First, you have a sample rate of 125 nanoseconds (time); second, you compare the sampling rate to the sampling frequency multiplied by two (Hertz). –Laurent Duval At 21:32 p.m. on October 18, 2016, Assuming no bandpass sampling is used and/or an anti-aliasing filter is used, the highest allowable frequency of the recorded signal is half the sampling rate.
What sampling rate is required for a signal having a frequency range of 10,000 Hz (1000 to 11,000 Hz)? The sampling rate must be at least twice the maximum frequency in the signal, according to the Nyquist theorem. In this case, the sampling rate should be 20,000 samples per second.
A signal with a bandwidth of 1000 Hz can be sampled at 1000 samples per second without loss of information. A signal with a bandwidth of 2000 Hz can be sampled at 2000 samples per second without loss of information. However, a signal with a bandwidth of 4000 Hz can't be sampled at 1000 samples per second or 2000 samples per second; instead it must be sampled at a rate of 40000/4000 = 100 000 samples per second.
Signals with very high frequencies may require extremely high sampling rates in order to avoid aliasing effects. For example, a signal with a bandwidth of 20000 Hz can be sampled at a rate of 100 000 samples per second without loss of information; however, signals with higher frequencies cannot be accurately represented without special care being taken when sampling them.
To sample a voice signal with frequencies up to 4 kHz, for example, a sampling rate of at least 8 kHz, or 8000 samples per second, is necessary; to sample an audio signal with frequencies up to 20 kHz, a sampling rate of at least 40,000 samples per second, or 40 kHz, is required.
For digital recording, a sampling rate of at least twice the highest frequency in the signal must be used; for example, if the signal has frequencies up to 4 kHz, a sampling rate of at least 8 kHz is needed. For better quality, higher rates are preferred.
The word "sample" comes from the Latin word "sampelare," meaning "to measure by weight." In mathematics, engineering, and science, a sample means a subset of a larger set for the purpose of estimating or predicting properties of the larger set. In statistics, a sample is a subset of observations taken from a population without replacement of elements. In computer science, a sample is a sequence of bytes or characters used to represent an image, video frame, or sound wave.
When reading about sampling rates in magazines or on the web, remember that they are usually given in terms of maximum sampling rates, not minimum. To get the minimum rate, you have to divide by 2 (or some other factor). For example, a magazine article might say that a particular DAW can handle sampling rates up to 96 kHz.
The frequency of a wave is the number of times it may repeat itself in one second. Remember that one second = 1000 milliseconds. So, if you divide the period of a wave by 1000 milliseconds, you get the frequency. 7.874 times 127 ms is divided by 1000 ms. This gives us 0.07874 Hz as the frequency of the wave.
Frequency is told in hertz (Hz). The unit of frequency is therefore "hz". One hertz is one cycle per second. Zero hertz is one cycle per minute. Seven-eighths of a hertz is very close to 1 hertz and is usually written as "HZ" instead of "7/8 HZ". A wave with this frequency could go up and down seven times in one second.
You can measure the frequency of waves on an electroencephalogram (EEG) using a device called a "electrode." Electrodes are small wires attached to a conductor such as skin or metal. When current is passed through the electrode, it creates a magnetic field around it. This means that any currents within the body that create their own magnetic fields will also affect the electrode. EEGs use many electrodes on the head to measure the electrical activity of the brain. The frequency of these waves can then be used to diagnose problems with the brain function.
Hertz's (Hz). Frequency is expressed in hertz (Hz), which equals one incident every second. One vibration per second, or cycle per second.
Frequency can be thought of as the number of times something occurs within a given period. For example, the frequency of my car's engine is about 500 Hz because it makes an HZ sound every other stroke of the piston. The frequency of some sounds is in hertz, while that of others is in kilohertz or megahertz.
For example, the human voice ranges from about 150 to 2000 Hz, with the average being about 1500 Hz. Musical instruments also range in frequency from about 20 Hz for a drum to over 1000 Hz for a violin string. Radio and television transmitters operate on frequencies between 300 KHz and 300 MHz. Cell phones use frequencies between 900 MHZ and 1800 MHZ while two satellites passing by Earth at 17,000 miles distance each day travel at around 740 MPH or 1240 KMHZ.
Sonic waves are vibrations that spread through anything vibrating, such as air molecules when noise is heard, water molecules when music is heard, and so on. The frequency determines how many times these waves oscillate within one second.
For example, if a signal at f = 21Hz is sampled at fs = 10Hz, the resultant (aliased) frequency is |n*fs-f|=|2*10-21|=1Hz. This shows that even though the signal was sampled at 10% of its period, it still can be seen at some other time interval within the sample.
The formula for calculating the aliased frequency is: fl=(m/n)*f0 where m is the number of samples per cycle and n is the sampling rate. In our example, m=10 and f0=21Hz so we get fl=21Hz.
In practice, an analog signal will be distorted by the sampling process and may not be able to be reconstructed exactly from its samples. However, this does not mean that it won't work; it just means that there will be some distortion caused by this reconstruction process. For example, if a sine wave at 100% amplitude is sampled at 10% amplitude, then it can be seen as a square wave with 50% amplitude. However, this square wave can be further sampled at 10% amplitude, which will result in another square wave with 25% amplitude, and so on.