3.17 - Digital Representation of Sound

Questions about digital representation of sound in terms of sampling rate and resolution, operation of an ADC and a DAC, Nyquist theorem, calculating sound sample sizes, MIDI and event messages.

What is meant by continuous?

An infinite number of possible values.

What is meant by discrete?

A fixed number of possible values.

What is meant by sample rate?

The frequency you record the amplitude of the sound measured in hertz (Hz).

What is meant by audio bit depth?

Number of bits allocated to represent the amplitude per sample.

How can you improve the accuracy of an audio recording?

• Increase sample rate

• Increase audio bit depth

What’s a disadvantage to increasing the sample rate?

Larger file size.

What’s the general formula to calculate sound sample size?

• The number of samples per second x The number of bits per sample x The length of the sample in seconds

• Sample Rate x Audio Bit Depth x Length of sample in seconds

Explain how an ADC converts an analogue signal to digital.

1. A microphone generates an analogue signal

2. The ADC samples the analogue signal at regular intervals (the sample rate), measuring the amplitude at each point

3. Each amplitude value is quantized - rounded to the nearest value representable within the bit depth

4. The quantized value is encoded as a binary number

5. This produces a stream of binary values that can be stored or processed digitally

Explain how a DAC converts a digital signal to an analogue signal.

1. Each binary value of a sample is converted into a corresponding voltage level

2. These voltage levels produce a stepped/staircase waveform

3. A low-pass filter smooths this into a continuous analogue signal

4. The signal is sent to an amplifier and then to a speaker to produce sound

How does increasing the frequency of a sound change its pitch?

The pitch becomes higher.

What’s the minimum sample rate that should be used in order to produce an accurate recording?

At least double the highest frequency in the original signal.

What’s Nyquist’s Theorem?

Nyquist’s Theorem states for an accurate representation of an analogue sound signal in digital form, the sample rate must be at least twice the frequency of the highest frequency in the sound signal.

Give an example of where Nyquist’s Theorum is used.

• Human hearing ranges up to ~20,000 Hz, so CD audio uses a sample rate of 44,100 Hz

If the highest frequency in a recording is 12KHz, what should the minimum sample rate be to satisfy Nyquist’s Theorem?

24KHz

What do event messages from a MIDI controller specify?

• Pitch

• Duration of a note

• Timbre

• Vibrato

• Volume changes

• Velocity

What does a MIDI file contain?

• A list of instructions from event messages describing how music should be played, rather than actual audio data

• When played back, a MIDI device or software synthesises the sound based on these instructions

• Because it stores instructions rather than audio, MIDI files are very small compared to WAV or MP3

What is an advantage of MIDI when composing music?

• Each note in a MIDI file can have an instrument specified to it

• This means a single MIDI file can simulate a full orchestra by assigning different instruments to different notes or channels

• Instruments can be swapped easily without re-recording, as no actual audio is stored

• This makes MIDI extremely flexible for composers