Added Kaiser window

sdrbase/dsp/fftwindow.cpp

@@ -18,12 +18,39 @@
 
 #include "dsp/fftwindow.h"
 
+FFTWindow::FFTWindow() :
+	m_kaiserAlpha(2.15) // beta = 6.76 first sidelobe at -70dB
+{
+	m_kaiserI0Alpha = zeroethOrderBessel(m_kaiserAlpha);
+}
+
+void FFTWindow::setKaiserAlpha(Real alpha)
+{
+	m_kaiserAlpha = alpha;
+	m_kaiserI0Alpha = zeroethOrderBessel(m_kaiserAlpha);
+}
+
+void FFTWindow::setKaiserBeta(Real beta)
+{
+	m_kaiserAlpha = beta / M_PI;
+	m_kaiserI0Alpha = zeroethOrderBessel(m_kaiserAlpha);
+}
+
 void FFTWindow::create(Function function, int n)
 {
 	Real (*wFunc)(Real n, Real i);
 
 	m_window.clear();
 
+	if (function == Kaiser) // Kaiser special case
+	{
+		for(int i = 0; i < n; i++) {
+			m_window.push_back(kaiser(n, i));
+		}
+
+		return;
+	}
+
 	switch(function) {
 		case Flattop:
 			wFunc = flatTop;
@@ -51,8 +78,9 @@ void FFTWindow::create(Function function, int n)
 			break;
 	}
 
-	for(int i = 0; i < n; i++)
+	for(int i = 0; i < n; i++) {
 		m_window.push_back(wFunc(n, i));
+	}
 }
 
 void FFTWindow::apply(const std::vector<Real>& in, std::vector<Real>* out)

sdrbase/dsp/fftwindow.h

@@ -36,18 +36,25 @@ public:
 		Flattop,
 		Hamming,
 		Hanning,
-		Rectangle
+		Rectangle,
+		Kaiser
 	};
 
+	FFTWindow();
+
 	void create(Function function, int n);
 	void apply(const std::vector<Real>& in, std::vector<Real>* out);
 	void apply(const std::vector<Complex>& in, std::vector<Complex>* out);
     void apply(std::vector<Complex>& in);
 	void apply(const Complex* in, Complex* out);
     void apply(Complex* in);
+	void setKaiserAlpha(Real alpha); //!< set the Kaiser window alpha factor (default 2.15)
+	void setKaiserBeta(Real beta);   //!< set the Kaiser window beta factor = pi * alpha
 
 private:
 	std::vector<float> m_window;
+	Real m_kaiserAlpha;    //!< alpha factor for Kaiser window
+	Real m_kaiserI0Alpha;  //!< zeroethOrderBessel of alpha above
 
 	static inline Real flatTop(Real n, Real i)
 	{
@@ -83,6 +90,36 @@ private:
 	{
 		return 1.0;
 	}
+
+	// https://raw.githubusercontent.com/johnglover/simpl/master/src/loris/KaiserWindow.C
+	inline Real kaiser(Real n, Real i)
+	{
+		Real K = ((2.0*i) / n) - 1.0;
+		Real arg = sqrt(1.0 - (K*K));
+		return zeroethOrderBessel(m_kaiserAlpha*arg) / m_kaiserI0Alpha;
+	}
+
+	static inline Real zeroethOrderBessel( Real x )
+	{
+		const Real eps = 0.000001;
+
+		//  initialize the series term for m=0 and the result
+		Real besselValue = 0;
+		Real term = 1;
+		Real m = 0;
+
+		//  accumulate terms as long as they are significant
+		while(term  > eps * besselValue)
+		{
+			besselValue += term;
+
+			//  update the term
+			++m;
+			term *= (x*x) / (4*m*m);
+		}
+
+		return besselValue;
+	}
 };
 
 #endif // INCLUDE_FFTWINDOWS_H

sdrgui/gui/glspectrumgui.ui

@@ -387,6 +387,11 @@
          <string>Rec</string>
         </property>
        </item>
+       <item>
+        <property name="text">
+         <string>Kai</string>
+        </property>
+       </item>
       </widget>
      </item>
      <item>

sdrgui/readme.md

@@ -364,6 +364,7 @@ Use this combo box to select which window is applied to the FFT:
   - **Ham**: Hamming
   - **Han**: Hanning (default)
   - **Rec**: Rectangular (no window)
+  - **Kai**: Kaiser with alpha = 2.15 (beta = 6.76) gives sidelobes < -70dB
 
 <h4>4.2. FFT size</h4>