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Convert digital filter transfer function data to second-order sections form
[sos,g] = tf2sos(b,a)
[sos,g] = tf2sos(b,a,'order')
[sos,g] = tf2sos(b,a,'order','scale')
sos = tf2sos(...)
tf2sos converts a transfer function representation of a given digital filter to an equivalent second-order section representation.
[sos,g] = tf2sos(b,a) finds a matrix sos in second-order section form with gain g that is equivalent to the digital filter represented by transfer function coefficient vectors a and b.
sos is an L-by-6 matrix
whose rows contain the numerator and denominator coefficients b_{ik} and a_{ik} of the second-order sections of H(z).
[sos,g] = tf2sos(b,a,'order') specifies the order of the rows in sos, where 'order' is
'down', to order the sections so the first row of sos contains the poles closest to the unit circle
'up', to order the sections so the first row of sos contains the poles farthest from the unit circle (default)
[sos,g] = tf2sos(b,a,'order','scale') specifies the desired scaling of the gain and numerator coefficients of all second-order sections, where 'scale' is:
'none', to apply no scaling (default)
'inf', to apply infinity-norm scaling
'two', to apply 2-norm scaling
Using infinity-norm scaling in conjunction with up-ordering minimizes the probability of overflow in the realization. Using 2-norm scaling in conjunction with down-ordering minimizes the peak round-off noise.
sos = tf2sos(...) embeds the overall system gain, g, in the first section, H_{1}(z), so that
Note Embedding the gain in the first section when scaling a direct-form II structure is not recommended and may result in erratic scaling. To avoid embedding the gain, use ss2sos with two outputs. |
[1] Jackson, L. B. Digital Filters and Signal Processing. 3rd ed. Boston: Kluwer Academic Publishers, 1996, chap. 11.
[2] Mitra, S. K. Digital Signal Processing: A Computer-Based Approach. New York: McGraw-Hill, 1998, chap. 9.
[3] Vaidyanathan, P. P. "Robust Digital Filter Structures." Handbook for Digital Signal Processing (S. K. Mitra and J. F. Kaiser, eds.). New York: John Wiley & Sons, 1993, chap. 7.
cplxpair | sos2tf | ss2sos | tf2ss | tf2zp | tf2zpk | zp2sos