filter :
: An analog linear filter for xreal-typed signals.

The filter primitive models a linear dynamical system, described by a Laplace s- domain transfer function and a transport delay.

The transport delay is set by the delay parameter. The transfer function of the primitive filter can be defined using one of the following two methods:

1) Specifying the DC gain, poles, and zeros of the filter

The first method specifies the transfer function with the following canonical form using the three parameters: gain, poles, and zeros.

             z(s)         (1+s/(2pi*fz1))(1+s/(2pi*fz2))...(1+s/(2pi*fzN))
H(s) = gain*----- = gain* ------------------------------------------------ ,
             p(s)         (1+s/(2pi*fp1))(1+s/(2pi*fp2))...(1+s/(2pi*fpM))

where fz1, fz2, … are the zero frequencies of the filter in Hz and fp1, fp2, … are the pole frequencies of the filter in Hz.

The gain parameter specifies the DC gain of the filter. The poles and zeros parameters specify the lists of pole and zero frequencies, respectively, using the following real array format:

poles = '{ real(fp1), imag(fp1), real(fp2), imag(fp2), ..., real(fpM), imag(fpM) }
zeros = '{ real(fz1), imag(fz1), real(fz2), imag(fz2), ..., real(fzN), imag(fzN) }

Note that both the real and imaginary parts of each pole/zero frequency must be specified. For instance, to specify a DC pole (i.e., fp=0), the poles parameter must contain ‘{0.0, 0.0}. As a special case, the zeros parameter with a value of ‘{0} implies that the filter has no zeros (i.e. z(s) = 1).

The parameters gain, poles, zeros, and delay can be alternatively defined by a parameter definition file named filename in the following Python format:

poles = [real(fp1), imag(fp1), real(fp2), imag(fp2), ..., real(fpM), imag(fpM)]
zeros = [real(fz1), imag(fz1), real(fz2), imag(fz2), ..., real(fzN), imag(fzN)]

2) Specifying the coefficients of the partial fraction decomposition form

The second method specifies the transfer function in a partial fraction decomposition form (i.e. a sum of rational forms). The method is only supported in the parameter definition file:

           b1_real + j*b1_imag                 bN_real + j*bN_imag
H(s) = ---------------------------- + ... + ---------------------------- ,
       (s + a1_real + j*a1_imag)^m1         (s + aN_real + j*aN_imag)^mN

The coefficients ai_real, ai_imag, bi_real, bi_imag, and mi shall be listed in the file named filename in the following Python format:

data = [ a1_real, a1_imag, b1_real, b1_imag, m1,
         a2_real, a2_imag, b2_real, b2_imag, m2,
         ...
         aN_real, aN_imag, bN_real, bN_imag, mN,
       ]

For both cases, the complex poles must be specified as conjugate pairs, otherwise an error will be reported.

Input/Output Terminals

Name	I/O	Type	Description
out	output	xreal	output signal
in	input	xreal	input signal

Parameters

Name	Type	Default	Unit	Description
gain	real	1.0	None	DC gain
poles	real array	‘{1.0e9, 0.0}	Hz	pole frequencies
zeros	real array	‘{0.0}	Hz	zero frequencies
delay	real	0.0	seconds	transport delay
filename	string	“”	None	parameter definition file

filter :: An analog linear filter for xreal-typed signals.

1) Specifying the DC gain, poles, and zeros of the filter

2) Specifying the coefficients of the partial fraction decomposition form

filter :
: An analog linear filter for xreal-typed signals.