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Functions
Windowing
Signal Processing (SP) Module

Windowing functions. More...

Functions

vec itpp::hamming (int size)
 Hamming window.
 
vec itpp::hanning (int n)
 Hanning window.
 
vec itpp::hann (int n)
 Hanning window compatible with matlab.
 
vec itpp::blackman (int n)
 Blackman window.
 
vec itpp::triang (int n)
 Triangular window.
 
vec itpp::sqrt_win (int n)
 Square root window.
 
vec itpp::chebwin (int n, double at)
 Dolph-Chebyshev window.
 

Detailed Description

Windowing functions.

Function Documentation

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.

Parameters
nlength of the Doplh-Chebyshev window
atattenutation of side lobe (in dB)
Returns
symmetric length n Doplh-Chebyshev window
Author
Kumar Appaiah and Adam Piatyszek (code review)

Definition 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().

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