Digital Audio Sampling

1. Digital Audio Sampling Digital vs. Analog (revisited), Sampling, Sample Rate, Bit Depth, and MORE! Music Tech 1, Fall 2012

2. Analog vs. Digital • What are the differences between analog and digital audio? • Analog is continuous, Digital is discrete • Analog is an infinite signal; Digital is a finite signal • Analog is measured in voltage; Digital is measured using binary digits 0 and 1

3. Discrete Signal • What does it mean that a digital signal is discrete • A discrete signal represented by a series of quantities or values. • What do we call these values? SAMPLES. • Sample = value, or set of values at a point in time and/or space

4. Samples • When capturing an analog signal it is first sampled, meaning it is “cut” into smaller segments according to some kind of time-point value. Each of these time-points are an individual sample. • A sampled signal is made up of numerous samples.

5. Samples

6. Sampling • The process of sampling is as follows: • Begin with a continuous electrical analog signal (or an acoustic signal) • Sample the signal using an analog-to-digital converter (ADC) • Convert the sampled digital signal into something that can be heard using a digial-to-analog converter (DAC). • The process of recording with a microphone and playing the sound back through speakers is an example of sampling. Microphones act as the ADC and the speakers and audio interface act as the DAC

7. Some sampling terms • These are some terms that you will need to know about sampling • DAC • ADC • Channel • Sampling rate • Nyquist theorem/Nyquist frequency • Bit • Bit depth • Bit rate

8. ADC, DAC, Channel • ADC = analog-to-digital converter; takes in a continuous analog signal and converts it into a discrete digital signal • DAC = digital-to-analog converter; takes a sampled/discrete digital audio signal and converts it to a physical voltage value and transmits it through speakers so we can hear it • Channels = refers to the number of output channels from a DAC; can be mono (1 channel) or stereo (2 channels) • ADC and DAC are more involved than this, but we will get into the nuts and bolts later in the music tech sequence

9. Sampling rate • Sampling rate – number of samples taken per second • Represented as a frequency value • Common sampling rates = 44.1 kHz, 48 kHz, 96 kHz • The sampling rate is generally twice the value of the highest frequency that one is attempting to capture/recreate • This is because of the Nyquist theorem

10. Nyquist theorem • The Nyquist theorem states that in order to capture and recreate an analog signal accurate, one must sample the signal at no less than twice the value of the highest frequency that is being sampled. • This 2x frequency is referred to as the Nyquist frequency • What is the range of human hearing? • Because the highest we can hear is 20,000 Hz, sampling at 44.1 kHz is well beyond 2x what we would ever want to capture, 44.1 is often the highest sampling rate that one would really need to use; • Higher sampling rates will yield higher resolution

11. Bit depth • Bit = short form for “binary digit” • Refers to each 0 and 1 as a bit • Bit depth is the number of bits in each sample • Bit depth also represents the resolution of the sampled sound • When thinking of bit depth think of it as both the number of bits/sample and as resolution. To describe it as one or the other is incomplete. • Common bit depths = 8bit, 16bit, 24bit

12. Bit rate • Bit rate is the total amount of information transmitted or received during sampling • Bit rate is really the combination of all other parameters of sampling. • Bit rate is obtained by multiplying the sampling rate with the bit depth and the number of output channels (either 1 or 2) BR = SR x BD x CH

13. Types of sampling • Three types of sampling • Oversampling – sampling above the Nf • Undersampling – sampling below the Nf • Critical sampling – sampling right at the Nf

14. Oversampling • Guarantees that all frequencies in the signal will be captured accurately. • Reduces noise, avoids aliasing and foldover and improves overall resolution • Oversampling is most desired when sampling and using digital audio (44.1 is an example of oversampling)

15. Undersampling • Sampling below the Nyquist frequency • Undersampling can result in lower resolution of sampled audio and can result in aliasing (meaning the audio samples become indistinguishable from one another) and can cause distortion • In certain types of audio sampling, undersampling is desired, but we will not be working with undersampling, and in general it should be thought of as an undesirable method of sampling

16. Critical sampling • Critical sampling is sampling directly at the Nyquist frequency. • Critical sampling will often not have a damaging affect on your sampled audio, but sampling right at the Nyquist frequency can cause aliasing and foldover (when the signal is moving faster than the sampling rate), or poorer resolution of the sampled audio. • Generally it is better to sample above the Nyquist frequency when possible and avoid critical sampling.

17. What to know? • We will discuss all of this in more detail in music tech 2, but, for the time being, be able to define and explain the following terms: • DAC • ADC • Channel • Sampling rate • Nyquist theorem/Nyquist frequency • Bit • Bit depth • Bit rate