tf2zpk(b, a)

Notes

If some values of b are too close to 0, they are removed. In that case, a BadCoefficients warning is emitted.

The b and a arrays are interpreted as coefficients for positive, descending powers of the transfer function variable. So the inputs $b = [b_0, b_1, ..., b_M]$ and $a =[a_0, a_1, ..., a_N]$ can represent an analog filter of the form:

$$H(s) = \frac {b_0 s^M + b_1 s^{(M-1)} + \cdots + b_M} {a_0 s^N + a_1 s^{(N-1)} + \cdots + a_N}$$

or a discrete-time filter of the form:

$$H(z) = \frac {b_0 z^M + b_1 z^{(M-1)} + \cdots + b_M} {a_0 z^N + a_1 z^{(N-1)} + \cdots + a_N}$$

This "positive powers" form is found more commonly in controls engineering. If :None:None:`M` and :None:None:`N` are equal (which is true for all filters generated by the bilinear transform), then this happens to be equivalent to the "negative powers" discrete-time form preferred in DSP:

$$H(z) = \frac {b_0 + b_1 z^{-1} + \cdots + b_M z^{-M}} {a_0 + a_1 z^{-1} + \cdots + a_N z^{-N}}$$

Although this is true for common filters, remember that this is not true in the general case. If :None:None:`M` and :None:None:`N` are not equal, the discrete-time transfer function coefficients must first be converted to the "positive powers" form before finding the poles and zeros.

Parameters

b : array_like

Numerator polynomial coefficients.

a : array_like

Denominator polynomial coefficients.

Returns

z : ndarray

Zeros of the transfer function.

p : ndarray

Poles of the transfer function.

k : float

System gain.

Return zero, pole, gain (z, p, k) representation from a numerator, denominator representation of a linear filter.

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._ltisys.TransferFunctionContinuous scipy.signal._ltisys.TransferFunction scipy.signal._signaltools.filtfilt scipy.signal._ltisys.TransferFunctionDiscrete

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