tf2sos (Signal Processing Toolbox)

Conversion of transfer function to second-order sections.

Syntax

[sos,g] = tf2sos(b,a)
[sos,g] = tf2sos(b,a,'order')
[sos,g] = tf2sos(b,a,'order','scale')
sos = tf2sos(...)

Description

tf2sos converts a transfer function representation of a given system 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 system 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, H₁(z), so that

See Also


`cplxpair`	Group complex numbers into complex conjugate pairs.
`sos2tf`	Conversion of second-order sections to transfer function.
`ss2sos`	Conversion of state-space to second-order sections.
`tf2ss`	Conversion of transfer function to state-space.
`tf2zp`	Conversion of transfer function to zero-pole-gain.
`zp2sos`	Conversion of zero-pole-gain to second-order sections.

References

[1] Jackson, L.B. Digital Filters and Signal Processing. 3rd ed. Boston: Kluwer Academic Publishers, 1996. Chapter 11.

[2] Mitra, S.K. Digital Signal Processing: A Computer-Based Approach. New York: McGraw-Hill, 1998. Chapter 9.

[3] Vaidyanathan, P.P. "Robust Digital Filter Structures." Handbook for Digital Signal Processing. S.K. Mitra and J.F. Kaiser, ed. Chapter 7. New York: John Wiley & Sons, 1993.

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