How to use envelope function in Matlab

Question

The following Matlab code generate a sound but it contain tak tak like sound which can be easily heard.Can someone removes this noise by using envelope function.

  Fs=44100;
  T=1/Fs;
  M=zeros(1,88);
  for I=7:88
    M(I)=round(36.8*(2^(1/12))^(I-6));
    end
    signal=[];
    FrTm=[50,3;50,3;52,3;54,3;50,3;54,3;52,3;45,3;50,3;50,3;52,3;54,3;50,6;
    49,3;1,3;50,3;50,3;52,3;54,3;55,3;54,3;52,3;50,3;49,3;45,3;47,3;49,3;50,6;
    50,3;1,3;47,5;49,1;47,3;45,3;47,3;49,3;50,3;1,3;45,5;47,1;45,3;43,3;42,6;
    45,3;1,3;47,5;49,1;47,3;45,3;47,3;49,3;50,3;47,3;45,3;50,3;49,3;52,3;50,6;
    50,6];
    for i=1:length(FrTm)
      x=FrTm(i,1);
      y=FrTm(i,2);
      F=M(x);
      time=0:1/Fs:y/18;
      sinewave=*sin(2*pi*10*F*time);

      signal=[signal sinewave];

     end

     stem(signal)
     sound(signal,Fs)

Answer 1

Here are two possible solutions. They are not perfect since the tak-tak is still here but it is much lower.

1. Applying a high-pass filter to remove the annoying sound which seems to be low frequency

   Fs=44100;
   T=1/Fs;
   M=zeros(1,88);
   for I=7:88
       M(I)=round(36.8*(2^(1/12))^(I-6));
   end
   signal=[];
   FrTm=[50,3;50,3;52,3;54,3;50,3;54,3;52,3;45,3;50,3;50,3;52,3;54,3;50,6;
   49,3;1,3;50,3;50,3;52,3;54,3;55,3;54,3;52,3;50,3;49,3;45,3;47,3;49,3;50,6;
   50,3;1,3;47,5;49,1;47,3;45,3;47,3;49,3;50,3;1,3;45,5;47,1;45,3;43,3;42,6;
   45,3;1,3;47,5;49,1;47,3;45,3;47,3;49,3;50,3;47,3;45,3;50,3;49,3;52,3;50,6;
   50,6];
   for i=1:length(FrTm)
       x=FrTm(i,1);
       y=FrTm(i,2);
       F=M(x)/4;
       time=0:1/Fs:y/18;
       sinewave=sin(2*pi*10*F*time);
   
       signal=[signal sinewave];
   
   end
   
   % Creating high-pass filter with passband frequency of 1000 Hz (may be too high)
   hpFilt = designfilt('highpassiir','FilterOrder',8, ...
       'PassbandFrequency',1000,'PassbandRipple',0.2, ...
   'SampleRate',Fs);
   % Filtering sound
   signal = filter(hpFilt,signal);
   
   sound(signal,Fs)
   

2. Taking the last value from each generated sine wave and finding the corresponding phase for the next sine wave, to make the sinus as continuous as possible

    Fs=44100;
    T=1/Fs;
    M=zeros(1,88);
    for I=7:88
        M(I)=round(36.8*(2^(1/12))^(I-6));
    end
    signal=[];
    FrTm=[50,3;50,3;52,3;54,3;50,3;54,3;52,3;45,3;50,3;50,3;52,3;54,3;50,6;
      49,3;1,3;50,3;50,3;52,3;54,3;55,3;54,3;52,3;50,3;49,3;45,3;47,3;49,3;50,6;
   50,3;1,3;47,5;49,1;47,3;45,3;47,3;49,3;50,3;1,3;45,5;47,1;45,3;43,3;42,6;
   45,3;1,3;47,5;49,1;47,3;45,3;47,3;49,3;50,3;47,3;45,3;50,3;49,3;52,3;50,6;
   50,6];
    previous_end_val = 0;
    for i=1:length(FrTm)
        x=FrTm(i,1);
        y=FrTm(i,2);
        F=M(x)/4;
        time=0:1/Fs:y/18;
   
        % Calculating required phase to match the end of previous sinewave
        phi = asin(previous_end_val);
        % Generating sinewave with phase phi
        sinewave=sin(2*pi*10*F*time + phi);
        previous_end_val = sinewave(end);
   
        signal=[signal sinewave];
   
    end
   
    sound(signal,Fs)
   

The first solution is not perfect: if you take too high passband frequency you could not hear the lowest audible frequencies. The second solution is faster and more elegant. Please ask if there is a method you don't understand.