filter_sel :
A selectable analog linear filter for xreal-typed signals

The filter_sel primitive models a continuous-time linear filter, of which Laplace s-domain transfer function can be selected from a set of multiple transfer functions by a wire-type selection signal sel. With this primitive, one can describe a linear AC transfer function that varies with a set of digital input values.

With the width of the input sel equal to k, as specified by the parameter width_sel, the primitive can have up to 2^k linear filters to select from. Each linear filter is indexed by an integer ranging from 0 to 2^k-1, which corresponds to the unsigned integer value of the input sel[k-1:0].

The parameters indices and data together describe the set of linear filters. First, the parameter indices is an integer-type array that lists the indices of the linear filters in the order that they are defined by the parameter data. The indices may be listed in an arbitrary order and may not span a complete set, but each index must be within the range of 0~2^k-1. For example, ‘{0, 3, 1} is possible when k=2. The special value of ‘{-1} is equivalent to a complete set of indices listed as ‘{0, 1, 2, …, 2^k-1}.

On the other hand, the parameter data is a real-type array defining each of the linear filters of which indices are listed in the parameter indices using a concatenated set of data values formatted as below (for the number of indices > 1):

    data = '{ ...
              // linear filter with index 'indices[i]'
              N,                                        // number of partial fraction terms
              a1_real, a1_imag, b1_real, b1_imag, m1,   // partial fraction term #1
              a2_real, a2_imag, b2_real, b2_imag, m2,   // partial fraction term #2
              ...
              aN_real, aN_imag, bN_real, bN_imag, mN,   // partial fraction term #N
              ...
           }

Each set of data values describing a single linear filter starts with the number of partial fraction terms (N), followed by a list of 5*N coefficients describing the N partial fraction terms. These coefficients describe an s-domain transfer function H(s) as expressed below:

               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

For illustration, the following example describes two linear filters index 0 and 1, respectively. The linear filter with index 0 describes a first-order filter with a single pole at 1GHz, while the linear filter with index 1 describes a second-order filter with complex poles at -4000+j*3000 and -4000-j*3000 rad/s. Both the filters have a gain of 1.

    indices = '{0, 1}
    data = '{1, 2*M_PI*1e9, 0.0, 2*M_PI*1e9, 0.0, 1,
             2, 4000, 3000, 0.0, 4167, 1, 4000, -3000, 0.0, -4167, 1}

When the parameter indices does not list a complete set of indices, the undefined linear filters are assumed to be a constant function outputting 0.0. When the parameter indices has only one index, the parameter data must omit the number of partial fraction terms (N) and list the coefficients only.

When the parameter filename is defined, the primitive reads the named file that defines the parameter values in Python format. For the above example, the parameters indices and data can be defined within a file as below:

    indices = [0, 1]
    data = [1, 6.283e9, 0.0, 6.283e9, 0.0, 1, 2, 4000, 3000, 0.0, 4167, 1, 4000, -3000, 0.0, -4167, 1]

The parameter delay sets the transport delay from the input to output in seconds. For synchronization reasons, the transport delay value must be at least a unit timestep.

Input/Output Terminals

Name	I/O	Type	Description
out	output	xreal	output signal
in	input	xreal	input signal
sel	input	wire	selection signal (binary-coded)

Parameters

Name	Type	Default	Unit	Description
width_sel	integer	1	None	width of selection bits
indices	int array	‘{0}	None	list of filter indices
data	real array	‘{0.0}	None	list of filter data
delay	real	0.0	seconds	transport delay
filename	string	“”	None	parameter definition file