edge frequency. The limits of the tolerances in the 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
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