Digital audio sampling is the process of turning a changing sound wave into a list of numbers a computer can store, edit, and play back. A microphone first converts air pressure changes into an analog voltage that varies smoothly with time. The computer then measures that voltage at evenly spaced moments, creating samples.
This matters because every song file, podcast, video soundtrack, and music app depends on accurate sampling.
Key Facts
- Sampling rate is the number of samples recorded each second, measured in hertz: 44,100 Hz means 44,100 samples per second.
- Bit depth is the number of bits used to store each sample, and it controls the number of possible amplitude levels: levels = 2^bits.
- Nyquist theorem: to record a frequency f accurately, the sampling rate must be at least 2f.
- The highest frequency that can be captured without aliasing is the Nyquist frequency: f_N = sampling rate / 2.
- CD audio uses 44.1 kHz sampling and 16-bit depth, giving 65,536 possible amplitude values per sample.
- Uncompressed audio data rate is approximately data rate = sampling rate × bit depth × number of channels.
Vocabulary
- Analog signal
- An analog signal is a smoothly varying signal that can have any value within a continuous range.
- Sample
- A sample is one measured value of a sound wave's amplitude at a specific instant in time.
- Sampling rate
- Sampling rate is how many times per second an analog sound wave is measured during recording.
- Bit depth
- Bit depth is the number of binary digits used to store each sample's amplitude.
- Aliasing
- Aliasing is a distortion that occurs when a signal is sampled too slowly, causing high frequencies to appear as false lower frequencies.
Common Mistakes to Avoid
- Confusing sampling rate with bit depth is wrong because sampling rate controls time resolution while bit depth controls amplitude resolution.
- Assuming a higher sampling rate always makes audio sound better is wrong because once the needed frequency range is captured, other factors like microphone quality and compression may matter more.
- Forgetting the factor of 2 in the Nyquist theorem is wrong because a wave must be sampled at least twice per cycle to avoid aliasing.
- Thinking binary numbers are the sound itself is wrong because they are stored measurements that must be converted back into a changing voltage to drive a speaker.
Practice Questions
- 1 A digital recorder samples audio at 48,000 Hz. How many samples are recorded in 10 seconds of mono audio?
- 2 A sound file uses 44,100 Hz sampling, 16-bit depth, and 2 channels. What is its uncompressed data rate in bits per second?
- 3 A recorder samples at 8,000 Hz. Explain whether it can accurately capture a 5,000 Hz tone and identify the problem if it cannot.