FFT Window functions

Author: pschatzmann

src/AudioLibs/AudioFFT.h

@@ -320,7 +320,7 @@ class AudioFFTBase : public AudioPrint {
         T windowedSample(T sample){
             T result = sample;
             if (cfg.window_function!=nullptr){
-                result = cfg.window_function->ratio(current_pos) * sample;
+                result = cfg.window_function->factor(current_pos) * sample;
             }
             return result;
         }

src/AudioLibs/FFT/FFTWindows.h

@@ -28,11 +28,11 @@ class WindowFunction {
   virtual void begin(int samples) {
     this->samples_minus_1 = -1.0f + samples;
     this->i_samples = samples;
-    this->i_half_samples = samples / 2;
+    this->i_half_samples = samples / 2 - 1;
   }
 
-  inline float ratio(int idx) {
-    return idx < i_half_samples ? factor(idx) : factor(i_samples-idx);
+  inline float factor(int idx) {
+    return idx < i_half_samples ? factor_internal(idx) : factor_internal(i_samples-idx-1);
   }
 
   inline int samples() { return i_samples; }
@@ -46,8 +46,12 @@ class WindowFunction {
   const float sixPi = 18.84955593f;
 
   // virtual function provide implementation in subclass
-  virtual float factor(int idx) = 0;
+  virtual float factor_internal(int idx) = 0;
 
+  inline float ratio(int idx) {
+    float result = (static_cast<float>(idx)) / samples_minus_1;
+    return result>1.0f ? 1.0f : result;
+  }
 
 };
 
@@ -63,26 +67,27 @@ class BufferedWindow : public WindowFunction {
   BufferedWindow(BufferedWindow const&) = delete;
   BufferedWindow& operator=(BufferedWindow const&) = delete;
 
-  virtual void begin(int samples) {
+  virtual void begin(int samples) override {
     // process only if there is a change
+    WindowFunction::begin(samples);
     if (p_wf->samples() != samples) {
       p_wf->begin(samples);
       len = samples / 2;
       buffer.resize(len);
       for (int j = 0; j < len; j++) {
-        buffer[j] = p_wf->ratio(j);
+        buffer[j] = p_wf->factor(j);
       }
     }
   }
 
-  inline float factor(int idx) {
-    return idx < len ? buffer[idx] : buffer[i_samples - idx];
-  }
-
  protected:
   WindowFunction* p_wf = nullptr;
   Vector<float> buffer{0};
   int len;
+
+  float factor_internal(int idx) override {
+    return idx < len ? buffer[idx] : buffer[i_samples - idx];
+  }
 };
 
 /**
@@ -93,7 +98,7 @@ class BufferedWindow : public WindowFunction {
 class Rectange : public WindowFunction {
  public:
   Rectange() = default;
-  float factor(int idx) { return 1.0f; }
+  float factor_internal(int idx) { return 1.0f; }
 };
 
 /**
@@ -104,7 +109,7 @@ class Rectange : public WindowFunction {
 class Hamming : public WindowFunction {
  public:
   Hamming() = default;
-  float factor(int idx) {
+  float factor_internal(int idx) {
     return 0.54f - (0.46f * cos(twoPi * ratio(idx)));
   }
 };
@@ -117,7 +122,7 @@ class Hamming : public WindowFunction {
 class Hann : public WindowFunction {
  public:
   Hann() = default;
-  float factor(int idx) {
+  float factor_internal(int idx) {
     return 0.54f * (1.0f - cos(twoPi * ratio(idx)));
   }
 };
@@ -130,7 +135,7 @@ class Hann : public WindowFunction {
 class Triangle : public WindowFunction {
  public:
   Triangle() = default;
-  float factor(int idx) {
+  float factor_internal(int idx) {
     return 1.0f - ((2.0f * fabs((idx - 1) -
                               (static_cast<float>(i_samples - 1) / 2.0f))) /
                   samples_minus_1);
@@ -146,7 +151,7 @@ class Triangle : public WindowFunction {
 class Nuttall : public WindowFunction {
  public:
   Nuttall() = default;
-  float factor(int idx) {
+  float factor_internal(int idx) override {
     float r = ratio(idx);
     return 0.355768f - (0.487396f * (cos(twoPi * r))) +
            (0.144232f * (cos(fourPi * r))) - (0.012604f * (cos(sixPi * r)));
@@ -162,7 +167,7 @@ class Nuttall : public WindowFunction {
 class Blackman : public WindowFunction {
  public:
   Blackman() = default;
-  float factor(int idx) {
+  float factor_internal(int idx)override {
     float r = ratio(idx);
     return 0.42323f - (0.49755f * (cos(twoPi * r))) +
            (0.07922f * (cos(fourPi * r)));
@@ -177,7 +182,7 @@ class Blackman : public WindowFunction {
 class BlackmanNuttall : public WindowFunction {
  public:
   BlackmanNuttall() = default;
-  float factor(int idx) {
+  float factor_internal(int idx) override{
     float r = ratio(idx);
     return 0.3635819f - (0.4891775f * (cos(twoPi * r))) +
            (0.1365995f * (cos(fourPi * r))) - (0.0106411f * (cos(sixPi * r)));
@@ -192,7 +197,7 @@ class BlackmanNuttall : public WindowFunction {
 class BlackmanHarris : public WindowFunction {
  public:
   BlackmanHarris() = default;
-  float factor(int idx) {
+  float factor_internal(int idx) override{
     float r = ratio(idx);
     return 0.35875f - (0.48829f * (cos(twoPi * r))) +
            (0.14128f * (cos(fourPi * r))) - (0.01168f * (cos(sixPi * r)));
@@ -207,7 +212,7 @@ class BlackmanHarris : public WindowFunction {
 class FlatTop : public WindowFunction {
  public:
   FlatTop() = default;
-  float factor(int idx) {
+  float factor_internal(int idx) override{
     float r = ratio(idx);
     return 0.2810639f - (0.5208972f * cos(twoPi * r)) +
            (0.1980399f * cos(fourPi * r));
@@ -222,7 +227,7 @@ class FlatTop : public WindowFunction {
 class Welch : public WindowFunction {
  public:
   Welch() = default;
-  float factor(int idx) {
+  float factor_internal(int idx) override{
     float tmp = (((idx - 1) - samples_minus_1 / 2.0f) / (samples_minus_1 / 2.0f));
     return 1.0f - (tmp*tmp);
   }