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127 lines
3.3 KiB
C++
127 lines
3.3 KiB
C++
/*
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Some window functions
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Copyright 2018 Ahmet Inan <inan@aicodix.de>
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*/
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#ifndef WINDOW_HH
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#define WINDOW_HH
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#include "kahan.hh"
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namespace DSP {
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template <int TAPS, typename TYPE>
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class Rect
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{
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TYPE w[TAPS];
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public:
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Rect()
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{
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for (int n = 0; n < TAPS; ++n)
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w[n] = TYPE(1);
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}
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inline TYPE operator () (int n) { return n >= 0 && n < TAPS ? w[n] : 0; }
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inline operator const TYPE * () const { return w; }
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};
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template <int TAPS, typename TYPE>
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class Hann
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{
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TYPE w[TAPS];
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public:
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Hann()
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{
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for (int n = 0; n < TAPS; ++n)
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w[n] = TYPE(0.5) * (TYPE(1) - std::cos(TYPE(2) * TYPE(M_PI) * TYPE(n) / TYPE(TAPS - 1)));
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}
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inline TYPE operator () (int n) { return n >= 0 && n < TAPS ? w[n] : 0; }
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inline operator const TYPE * () const { return w; }
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};
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template <int TAPS, typename TYPE>
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class Hamming
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{
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TYPE w[TAPS];
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public:
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Hamming()
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{
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for (int n = 0; n < TAPS; ++n)
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w[n] = TYPE(0.54) - TYPE(0.46) * std::cos(TYPE(2) * TYPE(M_PI) * TYPE(n) / TYPE(TAPS - 1));
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}
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inline TYPE operator () (int n) { return n >= 0 && n < TAPS ? w[n] : 0; }
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inline operator const TYPE * () const { return w; }
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};
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template <int TAPS, typename TYPE>
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class Lanczos
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{
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TYPE w[TAPS];
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TYPE sinc(TYPE x)
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{
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return TYPE(0) == x ? TYPE(1) : std::sin(TYPE(M_PI) * x) / (TYPE(M_PI) * x);
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}
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public:
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Lanczos()
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{
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for (int n = 0; n < TAPS; ++n)
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w[n] = sinc(TYPE(2 * n) / TYPE(TAPS - 1) - TYPE(1));
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}
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inline TYPE operator () (int n) { return n >= 0 && n < TAPS ? w[n] : 0; }
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inline operator const TYPE * () const { return w; }
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};
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template <int TAPS, typename TYPE>
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class Gauss
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{
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TYPE w[TAPS];
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public:
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Gauss(TYPE o)
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{
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for (int n = 0; n < TAPS; ++n)
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w[n] = std::exp(- TYPE(0.5) * std::pow((TYPE(n) - TYPE(TAPS - 1) / TYPE(2)) / (o * TYPE(TAPS - 1) / TYPE(2)), TYPE(2)));
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}
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inline TYPE operator () (int n) { return n >= 0 && n < TAPS ? w[n] : 0; }
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inline operator const TYPE * () const { return w; }
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};
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template <int TAPS, typename TYPE>
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class Kaiser
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{
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TYPE w[TAPS];
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/*
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i0() implements the zero-th order modified Bessel function of the first kind:
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https://en.wikipedia.org/wiki/Bessel_function#Modified_Bessel_functions:_I%CE%B1,_K%CE%B1
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$I_\alpha(x) = i^{-\alpha} J_\alpha(ix) = \sum_{m=0}^\infty \frac{1}{m!\, \Gamma(m+\alpha+1)}\left(\frac{x}{2}\right)^{2m+\alpha}$
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$I_0(x) = J_0(ix) = \sum_{m=0}^\infty \frac{1}{m!\, \Gamma(m+1)}\left(\frac{x}{2}\right)^{2m} = \sum_{m=0}^\infty \left(\frac{x^m}{2^m\,m!}\right)^{2}$
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We obviously can't use the factorial here, so let's get rid of it:
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$= 1 + \left(\frac{x}{2 \cdot 1}\right)^2 + \left(\frac{x}{2 \cdot 1}\cdot \frac{x}{2 \cdot 2}\right)^2 + \left(\frac{x}{2 \cdot 1}\cdot \frac{x}{2 \cdot 2}\cdot \frac{x}{2 \cdot 3}\right)^2 + .. = 1 + \sum_{m=1}^\infty \left(\prod_{n=1}^m \frac{x}{2n}\right)^2$
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*/
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TYPE i0(TYPE x)
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{
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Kahan<TYPE> sum(1.0);
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TYPE val = 1.0;
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// converges for -3*M_PI:3*M_PI in less than:
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// float: 25 iterations
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// double: 35 iterations
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for (int n = 1; n < 35; ++n) {
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val *= x / TYPE(2 * n);
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if (sum.same(val * val))
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return sum();
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}
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return sum();
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}
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public:
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Kaiser(TYPE a)
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{
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for (int n = 0; n < TAPS; ++n)
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w[n] = i0(TYPE(M_PI) * a * std::sqrt(TYPE(1) - std::pow(TYPE(2 * n) / TYPE(TAPS - 1) - TYPE(1), TYPE(2)))) / i0(TYPE(M_PI) * a);
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}
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inline TYPE operator () (int n) { return n >= 0 && n < TAPS ? w[n] : 0; }
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inline operator const TYPE * () const { return w; }
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};
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}
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#endif
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