filter_comb :
An analog comb filter for xreal-typed signals.

The filter_comb primitive models a continuous-time comb filter, which can be described by the following Laplace s-domain transfer function:

            a0 + a1*exp(-s*T)
    H(s) = -------------------
            b0 + b1*exp(-s*T)

where the numerator coefficients a0 and a1 are defined by the parameter array num_data (namely, num_data[0] and num_data[1], respectively), and the denominator coefficients b0 and b1 are defined by the parameter array den_data (namely, den_data[0] and den_data[1], respectively). The value of the coefficient b0 (i.e. den_data[0] value) must not be zero.

Such comb filters are typically realized by combining the input signal in(t) or output signal out(t) and their delayed signals (in(t-T) or out(t-T), respectively) in a feedforward or feedback manner:

    Feedforward type : out(t) = a0*in(t) + a1*in(t-T)
    Feedback type    : out(t) = (a0*in(t) - b1*out(t-T))/b0

and this primitive can express both types of comb filters. The delay T is defined by the parameter delay.

Note that the transfer function of a comb filter basically describes a discrete-time system with a sampling period of T. To avoid a series of discrete-time events being generated and slowing down the simulation, the filter_comb primitive computes its response using an approximate, equivalent continuous-time transfer function instead.

Optionally, one can also describe the deviation of the delay from its nominal value set by the parameter delay as a function of frequency f, using the parameter array delay_data. This parameter delay_data defines the coefficients of a single-input polynomial function in the same way that the parameter data does for the primitive poly_func. For instance, setting delay_data to ‘{d0, d1} implies that the delay T would vary as a linear function with the frequency f:

    T(f) = delay + (d0 + d1*f).

Such variation in the delay can cause shifts in the periodic patterns of the comb filter’s frequency response.

Input/Output Terminals

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

Parameters

Name	Type	Default	Unit	Description
num_data	real array	‘{1.0, 0.0}	None	numerator coefficients (a0, a1)
den_data	real array	‘{1.0, 0.0}	None	denominator coefficients (b0, b1)
delay	real	1n	seconds	delay (T)
delay_data	real array	‘{0.0}	seconds	delay variation data
filename	string	“”	None	parameter definition file