Sampling (signal processing) — Safekipedia Adventurer

In signal processing, sampling is a way to change a smooth flow of information, like a sound wave, into a set of separate numbers or "samples." Each sample shows the value of the signal at one moment in time. This is very useful because it lets computers store, process, and send complex signals.

A sampler takes these snapshots from the continuous signal. In an ideal situation, each sample matches the value of the original signal at that exact time. This helps us understand how digital audio, images, and other data can be made from real-world signals.

From these samples, the original signal can often be brought back, if the samples were taken fast enough. This maximum rate is called the Nyquist limit. When we use a special reconstruction filter, we can get a close copy of the original signal. This ability to change between continuous and separate forms is important for many technologies we use every day, like music players and mobile phones, making sampling a key idea in sound wave and digital communication.

Theory

Sampling is a way to change a continuous signal, like a sound wave, into a series of numbers. We do this by measuring the signal at regular time intervals. These intervals are called the sampling interval or sampling period.

The number of measurements we take each second is called the sampling frequency or sampling rate. It is measured in samples per second, sometimes called hertz. For example, 48 kHz means we take 48,000 samples every second.

When we want to change these samples back into a continuous signal, we use special math called interpolation. To prevent mistakes, signals are often passed through a low-pass filter before sampling. This helps make sure the reconstructed signal looks like the original one.

Practical considerations

Devices called analog-to-digital converters (ADCs) take samples of a continuous signal. Because of physical limits, these devices cannot perfectly copy the original signal. This leads to something called distortion.

Some types of distortion include aliasing, where higher frequencies look like lower ones; aperture error, which happens because the sample is an average over time; jitter, a shift in timing; and noise, random changes in the signal. Other distortions can come from the ADC’s limited speed (slew rate limit error) or from quantization, where the signal is rounded to a fixed number of levels. Methods like oversampling can help reduce some errors, but they also have limits and costs.

Applications

Digital audio systems use a method called pulse-code modulation (PCM) to change sound waves into numbers, or samples. These samples record the sound at certain times, so computers can store and play back audio. For recording music or other sounds people can hear — from 20 to 20,000 Hz — common sampling rates are 44.1 kHz (used for CDs), 48 kHz, 88.2 kHz, or 96 kHz. Higher sampling rates, like 96 kHz or 192 kHz, help make the sound clearer.

Video also uses sampling to change moving images into digital data. Standard-definition TV uses either 720 by 480 pixels (as in US NTSC systems) or 720 by 576 pixels (as in UK PAL systems). High-definition TV uses formats like 720p, 1080i, and 1080p, which have more pixels and sharper images. In digital video, the sampling rate relates to how many frames are shown each second, with common rates being 50 Hz for PAL and about 59.94 Hz for NTSC.

In 3D sampling, a grid of tiny cubes called voxels is used to make three-dimensional images from medical scans like X-ray computed tomography (CT), magnetic resonance imaging (MRI), and positron emission tomography (PET), as well as in other areas like seismic studies.

Sampling rate	Use
5,512.5 Hz	Supported in Flash.
8,000 Hz	Telephone and encrypted walkie-talkie, wireless intercom and wireless microphone transmission; adequate for human speech but without sibilance (ess sounds like eff (/s/, /f/)).
11,025 Hz	One quarter the sampling rate of audio CDs; used for lower-quality PCM, MPEG audio and for audio analysis of subwoofer bandpasses.
16,000 Hz	Wideband frequency extension over standard telephone narrowband 8,000 Hz. Used in most modern VoIP and VVoIP communication products.
22,050 Hz	One half the sampling rate of audio CDs; used for lower-quality PCM and MPEG audio and for audio analysis of low-frequency energy. Suitable for digitizing early 20th century audio formats such as 78s and AM Radio.
32,000 Hz	miniDV digital video camcorder, video tapes with extra channels of audio (e.g. DVCAM with four channels of audio), DAT (LP mode), Germany's Digitales Satellitenradio, NICAM digital audio, used alongside analogue television sound in some countries. High-quality digital wireless microphones. Suitable for digitizing FM radio.
37,800 Hz	CD-XA audio
44,055.9 Hz	Used by digital audio locked to NTSC color video signals (3 samples per line, 245 lines per field, 59.94 fields per second = 29.97 frames per second).
44,100 Hz	Audio CD, also most commonly used with MPEG-1 audio (VCD, SVCD, MP3). Originally chosen by Sony because it could be recorded on modified video equipment running at either 25 frames per second (PAL) or 30 frame/s (using an NTSC monochrome video recorder) and cover the 20 kHz bandwidth thought necessary to match professional analog recording equipment of the time. A PCM adaptor would fit digital audio samples into the analog video channel of, for example, PAL video tapes using 3 samples per line, 588 lines per frame, 25 frames per second.
47,250 Hz	world's first commercial PCM sound recorder by Nippon Columbia (Denon)
48,000 Hz	The standard audio sampling rate used by professional digital video equipment such as tape recorders, video servers, vision mixers and so on. This rate was chosen because it could reconstruct frequencies up to 22 kHz and work with 29.97 frames per second NTSC video, as well as 25 frame/s, 30 frame/s and 24 frame/s systems. With 29.97 frame/s systems, it is necessary to handle 1601.6 audio samples per frame, delivering an integer number of audio samples only every fifth video frame. Also used for sound with consumer video formats like DV, digital TV, DVD, and films. The professional serial digital interface (SDI) and High-definition Serial Digital Interface (HD-SDI) used to connect broadcast television equipment together use this audio sampling frequency. Most professional audio gear uses 48 kHz sampling, including mixing consoles, and digital recording devices.
50,000 Hz	First commercial digital audio recorders from the late 70s from 3M and Soundstream.
50,400 Hz	Sampling rate used by the Mitsubishi X-80 digital audio recorder.
64,000 Hz	Uncommonly used, but supported by some hardware and software.
88,200 Hz	Sampling rate used by some professional recording equipment when the destination is CD (multiples of 44,100 Hz). Some pro audio gear uses (or is able to select) 88.2 kHz sampling, including mixers, EQs, compressors, reverb, crossovers, and recording devices.
96,000 Hz	DVD-Audio, some LPCM DVD tracks, BD-ROM (Blu-ray Disc) audio tracks, HD DVD (High-Definition DVD) audio tracks. Some professional recording and production equipment is able to select 96 kHz sampling. This sampling frequency is twice the 48 kHz standard commonly used with audio on professional equipment.
176,400 Hz	Sampling rate used by HDCD recorders and other professional applications for CD production. Four times the frequency of 44.1 kHz.
192,000 Hz	DVD-Audio, some LPCM DVD tracks, BD-ROM (Blu-ray Disc) audio tracks, and HD DVD (High-Definition DVD) audio tracks, High-Definition audio recording devices and audio editing software. This sampling frequency is four times the 48 kHz standard commonly used with audio on professional video equipment.
352,800 Hz	Digital eXtreme Definition, used for recording and editing Super Audio CDs, as 1-bit Direct Stream Digital (DSD) is not suited for editing. 8 times the frequency of 44.1 kHz.
384,000 Hz	Maximum sample rate available in common software.
2,822,400 Hz	SACD, 1-bit delta-sigma modulation process known as Direct Stream Digital, co-developed by Sony and Philips.
5,644,800 Hz	Double-Rate DSD, 1-bit Direct Stream Digital at 2× the rate of the SACD. Used in some professional DSD recorders.
11,289,600 Hz	Quad-Rate DSD, 1-bit Direct Stream Digital at 4× the rate of the SACD. Used in some uncommon professional DSD recorders.
22,579,200 Hz	Octuple-Rate DSD, 1-bit Direct Stream Digital at 8× the rate of the SACD. Used in rare experimental DSD recorders. Also known as DSD512.
45,158,400 Hz	Sexdecuple-Rate DSD, 1-bit Direct Stream Digital at 16× the rate of the SACD. Used in rare experimental DSD recorders. Also known as DSD1024.

Undersampling

Main article: Undersampling

When a signal is sampled slower than a special rate, called its Nyquist rate, the samples might look like they are from a lower-frequency signal. This is called undersampling. Sometimes, this is done on purpose so the lower-frequency version still shows the original signal correctly and can be used again. Undersampling is also called bandpass sampling, harmonic sampling, IF sampling, and direct IF to digital conversion.

Oversampling

Main article: Oversampling

Oversampling is a method used in devices that change smooth, ongoing signals into digital form. It helps lower mistakes that can occur when changing digital signals back to smooth, ongoing ones. This makes the final result clearer and more exact.

Complex sampling

Complex sampling, also called I/Q sampling, takes two related waveforms at once. These pairs of samples are treated like complex numbers. This method helps reduce the number of samples needed to show a signal clearly.

When one waveform is the Hilbert transform of the other, it creates an analytic signal. This special signal lets the sampling rate be lowered without losing information. Instead of needing twice as many samples per second, only half as many complex samples are needed to capture the same details. This technique is useful in many areas of signal processing.

Main article: Complex number

Main articles: Hilbert transform, Analytic signal, Nyquist rate, Equivalent baseband waveform