spectrogram : add simple spectrogram tool (#17)

examples/spectrogram/fft.h

@@ -0,0 +1,91 @@
+#pragma once
+
+#include <cmath>
+
+// FFT routines taken from https://stackoverflow.com/a/37729648/4039976
+
+constexpr auto kMaxSamplesPerFrame = 1024;
+
+int log2(int N) {
+    int k = N, i = 0;
+    while(k) {
+        k >>= 1;
+        i++;
+    }
+    return i - 1;
+}
+
+int reverse(int N, int n) {
+    int j, p = 0;
+    for(j = 1; j <= log2(N); j++) {
+        if(n & (1 << (log2(N) - j)))
+            p |= 1 << (j - 1);
+    }
+    return p;
+}
+
+void ordina(float * f1, int N) {
+    float f2[2*kMaxSamplesPerFrame];
+    for (int i = 0; i < N; i++) {
+        int ir = reverse(N, i);
+        f2[2*i + 0] = f1[2*ir + 0];
+        f2[2*i + 1] = f1[2*ir + 1];
+    }
+    for (int j = 0; j < N; j++) {
+        f1[2*j + 0] = f2[2*j + 0];
+        f1[2*j + 1] = f2[2*j + 1];
+    }
+}
+
+void transform(float * f, int N) {
+    ordina(f, N);    //first: reverse order
+    float * W;
+    W = (float *)malloc(N*sizeof(float));
+    W[2*1 + 0] = cos(-2.*M_PI/N);
+    W[2*1 + 1] = sin(-2.*M_PI/N);
+    W[2*0 + 0] = 1;
+    W[2*0 + 1] = 0;
+    for (int i = 2; i < N / 2; i++) {
+        W[2*i + 0] = cos(-2.*i*M_PI/N);
+        W[2*i + 1] = sin(-2.*i*M_PI/N);
+    }
+    int n = 1;
+    int a = N / 2;
+    for(int j = 0; j < log2(N); j++) {
+        for(int i = 0; i < N; i++) {
+            if(!(i & n)) {
+                int wi = (i * a) % (n * a);
+                int fi = i + n;
+                float a = W[2*wi + 0];
+                float b = W[2*wi + 1];
+                float c = f[2*fi + 0];
+                float d = f[2*fi + 1];
+                float temp[2] = { f[2*i + 0], f[2*i + 1] };
+                float Temp[2] = { a*c - b*d, b*c + a*d };
+                f[2*i + 0]  = temp[0] + Temp[0];
+                f[2*i + 1]  = temp[1] + Temp[1];
+                f[2*fi + 0] = temp[0] - Temp[0];
+                f[2*fi + 1] = temp[1] - Temp[1];
+            }
+        }
+        n *= 2;
+        a = a / 2;
+    }
+    free(W);
+}
+
+void FFT(float * f, int N, float d) {
+    transform(f, N);
+    for (int i = 0; i < N; i++) {
+        f[2*i + 0] *= d;
+        f[2*i + 1] *= d;
+    }
+}
+
+void FFT(float * src, float * dst, int N, float d) {
+    for (int i = 0; i < N; ++i) {
+        dst[2*i + 0] = src[i];
+        dst[2*i + 1] = 0.0f;
+    }
+    FFT(dst, N, d);
+}