echomap::WindowFunctions::Welch Struct Reference

The Welch parabolic window. More...

#include <WindowFunctions.hpp>

Static Public Member Functions
static float	operator() (std::size_t index, std::size_t size) noexcept
	Maps the index into the Welch function.

Detailed Description

The Welch parabolic window.

Definition at line 255 of file WindowFunctions.hpp.

Member Function Documentation

operator()()

float echomap::WindowFunctions::Welch::operator() ( std::size_t index, std::size_t size )

staticnoexcept

Maps the index into the Welch function.

For a window of size \( M \), let \( N = M - 1 \).

\[ w[n] = 1 - \left( \frac{n - \frac{N}{2}}{\frac{N}{2}} \right)^2 \]

for index \( n \).

The Welch window is a single parabolic section with zero-valued endpoints and a maximum at the centre.

Parameters

index	The index within the window.
size	The size of the window.

Returns

The Welch-mapped index.

Definition at line 96 of file WindowFunctions.cpp.

{
    if (size <= 1)
        return 1.0f;
 
    const auto centre = static_cast<float>(size - 1) / 2.0f;
    const auto x = (static_cast<float>(index) - centre) / centre;
    return 1.0f - x * x;
}

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The documentation for this struct was generated from the following files:

• src/objects/factories/WindowFunctions.hpp
• src/objects/factories/WindowFunctions.cpp