The sampling frequency, also known as the sampling rate or sampling rate, defines the sampling rate fromContinuous signalExtracted from and composed ofDiscrete signalNumber of samples, which useshertz(Hz).The reciprocal of the sampling frequency issampling period Or calledSampling time, which is between samplestime interval。Generally speaking, the sampling frequency refers to how many signal samples can be collected by the computer per unit time.[1]
Continuous signalIt changes in time (or space) in some way, andSampling processIt is to measure the value of continuous signal in time (or space) with T as the unit interval.T is calledSampling interval。In practice, if the signal is a function of time, usually their sampling interval is very small, usuallymillisecond、MicrosecondThe magnitude of.The sampling process produces a series of numbers called samples.The sample represents the original signal.Each sample corresponds to the specific measurement of this samplepoint of time, and the reciprocal of the sampling interval, 1/T is the sampling frequency, fs, and its unit is sample/second, that ishertz(hertz)。
Generally speaking, the sampling frequency refers to how many signal samples can be collected by the computer per unit time. For example, for waveform recording, the sampling frequency can describe the waveformquality standard。The higher the sampling frequency, that is, the shorter the sampling intervalsample data The more, the more accurate the representation of the signal waveform.Sampling frequency vs. rawsignal frequency There is a certain relationship betweenNyquistIn theory, only when the sampling frequency is higher than twice the maximum frequency of the original signal, can the digitalSignal representationThe signal of is restored to the original signal.
In the scientific field, the commonly used sampling rates are:
Sampling is to take a signal (i.econtinuous function ）Convert to a numerical sequence (i.e., in time or spaceDiscrete function）。The sampling theorem points out that if the signal is infinite and the sampling frequency is higher thanSignal bandwidthThe original continuous signal can be completely reconstructed from the sample.
Band limitSignal transformationIts speed is limited by its highest frequency component, that is, its discrete time sampling ability to show signal details is limited.
The sampling theorem means that if the signal bandwidth is less than half of the sampling frequency (i.eNyquist frequency）, then these discreteSampling pointIt can fully represent the original signal.Frequency components above or at Nyquist frequency will causeAliasing phenomenon。Most applications require avoiding aliasing. The severity of the aliasing problem is the same asAliasing frequency componentOfRelative strengthof
The sampling frequency must be greater thanSampling signalAnother equivalent is that the Nyquist frequency must be greater than the bandwidth of the sampled signal.If the bandwidth of the signal is 100Hz, the sampling frequency must be greater than 200Hz to avoid aliasing.In other words, the sampling frequency must be at least twice the frequency of the maximum frequency component in the signal, otherwise, it cannotSignal samplingRestore the original signal in.
stayAnalog videoIn the system, the sampling rate is defined asFrame rateandField frequency, rather than the conceptual pixel clock.The image sampling frequency is the cycle speed of the integration period of the sensor.Since the integration period is far less than the time required for repetition, the sampling frequency may beSampling timeThe reciprocal of is different.
The confusion phenomenon of high-frequency luminance componentsMoire appear.
Aliasing
Announce
edit
If the above sampling conditions cannot be met, the sampled signal frequency will overlap[1]That is, the frequency component higher than half of the sampling frequency will be reconstructed into a signal lower than half of the sampling frequency.The distortion caused by this spectrum overlap is calledAliasingThe reconstructed signal is called the overlapping substitute of the original signal, because the two signals have the sameSample value。
A chord signal whose frequency is exactly half of the sampling frequency will usually be mixed into another chord signal with the same frequency, but its phase and amplitude have changed.
The following two measures can avoid the occurrence of aliasing:
1) Increase the sampling frequency to the maximumsignal frequency More than twice of;
2) Introductionlow pass filter Or increase the parameters of the low-pass filter;This low-pass filter is commonly referred to asAnti aliasing filter
Anti aliasingwave filterThe bandwidth of the signal can be limited to meet the conditions of the sampling theorem.In theory, this is feasible, but it is impossible to do it in practice.Because the filter cannot completely filter the signal above Nyquist frequency, there is always some "small" energy in addition to the bandwidth required by the sampling theorem.However, the anti aliasing filter can make these energies small enough to be negligible.
In some cases, people want the sampling frequency to exceedSignal bandwidthTwice as much so you can use itdigital filter Replace the analog anti aliasing filter with poor performance. This process is calledOversampling。
