signalsmith::windows::Kaiser Class Reference

#include <windows.h>

Detailed Description

The Kaiser window (almost) maximises the energy in the main-lobe compared to the side-lobes.

Kaiser windows can be constructing using the shape-parameter (beta) or using the static with???() methods.

Static Methods
static double	bandwidthToEnbw (double bandwidth, bool heuristicOptimal=false)
	Equivalent noise bandwidth (ENBW), a measure of frequency resolution. More...
Bandwidth methods
static Kaiser	withBandwidth (double bandwidth, bool heuristicOptimal=false)
static double	bandwidthToBeta (double bandwidth, bool heuristicOptimal=false)
	Returns the Kaiser shape where the main lobe has the specified bandwidth (as a factor of 1/window-length). More...
static double	betaToBandwidth (double beta)
Performance methods
static double	bandwidthToEnergyDb (double bandwidth, bool heuristicOptimal=false)
	Total energy ratio (in dB) between side-lobes and the main lobe. More...
static double	energyDbToBandwidth (double energyDb, bool heuristicOptimal=false)
static double	bandwidthToPeakDb (double bandwidth, bool heuristicOptimal=false)
	Peak ratio (in dB) between side-lobes and the main lobe. More...
static double	peakDbToBandwidth (double peakDb, bool heuristicOptimal=false)

Methods
	Kaiser (double beta)
	Set up a Kaiser window with a given shape. beta is pi*alpha (since there is ambiguity about shape parameters) More...
double	operator() (double unit)
	Return the window's value for position in the range [0, 1]. More...
template<typename Data >
void	fill (Data &&data, int size) const
	Fills an arbitrary container with a Kaiser window. More...

Constructor & Destructor Documentation

Kaiser()

signalsmith::windows::Kaiser::Kaiser ( double  beta )

inline

Set up a Kaiser window with a given shape. beta is pi*alpha (since there is ambiguity about shape parameters)

Method Details

bandwidthToBeta()

static double signalsmith::windows::Kaiser::bandwidthToBeta ( double  bandwidth, bool  heuristicOptimal = false  )

inlinestatic

Returns the Kaiser shape where the main lobe has the specified bandwidth (as a factor of 1/window-length).

You can see that the main lobe matches the specified bandwidth.

If heuristicOptimal is enabled, the main lobe width is slightly wider, improving both the peak and total energy - see bandwidthToEnergyDb() and bandwidthToPeakDb().

The main lobe extends to ±bandwidth/2.

bandwidthToEnbw()

static double signalsmith::windows::Kaiser::bandwidthToEnbw ( double  bandwidth, bool  heuristicOptimal = false  )

inlinestatic

Equivalent noise bandwidth (ENBW), a measure of frequency resolution.

Measured ENBW, with and without the heuristic bandwidth adjustment.

This approximation is accurate to ±0.05 up to a bandwidth of 22.

bandwidthToEnergyDb()

static double signalsmith::windows::Kaiser::bandwidthToEnergyDb ( double  bandwidth, bool  heuristicOptimal = false  )

inlinestatic

Total energy ratio (in dB) between side-lobes and the main lobe.

Measured main/side lobe energy ratio. You can see that the heuristic improves performance for all bandwidth values.

This function uses an approximation which is accurate to ±0.5dB for 2 ⩽ bandwidth ≤ 10, or 1 ⩽ bandwidth ≤ 10 when heuristicOptimalis enabled.

bandwidthToPeakDb()

static double signalsmith::windows::Kaiser::bandwidthToPeakDb ( double  bandwidth, bool  heuristicOptimal = false  )

inlinestatic

Peak ratio (in dB) between side-lobes and the main lobe.

,Measured main/side lobe peak ratio. You can see that the heuristic improves performance, except in the bandwidth range 1-2 where peak ratio was sacrificed to improve total energy ratio.

This function uses an approximation which is accurate to ±0.5dB for 2 ⩽ bandwidth ≤ 9, or 0.5 ⩽ bandwidth ≤ 9 when heuristicOptimalis enabled.

fill()

template<typename Data >

void signalsmith::windows::Kaiser::fill ( Data &&  data, int  size  ) const

inline

Fills an arbitrary container with a Kaiser window.

operator()()

double signalsmith::windows::Kaiser::operator() ( double  unit )

inline

Return the window's value for position in the range [0, 1].