If we know the period in which one oscillation is completed, we can calculate the frequency, dividing 1 by the period. This is exactly what our sampling rate is in the illustration — it will give us a very basic digital signal without a loss in quality. The signal shown in green in the bottom illustration has a much higher frequency. It completes one oscillation in 1 second, thus its frequency is 1 Hz.
This sampling provides a very basic digital representation of these signals without the loss of quality. The sampling theorem was derived and proved nearly simultaneously by many scientists working independently across the globe. In English, it is known as the sampling theorem, but sometimes the name of two of its creators is also used: the Nyquist—Shannon sampling theorem.
In Russian, the name of the Russian scientist who proved it around the same time is used: the Kotelnikov theorem. Some other people credited with this discovery are Whittaker and Raabe. Sampling rates are generally decided in accordance with the sampling theorem, but which maximum frequency of the signal is chosen, as well as whether the sampling rate is double or higher than double the frequency of the original, depends on the intended purpose of the digital signal.
In some situations frequencies higher than double of the frequencies of the original signal are used, to ensure high quality of the signal. In other cases, the range of frequencies is selected from the entire audible spectrum for people , as the sampling for the audio CDs, which happens at 44, Hz.
It ensures that the sounds of the highest frequency that the human ear can generally hear, at 20, Hz, are sampled at the correct frequency double of the highest frequency that the human ear can hear, or 44, Hz. It is interesting to note that the threshold of the audible frequencies changes with age. For example, young people can hear up to about 18, Hz.
With age, this threshold decreases to 15, Hz or lower. Some manufacturers use this ability of younger people by providing special services for them. Smartphones, for example, have applications that allow one to set a ringtone at a very high frequency above 15, Hz, to ensure that most adults cannot hear it. When producing high-quality audio, the manufacturers try to include young people and people with a really good hearing in the frequency calculations, hence the choice of 22, Hz times two.
The sampling rate for audio used in video recordings is even higher, at 48, Hz. In some cases, the opposite is true and the frequency band targeted is small. For example, only the frequencies that are the range of the human voice may be considered, when the quality of the signal is not essential.
This is common for communication devices like phones, for example. They are sampled at only 8, Hz. Indeed, not many people use their phones to transmit orchestra performances, therefore this choice of frequencies is sufficient. This article was written by Kateryna Yuri. Parallel Resistance Calculator. Parallel Inductance Calculator. Capacitor Impedance Calculator. Mutual Inductance Calculator — Parallel Inductances. Mutual Inductance Calculator — Inductances in Series.
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More details. Unit Converter Convert units of measurement easily! This site will not work properly because your browser does not support JavaScript! Share a link to the calculator, including the input values. Definitions and Formulas Sampling is the technique used for recording analog information like audio signals or images by recording their snapshots at periodic intervals.
The sampling interval or sampling period T s is the reciprocal of the sampling frequency: The Nyquist-Shannon sampling theorem states that to restore a signal, a sufficient sample rate must be greater than twice the highest frequency of the signal being sampled. A representation of an analog sound signal on the graph. Time intervals at which the signal is sampled are shown in orange.
Two different analog signals in dark blue and in pink on the top graph are represented by the same digital signal in light blue in the bottom graph. Random Term. AMS Publications. Modify or suggest a term. Glossary History. View source. Folding frequency From Glossary of Meteorology. Jump to: navigation , search. Also called Nyquist frequency. The highest frequency that can be measured using discretely sampled data. Stated another way, a minimum of two data points is needed to define a wave , hence the period of the smallest wave i.
The word "folding" comes about because any frequencies that are higher than the Nyquist frequency in a continuous signal will be aliased or folded into lower frequencies when the signal is discretely sampled.
To avoid this severe problem, the original signal must be filtered by analog or physical methods to remove all frequencies higher than the Nyquist frequency before the signal is sampled or digitized.
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