语音信号处理，包括语音信号的获取，谱分析，滤波

%% 读取信号并观察采样频率 [highFreqNoise, Fs_noise] = audioread('highFrequencyNoise.wav'); [voicePlusNoise, Fs_voice] = audioread('voiceWithHighFrequencyNoise.wav'); % 绘制信号 t_noise = (0:length(highFreqNoise)-1)/Fs_noise; t_voice = (0:length(voicePlusNoise)-1)/Fs_voice; figure; % 创建新图形窗口 subplot(2,1,1); plot(t_noise, highFreqNoise); title('高频噪声信号'); xlabel('时间t'); ylabel('幅值'); % 高频噪声信号的频谱图 Y_noise = fft(highFreqNoise); P2_noise = abs(Y_noise/length(highFreqNoise)); P1_noise = P2_noise(1:length(highFreqNoise)/2+1); f_noise = Fs_noise*(0:(length(highFreqNoise)/2))/length(highFreqNoise); subplot(2,1,2); plot(f_noise, P1_noise); title('高频噪声信号频谱'); xlabel('频率(Hz)'); ylabel('幅度'); figure; % 创建新图形窗口 subplot(2,1,1); plot(t_voice, voicePlusNoise); title('高频噪声+人声'); xlabel('时间t'); ylabel('幅值'); % 高频噪声信号+人声的频谱图 Y_noise = fft(voicePlusNoise); P4_noise = abs(Y_noise/length(voicePlusNoise)); P3_noise = P4_noise(1:length(voicePlusNoise)/2+1); f_noise = Fs_noise*(0:(length(voicePlusNoise)/2))/length(voicePlusNoise); subplot(2,1,2); plot(f_noise, P3_noise); title('高频噪声信号+人声频谱'); xlabel('频率(Hz)'); ylabel('幅度'); %% 信号的运算 % 假设已经有了两个信号 highFreqNoise 和 voicePlusNoise，以及它们的采样频率 Fs_noise 和 Fs_voice % 这里我们使用之前的代码段中定义的操作 % 反褶（翻转）操作 flippedSignal = flipud(voicePlusNoise); t_flipped = (0:length(flippedSignal)-1)/Fs_voice; % 更新时间向量 % 平移（例如延迟0.5秒） delay = 0.5; shiftedSignal = circshift(voicePlusNoise, round(Fs_voice*delay)); t_shifted = (0:length(shiftedSignal)-1)/Fs_voice; % 更新时间向量 % 相加 % 确保两个信号长度一致 minLength = min(length(highFreqNoise), length(voicePlusNoise)); highFreqNoise1 = highFreqNoise(1:minLength); voicePlusNoise1 = voicePlusNoise(1:minLength); addedSignal = highFreqNoise1 + voicePlusNoise1; % 由于修改了信号长度，需要重新计算 t_voice t_voice = (0:minLength-1)/Fs_voice; % 相乘 multipliedSignal = highFreqNoise1 .* voicePlusNoise1; t_multiplied = (0:length(multipliedSignal)-1)/Fs_voice; % 更新时间向量 % 绘制这些操作的结果 figure; % 创建新图形窗口 subplot(4,1,1); plot(t_flipped, flippedSignal); title('反褶'); xlabel('Time (seconds)'); ylabel('Amplitude'); subplot(4,1,2); plot(t_shifted, shiftedSignal); title('平移'); xlabel('Time (seconds)'); ylabel('Amplitude'); subplot(4,1,3); plot(t_voice, addedSignal); title('相加'); xlabel('Time (seconds)'); ylabel('Amplitude'); subplot(4,1,4); plot(t_multiplied, multipliedSignal); title('相乘'); xlabel('Time (seconds)'); ylabel('Amplitude'); % 创建新图形窗口 figure; % 反褶信号的频谱图 Y_flipped = fft(flippedSignal); P2_flipped = abs(Y_flipped/length(flippedSignal)); P1_flipped = P2_flipped(1:length(flippedSignal)/2+1); f_flipped = Fs_voice*(0:(length(flippedSignal)/2))/length(flippedSignal); subplot(4,1,1); plot(f_flipped, P1_flipped); title('反褶的频谱'); xlabel('Frequency (Hz)'); ylabel('|P1(f)|'); % 平移信号的频谱图 Y_shifted = fft(shiftedSignal); P2_shifted = abs(Y_shifted/length(shiftedSignal)); P1_shifted = P2_shifted(1:length(shiftedSignal)/2+1); f_shifted = Fs_voice*(0:(length(shiftedSignal)/2))/length(shiftedSignal); subplot(4,1,2); plot(f_shifted, P1_shifted); title('平移的频谱'); xlabel('Frequency (Hz)'); ylabel('|P1(f)|'); % 相加信号的频谱图 Y_added = fft(addedSignal); P2_added = abs(Y_added/length(addedSignal)); P1_added = P2_added(1:length(addedSignal)/2+1); f_added = Fs_voice*(0:(length(addedSignal)/2))/length(addedSignal); subplot(4,1,3); plot(f_added, P1_added); title('相加的频谱'); xlabel('Frequency (Hz)'); ylabel('|P1(f)|'); % 相乘信号的频谱图 Y_multiplied = fft(multipliedSignal); P2_multiplied = abs(Y_multiplied/length(multipliedSignal)); P1_multiplied = P2_multiplied(1:length(multipliedSignal)/2+1); f_multiplied = Fs_voice*(0:(length(multipliedSignal)/2))/length(multipliedSignal); subplot(4,1,4); plot(f_multiplied, P1_multiplied); title('相乘的频谱'); xlabel('Frequency (Hz)'); ylabel('|P1(f)|'); %% 傅里叶级数合成 % % 例：生成一个简单的周期信号 % f_synthetic = 2000; % 以 2000 Hz 为例 % syntheticSignal = sin(2*pi*f_synthetic*t_noise); % % % 傅里叶变换 % Y_synthetic = fft(syntheticSignal); % P2_synthetic = abs(Y_synthetic/length(syntheticSignal)); % P1_synthetic = P2_synthetic(1:length(syntheticSignal)/2+1); % f_synthetic = Fs_noise*(0:(length(syntheticSignal)/2))/length(syntheticSignal); % figure; % 创建新图形窗口 % plot(f_synthetic, P1_synthetic); % title('傅里叶级数合成'); % xlabel('Frequency (Hz)'); % ylabel('|P1(f)|'); %% 设计滤波器并去噪 % 设计低通滤波器 % 指定截止频率 cutoff_freq = 1000; % 以 1000 Hz 为例，根据需要调整 order = 20; % 滤波器阶数，可以根据需要调整 % 设计滤波器 lpFilt = designfilt('lowpassfir', 'FilterOrder', order, ... 'CutoffFrequency', cutoff_freq, ... 'SampleRate', Fs_voice); % 应用滤波器 filtered_voice_lp = filter(lpFilt, voicePlusNoise); % 绘制去噪后的信号 t_filtered_lp = (0:length(filtered_voice_lp)-1)/Fs_voice; figure; subplot(2,1,1); plot(t_filtered_lp, filtered_voice_lp); title('经过低通滤波器的信号时域谱'); xlabel('Time (seconds)'); ylabel('Amplitude'); % 对滤波后的信号进行快速傅里叶变换 Y_filtered_voice_lp = fft(filtered_voice_lp); L = length(filtered_voice_lp); % 信号的长度 % 计算双边频谱 P2 和单边频谱 P1 P2 = abs(Y_filtered_voice_lp/L); P1 = P2(1:L/2+1); P1(2:end-1) = 2*P1(2:end-1); % 定义频率轴 f = Fs_voice*(0:(L/2))/L; % 绘制频谱图 subplot(2,1,2); plot(f, P1) title('经过低通滤波器的信号频域谱') xlabel('Frequency (Hz)') ylabel('|P1(f)|') %% 播放去噪后的音频 % 播放去噪后的音频 disp('Playing low-pass filtered voice signal...'); sound(filtered_voice_lp, Fs_voice); pause(length(filtered_voice_lp)/Fs_voice + 1);