add cola_check and webrtc window

Author: wangwei

COLA_check.m

@@ -0,0 +1,23 @@
+% # COLA check:
+% # from scipy import signal
+% # print(signal.check_COLA(signal.windows.hamming(400,sym=False),400,300))
+% #
+frameLength = 256;
+overlap = 128;
+inc = frameLength - overlap;
+N_FFT = 512;
+
+window = sqrt(hamming(frameLength+1));
+window = window(1:frameLength);
+% window = KaiserBesselDerived(1.5,256);
+
+win = zeros(1,inc*9+overlap)';
+frameNum = fix((length(win)-overlap)/inc);
+win_ind = zeros(frameNum,length(win));
+figure,
+for n = 1:frameNum
+    win_ind(n,(n-1)*inc+1:(n-1)*inc+frameLength) = window.^2;
+    hold on,plot(win_ind(n,:))
+end
+win_sum = sum(win_ind);  % overlap-add window
+hold on,plot(win_sum);

KaiserBesselDerived.m

@@ -0,0 +1,34 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%  webrtc window
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function window = KaiserBesselDerived(alpha,length)
+
+    half = fix((length + 1) / 2);
+    sum = 0.0;
+    window = zeros(1,length);
+
+    for i = 0: half
+    
+        r = (4.0 * i) / length - 1.0;
+        sum = sum + I0(pi * alpha * sqrt(1.0 - r * r));
+        window(i+1) = sum;
+    end
+    i = length - 1:-1:half;
+%     for i = length - 1; i >= half; --i)
+    
+        window(length - i) = sqrt(window(length - i) / sum);
+        window(i+1) = window(length - i);
+%     end
+    if (mod(length,2) == 1)
+    
+        window(half - 1) = sqrt(window(half - 1) / sum);
+    end
+    
+end
+function i0 = I0(x)
+
+    y = x / 3.75;
+
+    y = y*y;
+    i0 = 1.0 + y * (3.5156229 + y * (3.0899424 + y * (1.2067492 + y * (0.2659732 + y * (0.360768e-1 + y * 0.45813e-2)))));
+end