我正在尝试破译隐藏在非常嘈杂(听起来像带有额外低无人机的白噪声)音频文件(.wav)中的消息。该消息是一个六位数字。我没有被告知噪音的任何细节。我尝试使用低通滤波器,希望消除大部分较高的频率可以让我听到数字,但是,我似乎也无法摆脱足够低的无人机来足够好地听到声音。我的尝试如下(最后包含了使用的函数'freq_space_low_pass_filter'):
[data, SampleRate, NbitsPerSample]=wavread('noisy_msg6.wav');
y=data(:,1); % we will work only with one channel in this demo
N=length(y); %number of sample points
t=( (1:N)*1/SampleRate ).'; % time spacing is 1/SampleRate and we want column vector
Y=fft(y);
spectrum_freq=fourier_frequencies(SampleRate, N);
Freq3db=100;
[spectrum_filtered,g_vs_freq]=freq_space_low_pass_filter(Y, SampleRate, Freq3db);
y_filtered=ifft(spectrum_filtered);
y_filtered=real(y_filtered);
wavwrite(y_filtered/(0.1+max(y_filtered)), SampleRate, NbitsPerSample, 'noisy_msg6_filtered.wav');
%%%%%%%%down sampling%%%%%%%%
indexes=(abs(spectrum_freq) < 10*Freq3db);
spectrum_freq_down_sampled = spectrum_freq(indexes);
spectrum_down_sampled = spectrum_filtered(indexes);
N_down_sampled = length(spectrum_down_sampled);
spectrum_down_sampled=spectrum_down_sampled*N_down_sampled/N;
SampleRate_down_sampled=SampleRate*N_down_sampled/N;
y_down_sampled=real(ifft(spectrum_down_sampled));
t_down_sampled = ( (1:N_down_sampled)*1/SampleRate_down_sampled ).';
sound(y_down_sampled, SampleRate_down_sampled)
function [spectrum_filtered,g]=freq_space_low_pass_filter(spectrum, SampleRate, Freq3db)
%% applies low pass filter in the frequency domain
% spectrum - result of fft on time series data (column vector is expected)
% SampleRate - measured in Hz, 1/dt where dt spacing of the points in time domain
% Freq3db - desired 3db roll off point in Hz
N=length(spectrum);
function G=filter_gain(freq, Freq3db)
G=1./(1+1i*freq/Freq3db); % this corresponds to low pass RC filter
end
spectrum_freq=fourier_frequencies(SampleRate, N);
% calculate filter gain for each spectrum frequency
g=filter_gain(spectrum_freq, Freq3db);
spectrum_filtered=spectrum.*g;
结尾
任何和所有的帮助将不胜感激。谢谢!