Digital Filters Using MATLAB by Lars Wanhammar & Tapio Saramäki

Author:Lars Wanhammar & Tapio Saramäki
Language: eng
Format: epub
ISBN: 9783030240639
Publisher: Springer International Publishing

where T is the sampling period. The sample period is in most SC filters partitioned into two, or several, phases. Hence, a delay of z−1/2 represents a delay of half a sample period.

For the discrete-time filter to retain the essential properties of the analog filter, the jω-axis should be mapped onto the unit circle in the z-plane, and for a stable filter, the left-hand side of the s-plane should map to the interior of the unit circle.

In this case, the interior of the unit circle in the z-plane corresponds to a strip of the s-plane: σ ≤ 0 and ωa = ± 2/T, as shown in Fig. 9.8. Hence, the LDI transformation only yields a stable digital filter if the pole-zero configuration of the analog filter is contained within this strip.

Fig. 9.8a) s-plane, b) z-plane using the LDI transformation

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