音频相关的处理函数

std::vector<double> 
hann_windows(int window_length = N_FFT,bool periodic = true)  
{  
	int N = window_length;  
	if (periodic) {  
		N = window_length + 1; // 如果是周期性窗口，窗口长度加1  
	}  
	auto M = N - 1;  
	auto double_PI = 2 * M_PI;  
	std::vector<double> window(window_length);  
	for (int n = 0; n < window_length; ++n) {  
		double normalized_n = static_cast<double>(n) / M;  
		window[n] = 0.5 - 0.5 * cos( double_PI * normalized_n);  
		// 或者使用等效的公式：  
		// window[n] = pow(sin(M_PI * normalized_n), 2);  
	}  
	  
	return window;  
}