scipy.signal.tf2zpk¶
- scipy.signal.tf2zpk(b, a)[source]¶
Return zero, pole, gain (z,p,k) representation from a numerator, denominator representation of a linear filter.
Parameters: b : ndarray
Numerator polynomial.
a : ndarray
Denominator polynomial.
Returns: z : ndarray
Zeros of the transfer function.
p : ndarray
Poles of the transfer function.
k : float
System gain.
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 and can represent an analog filter of the form:
or a discrete-time filter of the form:
This “positive powers” form is found more commonly in controls engineering. If M and 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:
Although this is true for common filters, remember that this is not true in the general case. If M and 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.