def systemFunction(self):
"""
:returns: A ``SystemFunction`` equivalent to this difference
equation
"""
return SystemFunction(
poly.Polynomial(util.reverseCopy(self.dCoeffs)),
poly.Polynomial([-c for c in util.reverseCopy(self.cCoeffs)] \
+ [1]))
def systemFunction(self):
"""
@returns: A C{SystemFunction} equivalent to this difference
equation
"""
return SystemFunction(
poly.Polynomial(util.reverseCopy(self.dCoeffs)),
poly.Polynomial([-c for c in util.reverseCopy(self.cCoeffs)] \
+ [1]))
def poles(self):
"""
:returns: a list of the poles of the system
"""
# The poles of a system are the roots of the denominator
# polynomial in z, which is 1/R. To get that polynomial,
# reverse the coefficients of our polynomial (which is in R).
# make polynomials of z
num = util.reverseCopy(self.numerator.coeffs)
den = util.reverseCopy(self.denominator.coeffs)
# kill off zero-valued leading coeffs (although they don't
# seem to bother numpy)
while len(num) > 1 and num[0] == 0:
num = num[1:]
while len(den) > 1 and den[0] == 0:
den = den[1:]
# cancel poles at zero with zeros at zero
while len(num) > 0 and len(den) > 0 and num[-1] == den[-1] == 0:
num = num[:-1]
den = den[:-1]
return poly.Polynomial(den).roots()
def poles(self):
"""
@returns: a list of the poles of the system
"""
# The poles of a system are the roots of the denominator
# polynomial in z, which is 1/R. To get that polynomial,
# reverse the coefficients of our polynomial (which is in R).
# make polynomials of z
num = util.reverseCopy(self.numerator.coeffs)
den = util.reverseCopy(self.denominator.coeffs)
# kill off zero-valued leading coeffs (although they don't
# seem to bother numpy)
while len(num) > 1 and num[0] == 0:
num = num[1:]
while len(den) > 1 and den[0] == 0:
den = den[1:]
# cancel poles at zero with zeros at zero
while len(num) > 0 and len(den) > 0 and num[-1]==den[-1]==0:
num = num[:-1]
den = den[:-1]
return poly.Polynomial(den).roots()
def differenceEquation(self):
"""
:returns: a ``DifferenceEquation`` representation of this same system
"""
# Orders of the output and input parts
k = self.denominator.order
j = self.numerator.order
# Generate an error if the coefficient of y[n] is 0
a0 = float(self.denominator.coeffs[-1])
assert not a0 == 0, "Coefficient of y[n] must be non-zero"
# Now derive coefficient lists c and d of this form
# y[n] = c_0 y[n-1] + c_{k-1} y[n-k] +
# d_0 x[n] + d_1 x[n-1] + ... + d_j x[n-j]
# Coefficients for newest state and input are at the front;
# these are the least delayed, so we have to reverse the
# coeffs in the polynomials
cCoeffs = [-a/a0 for a in \
util.reverseCopy(self.denominator.coeffs[:-1])]
dCoeffs = [b/a0 for b in \
util.reverseCopy(self.numerator.coeffs)]
return DifferenceEquation(dCoeffs, cCoeffs)
def differenceEquation(self):
"""
@returns: a C{DifferenceEquation} representation of this same system
"""
# Orders of the output and input parts
k = self.denominator.order
j = self.numerator.order
# Generate an error if the coefficient of y[n] is 0
a0 = float(self.denominator.coeffs[-1])
assert not a0 == 0, "Coefficient of y[n] must be non-zero"
# Now derive coefficient lists c and d of this form
# y[n] = c_0 y[n-1] + c_{k-1} y[n-k] +
# d_0 x[n] + d_1 x[n-1] + ... + d_j x[n-j]
# Coefficients for newest state and input are at the front;
# these are the least delayed, so we have to reverse the
# coeffs in the polynomials
cCoeffs = [-a/a0 for a in \
util.reverseCopy(self.denominator.coeffs[:-1])]
dCoeffs = [b/a0 for b in \
util.reverseCopy(self.numerator.coeffs)]
return DifferenceEquation(dCoeffs, cCoeffs)