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AD1891JP Datasheet(PDF) 8 Page - Analog Devices |
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AD1891JP Datasheet(HTML) 8 Page - Analog Devices |
8 / 20 page AD1890/AD1891 –8– REV. 0 Polyphase Filter Bank Model Although less intuitively understandable than the interpolation/ decimation model, the polyphase filter bank model is useful to explore because it more accurately portrays the operation of the actual AD1890/AD1891 SamplePort hardware. In the polyphase filter bank model, the stored FIR filter coefficients are thought of as the impulse response of a highly oversampled 0 to 20 kHz low-pass prototype filter, as shown in Figure 2. If this low-pass filter is oversampled by a factor of N, then it can be conceptu- ally decomposed into N different “subfilters,” each filter consist- ing of a different subset of the original set of impulse response samples. If the temporal position of each of the subfilters is maintained, then they can be summed to recreate the original oversampled impulse response. Since the original impulse response is highly oversampled, the more sparsely sampled subfilters still individually meet the Nyquist criterion (i.e., they are adequately sampled). The baseband magnitude and phase responses of the subfilters are identical. The out-of-band (i.e., alias) regions of the subfilters however have phase responses which are shifted relative to one another, in a manner that causes them to cancel when they are summed. The subfilter coefficients are then aligned to the left, as shown in Figure 3, so that the first coefficient of each subfilter is aligned to the first point on a coarse time scale. (This concep- tual step accounts for how the hardware implementation is able to operate at the slower rate corresponding to the coarse time scale.) Each subfilter has been shifted in time by a different amount, and though they still share identical magnitude responses, they now have in-band phase responses which have fractionally different slopes (i.e., group delays). AMP TIME OVERSAMPLED LOW PASS FILTER IMPULSE RESPONSE DECOMPOSED INTO FOUR SUBFILTERS PHASE 0 Deg 90 180 270 1/4Fs 1/2Fs 3/4Fs Fs FREQ AMP 1/4Fs 1/2Fs 3/4Fs Fs 1/4Fs 1/2Fs 3/4Fs Fs 1/4Fs 1/2Fs 3/4Fs Fs 1/4Fs 1/2Fs 3/4Fs Fs Figure 2. Four Polyphase Subfilters in the Time and Frequency Domains |
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