Characteristic polynomials class. More...

Public Member Functions
def	__init__
	Compute characteristic polynomials and characteristic constants.
def	symmetrizeTZ
	A list of transmission zeros in unnormalized frequency (Hz) is symmetrized in the normalized frequency axis.
def	checkUnormSymTZ
	Check if list of transmission zeros (in Hz) is symmetric with respect to center frequency f0.
def	checkNormSymTZ
	Check if list of normalized transmission zeros is symmetric with respect to zero.
def	polyStr
	Return string with polynomial coefficients separated by commas.
def	saveCharPolys
	Save Characteristic Polynomials and constants in output file.

Detailed Description

Characteristic polynomials class.

Characteristic polynomials and constants are defined as [TN 101 eq. (1)] :

$S_{11}(s) = \left[ \frac{F(s)}{\epsilon_r E(s)} \right], S_{12}(s) = S_{21} = \left[ \frac{P(s)}{\epsilon E(s)} \right], S_{22}(s) = \left[ \frac{(-1)^N F(s)^*}{\epsilon_r E(s)} \right]$

where $ F(s)^* = F^*(-s) $ is the 'Paraconjugate' polynomial of $ F(s) $ [Cameron pp. 208 footnote] and is computed using polyConj function.

Definition at line 83 of file libfreefilters.py.

Constructor & Destructor Documentation

def libfreefilters.CharPolys.__init__	(	self,
		P,
		FT,
		symmetrizeZeros = `None`
	)

Compute characteristic polynomials and characteristic constants.

        @param P = Parameter class instance containing filter, synthesis and sweep parameters.
        @param  FT = Frequency transformation class instance.
        @param symmetrizeZeros = Automatically symmetrize Generalized Chebyshev zeros in Hz in order to compute a folded matrix with uniform Q in resonators. 
                                                     Equivalent to answering "Yes" in the GUI when it asks the user if he wants to symmetrize Generalized Chebyshev zeros in Hz.
        @return CharPolys class instance.

Characteristic polynomial $ P(s) $ Characteristic polynomial $ E(s) $ Characteristic polynomial $ F(s) $ Characteristic polynomial $F_{22}(s)$ Characteristic constant $\epsilon$ in the denominator of $S_{12}$ and $S_{21}$ Characteristic constant $\epsilon_R$ in the denominator of $S_{11}$ Roundoff error estimation in the computation of lossless characteristic polynomials, given by the rootsErr return value in CharPolys.factorization method. Value 'a' of the (s-a)/(s+a) zero/pole added in lossy filters synthesis case 3.

Definition at line 93 of file libfreefilters.py.

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Member Function Documentation

def libfreefilters.CharPolys.checkNormSymTZ	(	self,
		TZ
	)

Check if list of normalized transmission zeros is symmetric with respect to zero.

Parameters

TZ	= List of normalized transmission zeros.

Returns: symmetricFlag = True is zeros are symmetric with relative error < 1e-3, False otherwise.

Definition at line 282 of file libfreefilters.py.

Referenced by libfreefilters.CharPolys.__init__().

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def libfreefilters.CharPolys.checkUnormSymTZ	(	self,
		TZ,
		FT
	)

Check if list of transmission zeros (in Hz) is symmetric with respect to center frequency f0.

Parameters

TZ	= List of transmission zeros in Hz.
FT	= Frequency transform class instance. It will be used to get f0.

Returns: symmetricFlag = True is zeros are symmetric with relative error < 1e-3, False otherwise.

Definition at line 264 of file libfreefilters.py.

Referenced by libfreefilters.CharPolys.__init__().

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def libfreefilters.CharPolys.polyStr	(	self,
		pol,
		prec
	)

Return string with polynomial coefficients separated by commas.

Rounds polynomial coefficients to given precision using complexStr() function.

Parameters

pol	= Polynomial (numpy.poly1d object).
prec	= Number of significant digits (int).

Returns: stcoef = String representation of pol.

Definition at line 302 of file libfreefilters.py.

References libcommonfunc.complexStr().

Referenced by libfreefilters.CharPolys.saveCharPolys().

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def libfreefilters.CharPolys.saveCharPolys	(	self,
		P,
		prec
	)

Save Characteristic Polynomials and constants in output file.

Rounds polynomial coefficients to given precision using complexStr() function. Polynomials are of type numpy.poly1d.

Parameters

P	= Parameter class instance.
prec	= Number of correct significant digits to print.

Definition at line 321 of file libfreefilters.py.

References libcommonfunc.complexStr(), libfreefilters.CharPolys.eps, libfreefilters.CharPolys.epsR, libfreefilters.CharPolys.Es, libfreefilters.CharPolys.Fs, libcommonfunc.myPrint(), libcommonfunc.pkgNameVersion(), libfreefilters.CharPolys.polyStr(), and libfreefilters.CharPolys.Ps.

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def libfreefilters.CharPolys.symmetrizeTZ	(	self,
		TZ,
		FT
	)

A list of transmission zeros in unnormalized frequency (Hz) is symmetrized in the normalized frequency axis.

The positive zeros are averaged with the corresponding negative zeros in the normalized frequency axis.

Parameters

TZ	= List of transmission zeros. Unnormalized frequency (Hz).
FT	= Frequency transform class instance.

Returns: TZsym = List of transmission zeros, symmetrized n the normalized frequency axis. Unnormalized frequency (Hz).

Definition at line 245 of file libfreefilters.py.

Referenced by libfreefilters.CharPolys.__init__().

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The documentation for this class was generated from the following file:

libfreefilters.py

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation