Frequency Response Function

This function evaluates a rational matrix at given (complex) arguments. If the rational matrix corresponds to a linear, dynamic filter, then this rational function is also called transfer function of the filter and the values of the function on the complex unit circle are called frequency response of the filter.

Usage

zvalues(obj, z, f, n.f, sort.frequencies, ...)

# S3 method for default
zvalues(obj, z = NULL, f = NULL, n.f = NULL, sort.frequencies = FALSE, ...)

# S3 method for polm
zvalues(obj, z = NULL, f = NULL, n.f = 5, sort.frequencies = FALSE, ...)

# S3 method for lpolm
zvalues(obj, z = NULL, f = NULL, n.f = 5, sort.frequencies = FALSE, ...)

# S3 method for lmfd
zvalues(obj, z = NULL, f = NULL, n.f = 5, sort.frequencies = FALSE, ...)

# S3 method for rmfd
zvalues(obj, z = NULL, f = NULL, n.f = 5, sort.frequencies = FALSE, ...)

# S3 method for stsp
zvalues(obj, z = NULL, f = NULL, n.f = 5, sort.frequencies = FALSE, ...)

Arguments

obj

(rational) matrix object, i.e. a polm, lpolm, lmfd, rmfd, stsp object. or an object which may be coerced to a polynomial matrix with polm(obj). The default S3 method acts as a constructor for zvalues objects: and array object and z are supplied, corresponding to the evaluated object at the values of z. (Numeric or complex) vectors or matrices are coerced arrays. If f is supplied instead of z, then z is considered to be exp(complex(imaginary = (-2*pi)*f)).

z

(numeric or complex) vector, points at which to evaluate the rational matrix. Theses values are stored as attribute and can be accessed through zvalues_obj$z.

f

(numeric) vector of frequencies. If z = NULL then z is set to z = exp(complex(imaginary = (-2*pi)*f)). If z is non NULL, then f is set to f = -Arg(z)/(2*pi). Theses values can be accessed through zvalues_obj$f.

n.f

(integer) number of frequencies. If z = f = NULL then a grid of frequencies f = (0:(n.f-1))/n.f is used (and z is generated as explained above).

sort.frequencies

boolean, sort frequencies

...

optional additional parameters

Value

Object of type zvalues

Details

A zvalues object is simply a (complex valued) 3-dimensional array of dimension \((m,n,n.f)\) with attribute z and class attribute c('zvalues','ratm'). The dimensions \((m,n,n.f)\) may also be zero, where n.f is the length of z.

z and f can be accessed through zvalues_obj$z and zvalues_obj$z, respectively.

If you only need the value of the matrix evaluated at one point, then use zvalue(obj, z).

Examples

(vv = zvalues(1:3, z = 4:6))
#> ( 1 x 1 ) frequency response
#>      z[1] [,1] z[2] [,1] z[3] [,1]
#> [1,]         1         2         3
(mm = zvalues(matrix(1:4, 2, 2), z = 1))
#> ( 2 x 2 ) frequency response
#>      z[1] [,1]  [,2]
#> [1,]         1     3
#> [2,]         2     4
(aa = zvalues(array(1:8, dim = c(2,2,2)), f = c(0.2, 0.8)))
#> ( 2 x 2 ) frequency response
#>      z[1] [,1]  [,2] z[2] [,1]  [,2]
#> [1,]         1     3         5     7
#> [2,]         2     4         6     8
(ll = test_lmfd(dim = c(2,2), bpoles = 1, bzeroes = 1))
#> ( 2 x 2 ) left matrix fraction description a^(-1)(z) b(z) with degrees (p = 1, q = 1)
#> left factor a(z):
#>      z^0 [,1]  [,2]   z^1 [,1]       [,2]
#> [1,]        1     0 -0.5713466 -0.7654262
#> [2,]        0     1 -0.5666530  0.4836197
#> right factor b(z):
#>        z^0 [,1]       [,2]   z^1 [,1]        [,2]
#> [1,] -0.1517956 -0.8511016  0.4050516  0.19158946
#> [2,]  0.7227983  0.2260162 -0.4814751 -0.03886025
zvalues(ll)
#> ( 2 x 2 ) frequency response
#>        z[1] [,1]         [,2]           z[2] [,1]                  [,2]
#> [1,] 2.771387+0i -4.130057+0i 0.0127468-0.482435i -0.5347017+0.1780572i
#> [2,] 1.221160+0i -1.451284+0i 0.1271643+0.369789i  0.0553169+0.3321085i
#>                z[3] [,1]                  [,2]           z[4] [,1]
#> [1,] -0.320849-1.038616i -0.6555192-0.3774208i -0.320849+1.038616i
#> [2,]  0.686564+1.743213i  0.3221108+0.8308292i  0.686564-1.743213i
#>                       [,2]           z[5] [,1]                  [,2]
#> [1,] -0.6555192+0.3774208i 0.0127468+0.482435i -0.5347017-0.1780572i
#> [2,]  0.3221108-0.8308292i 0.1271643-0.369789i  0.0553169-0.3321085i