Nyquist’s Theorem

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• Questions?
• Nyquist’s Theorem
  • Video
    • Picking values from a wave…?
      • = sampling
      • Can see it in zoomed-in view of sound wave in a sound-processing program
        
    • Nyquist: must sample wave at least twice per cycle in order to reproduce wave
      
  • Example
    • (See section 7.2 of the textbook for information on working with sound in Matlab)
      

      >> [s,f] = audioread( 'Vogelfaenger.wav' );
      >> sound( s, f );
      >> s2 = s( 1:2:end, 1:2 );   % The sound sampled at half the original rate
      >> sound( s2, f/2 );
      >> s8 = s2( 1:4:end, 1:2 );  % Sampled at 1/8 original rate
      >> sound(s8,f/8);
      >> f/8                       % Aliasing could be a threat at 1/8 original rate
      ans =
         5.5125e+03
      >> s16 = s8( 1:2:end, 1:2 ); % 1/16 original rate
      >> f/16                      % Anything over about 1300 cps will alias
      ans =
         2.7562e+03
      >> sound( s16, f/16 );
      >> sound( s2, f );           % Play sound with incorrectly high sampling rate

• Vector lab
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  • Plotting
  • Read sections 6.1 and 6.2

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