Sound in Matlab & Nyquist’s Theorem

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Questions?

Coding (and other) book activities: are they graded?

No. They’re good practice for you, but I treat all the book’s interactive activities as optional.

Nyquist’s Theorem

The theorem: to correctly reproduce a sampled waveform, you must sample it at least twice per cycle (i.e., at a frequency at least double the highest frequency in the waveform).



Goal: Read a sound file into Matlab and then resample it to ever-lower sampling rates until we can hear Nyquist aliasing.

Reading Sounds

Relevant ideas from the reading

• wavread function reads .wav files into Matlab (but note: in the latest Matlab the function is now audioread)
• A typical use of audioread looks like [ySound,frequency] = audioread( 'filename.wav' )
• The amplitude of a wave controls its volume
• Sinusoidal waves make pure tones

Here’s what we did in Matlab to read and play a sound file:

>>[ ySound, freq ] = audioread( 'Vogelfaenger.wav' );
>> sound( ySound, freq )

Resampling

In other words, pick every 2nd sample, every 4th sample, etc.

Relevant ideas from the reading

• Matlab has a way to pick sub-vectors out of a vector
• For example, myArray( [3,4,5] ) would pick out elements 3, 4, and 5
• You can also use the colon operator to construct the indexing vector
• And you can replace elements with, e.g., myArray( [3,4,5] ) = [10,20,30]

Here’s how we resampled the music clip and played the results:

>> ySound2 = ySound( 2:2:length(ySound), : );
>> freq2 = freq / 2;
>> sound( ySound2, freq2 )
>> ySound12 = ySound( 1:12:length(ySound), : );
>> freq12 = freq/12;
>> sound( ySound12, freq12 )

Next

Plotting in Matlab

Read sections 6.3 and 6.4

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