c++实现LPCC算法

根据提供的引用[1]，LPCC算法是一种声音识别算法，可以使用C++实现。下面是一个简单的C++实现LPCC算法的例子：

#include <iostream>
#include <cmath>
#include <vector>
#include <Eigen/Dense>

using namespace std;
using namespace Eigen;

// 计算倒谱系数
vector<double> calcLPCC(vector<double> &signal, int p, int n) {
    // 预加重
    for (int i = 1; i < signal.size(); i++) {
        signal[i] -= 0.95 * signal[i - 1];
    }

    // 分帧
    int frameSize = n;
    int frameShift = n / 2;
    int numFrames = ceil((double) signal.size() / frameShift);
    MatrixXd frames(numFrames, frameSize);
    for (int i = 0; i < numFrames; i++) {
        for (int j = 0; j < frameSize; j++) {
            int index = i * frameShift + j;
            if (index < signal.size()) {
                frames(i, j) = signal[index];
            } else {
                frames(i, j) = 0;
            }
        }
    }

    // 加窗
    VectorXd window(frameSize);
    for (int i = 0; i < frameSize; i++) {
        window(i) = 0.54 - 0.46 * cos(2 * M_PI * i / (frameSize - 1));
    }
    for (int i = 0; i < numFrames; i++) {
        for (int j = 0; j < frameSize; j++) {
            frames(i, j) *= window(j);
        }
    }

    // 傅里叶变换
    MatrixXcd spectrum(numFrames, frameSize);
    for (int i = 0; i < numFrames; i++) {
        VectorXd frame = frames.row(i);
        VectorXcd spectrumFrame = VectorXcd::Zero(frameSize);
        for (int j = 0; j < frameSize; j++) {
            for (int k = 0; k < frameSize; k++) {
                spectrumFrame(j) += frame(k) * exp(-2 * M_PI * j * k / frameSize);
            }
        }
        spectrum.row(i) = spectrumFrame;
    }

    // 梅尔滤波器组
    int numFilters = 20;
    int sampleRate = 16000;
    int fftSize = frameSize;
    int lowFreq = 0;
    int highFreq = sampleRate / 2;
    MatrixXd filterBank(numFilters, fftSize / 2 + 1);
    for (int i = 0; i < numFilters; i++) {
        double melLow = 1127 * log(1 + (lowFreq + i * (highFreq - lowFreq) / (numFilters + 1)) / 700);
        double melHigh = 1127 * log(1 + (lowFreq + (i + 2) * (highFreq - lowFreq) / (numFilters + 1)) / 700);
        for (int j = 0; j < fftSize / 2 + 1; j++) {
            double freq = j * sampleRate / fftSize;
            if (freq < lowFreq || freq > highFreq) {
                filterBank(i, j) = 0;
            } else {
                double mel = 1127 * log(1 + freq / 700);
                if (mel < melLow) {
                    filterBank(i, j) = 0;
                } else if (mel < (melLow + melHigh) / 2) {
                    filterBank(i, j) = 2 * (mel - melLow) / (melHigh - melLow);
                } else if (mel < melHigh) {
                    filterBank(i, j) = 2 * (melHigh - mel) / (melHigh - melLow);
                } else {
                    filterBank(i, j) = 0;
                }
            }
        }
    }

    // 梅尔倒谱系数
    MatrixXd mfcc(numFrames, p);
    for (int i = 0; i < numFrames; i++) {
        VectorXcd spectrumFrame = spectrum.row(i);
        VectorXd powerSpectrumFrame = spectrumFrame.array().abs2();
        VectorXd filteredSpectrumFrame = filterBank * powerSpectrumFrame.segment(0, fftSize / 2 + 1);
        VectorXd logSpectrumFrame = filteredSpectrumFrame.array().log();
        VectorXd dctSpectrumFrame = VectorXd::Zero(p);
        for (int j = 0; j < p; j++) {
            for (int k = 0; k < numFilters; k++) {
                dctSpectrumFrame(j) += logSpectrumFrame(k) * cos(M_PI * j * (k + 0.5) / numFilters);
            }
        }
        mfcc.row(i) = dctSpectrumFrame;
    }

    // LPC系数
    MatrixXd lpc(numFrames, p + 1);
    for (int i = 0; i < numFrames; i++) {
        VectorXd mfccFrame = mfcc.row(i);
        VectorXd autocorrFrame = VectorXd::Zero(p + 1);
        for (int j = 0; j <= p; j++) {
            for (int k = 0; k < frameSize - j; k++) {
                autocorrFrame(j) += frames(i, k) * frames(i, k + j);
            }
        }
        MatrixXd toeplitzMatrix(p, p);
        for (int j = 0; j < p; j++) {
            for (int k = 0; k < p; k++) {
                toeplitzMatrix(j, k) = autocorrFrame(abs(j - k));
            }
        }
        VectorXd lpcFrame = toeplitzMatrix.fullPivHouseholderQr().solve(-autocorrFrame.tail(p));
        lpc.row(i) << 1, lpcFrame.transpose();
    }

    // LPCC系数
    MatrixXd lpcc(numFrames, p);
    for (int i = 0; i < numFrames; i++) {
        VectorXd lpcFrame = lpc.row(i);
        VectorXd lpccFrame = VectorXd::Zero(p);
        for (int j = 0; j < p; j++) {
            for (int k = 0; k < p - j; k++) {
                lpccFrame(j) += (k + 1) * lpcFrame(k + j) * mfcc(i, k);
            }
        }
        lpcc.row(i) = lpccFrame;
    }

    // 归一化
    for (int i = 0; i < p; i++) {
        double mean = lpcc.col(i).mean();
        double std = sqrt((lpcc.col(i).array() - mean).square().sum() / numFrames);
        lpcc.col(i) = (lpcc.col(i).array() - mean) / std;
    }

    // 取平均
    vector<double> result(p);
    for (int i = 0; i < p; i++) {
        result[i] = lpcc.col(i).mean();
    }

    return result;
}

int main() {
    vector<double> signal = {0.707, 0.707, -0.707, -0.707};
    vector<double> lpcc = calcLPCC(signal, 10, 4);
    for (int i = 0; i < lpcc.size(); i++) {
        cout << lpcc[i] << " ";
    }
    cout << endl;
    return 0;
}