IT++
4.3.1
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Windowing functions. More...
Functions | |
vec | itpp::hamming (int size) |
Hamming window. More... | |
vec | itpp::hanning (int n) |
Hanning window. More... | |
vec | itpp::hann (int n) |
Hanning window compatible with matlab. More... | |
vec | itpp::blackman (int n) |
Blackman window. More... | |
vec | itpp::triang (int n) |
Triangular window. More... | |
vec | itpp::sqrt_win (int n) |
Square root window. More... | |
vec | itpp::chebwin (int n, double at) |
Dolph-Chebyshev window. More... | |
Windowing functions.
ITPP_EXPORT vec itpp::hamming | ( | int | size | ) |
Hamming window.
The n
size Hamming window is a vector \(w\) where the \(i\)th component is
\[ w_i = 0.54 - 0.46 \cos(2\pi i/(n-1)) \]
Definition at line 43 of file window.cpp.
References itpp::cos(), and itpp::pi.
Referenced by itpp::fir1(), and itpp::FIR_Fading_Generator::Jakes_filter().
ITPP_EXPORT vec itpp::hanning | ( | int | n | ) |
Hanning window.
The n
size Hanning window is a vector \(w\) where the \(i\)th component is
\[ w_i = 0.5(1 - \cos(2\pi (i+1)/(n+1)) \]
Observe that this function is not the same as the hann() function which is defined as in matlab.
Definition at line 56 of file window.cpp.
References itpp::cos(), and itpp::pi.
Referenced by itpp::spectrum().
ITPP_EXPORT vec itpp::hann | ( | int | n | ) |
Hanning window compatible with matlab.
The n
size Hanning window is a vector \(w\) where the \(i\)th component is
\[ w_i = 0.5(1 - \cos(2\pi i/(n-1)) \]
Definition at line 67 of file window.cpp.
References itpp::cos(), and itpp::pi.
ITPP_EXPORT vec itpp::blackman | ( | int | n | ) |
Blackman window.
The n
size Blackman window is a vector \(w\) where the \(i\)th component is
\[ w_i = 0.42 - 0.5\cos(2\pi i/(n-1)) + 0.08\cos(4\pi i/(n-1)) \]
Definition at line 77 of file window.cpp.
References itpp::cos(), and itpp::pi.
ITPP_EXPORT vec itpp::triang | ( | int | n | ) |
Triangular window.
The n
size triangle window is a vector \(w\) where the \(i\)th component is
\[ w_i = w_{n-i-1} = \frac{2(i+1)}{n+1} \]
for n
odd and for n
even
\[ w_i = w_{n-i-1} = \frac{2i+1}{n} \]
Definition at line 87 of file window.cpp.
ITPP_EXPORT vec itpp::sqrt_win | ( | int | n | ) |
Square root window.
The square-root of the Triangle window. sqrt_win(n) = sqrt(triang(n))
Definition at line 103 of file window.cpp.
References itpp::sqrt().
ITPP_EXPORT vec itpp::chebwin | ( | int | n, |
double | at | ||
) |
Dolph-Chebyshev window.
The length n
Dolph-Chebyshev window is a vector \(w\) whose \(i\)th transform component is given by
\[ W[k] = \frac{T_M\left(\beta \cos\left(\frac{\pi k}{M}\right) \right)}{T_M(\beta)},k = 0, 1, 2, \ldots, M - 1 \]
where T_n(x)
is the order n
Chebyshev polynomial of the first kind.
n | length of the Doplh-Chebyshev window |
at | attenutation of side lobe (in dB) |
n
Doplh-Chebyshev windowDefinition at line 119 of file window.cpp.
References itpp::acosh(), itpp::cheb(), itpp::concat(), itpp::cos(), itpp::cosh(), itpp::elem_mult(), itpp::ifft_real(), itpp::is_even(), it_assert, itpp::linspace(), itpp::pi, itpp::pow10(), itpp::reverse(), itpp::Vec< Num_T >::right(), itpp::sin(), and itpp::to_cvec().