Kaiser FIR Filter

Kaiser FIR Filter¤

`neojax.nn.kaiser_fir_filter.KaiserFIRFilter` ¤

FIR Filter with Kaiser window.

Computes

\[ h_K(x) = 2 f_c \cdot \text{sinc}(2 f_c x) \cdot w_K(x) \]

where \(w_K(x)\) is the window function, \(f_c\) the cutoff frequency and \(h_K(x)\) is the practical approximation of \(\psi(x)\), the ideal continuous-time low-pass filter (as in appendix C of StyleGAN3 and scipy.signal.firwin).

Part of the filtered leaky ReLU of the CNO.

Parameters:

Name	Type	Description	Default
`cutoff_freq`	`float \| int`	Cutoff frequency \(f_c\) (same unit as `sampling_freq`). Has to be in the open interval `(0, sampling_freq / 2)`.	required
`num_taps`	`int`	Discrete spatial locations, i.e. taps, where the filter is defined. Default is `12`, as in the `CNO` configuration.	`12`
`half_band_width`	`float \| int`	Half-width of the transition band, i.e. \(f_h\). Same as `scipy.signal.firwin`'s `width / 2`. Default is `0.8`.	`0.8`
`sampling_fac`	`int`	Up-/ and downsampling factor. Multiplication factor for `num_taps` and `sampling_freq`. Needed due to zero-padding or strided sampling. Default is `2`.	`2`
`sampling_freq`	`float \| int`	The sampling frequency or rate \(s\)/\(f_s\). Default is 2.	`2.0`
`normalize`	`bool`	Whether to normalize the filter, i.e. enforce \(\sum_i h_{K}\left[i\right] = 1\). Default is `True`.	`True`

Raises:

Type	Description
`ValueError`	If `cutoff_freq` is not in `(0, sampling_freq / 2)`.

Internal Attributes

These fields store the internal layer states.

_filter (tuple[float, ...]): The filter stencil.

Cite

Alias-Free Generative Adversarial Networks

@inproceedings{Karras2021,
    author = {Tero Karras and Miika Aittala and
    Samuli Laine and Erik H\"ark\"onen and
    Janne Hellsten and Jaakko Lehtinen and Timo Aila},
    title = {Alias-Free Generative Adversarial Networks},
    booktitle = {Proc. NeurIPS},
    year = {2021}
}

`filter` `property` ¤

Assembled static filter stencil tuple with shape (num_taps,).

Kaiser FIR Filter