Suppose an engineer specifies the need to capture 2. That means we need samples of 15th of the amplitude at 15 times the fundamental frequency, or 15 kHz:.
Can the given ADC—12 bits with a 2. The amplitude of the 15th harmonic comes to:. The ADC can measure ? In fact the ADC can measure amplitudes out to several thousand harmonics. Thankfully, real-world square waves have finite rise and fall times and do not include that many harmonics.
Also, cables, connectors, components, and circuits attenuate many of the higher-frequency harmonics as a matter of course. To remove higher-frequency harmonics before they reach the ADC you need an anti-alias filter. The filter must have a cutoff frequency such that it will not attenuate the 15th harmonic. The Microchip Technology FilterLab software calculates the response for an 8-pole Butterworth filter. I adjusted the cut-off frequency to get an attenuation of See the Bode plot below.
So although we started with a 1-kHz square wave, we must sample at a much greater rate. Again, a Chebychev low-pass filter offers a faster cutoff but the filter attenuates some of the signals below 15 kHz. Most signals in process industries do not require such a high sample rate. I provide the square wave example to illustrate that what look like low-frequency signals can include high-frequency components you must take into account when you think about an anti-alias filter.
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Your primary consideration at this point should be to use a device with the correct resolution and remove noise in order to prevent quantization errors. Arbitrary signals contain harmonic components that are spread out over a broad spectrum, and the frequency content may exceed the Nyquist frequency.
This means any frequency content you try to sample above the Nyquist frequency will cause aliasing. When the input signal is quantified, the digital output will reflect a distorted version of the original input. This issue with sampling and aliasing is illustrated in the figure below. The graph shows a spectrum for an arbitrary signal red curve.
Note that the sampling rate fs is set higher than the end of the spectrum. However, the Nyquist frequency half the sampling rate falls into the middle of the spectrum. Any frequency components below the Nyquist frequency can be accurately sampled, while all higher order frequencies will be aliased and will be interpreted incorrectly as low frequency components by the ADC.
Schematic showing aliasing and distortion with an arbitrary analog signal. In this example situation, you have two options to prevent the digitized output from failing to accurately reflect the input analog signal:. Increase the sampling rate so that the Nyquist frequency is larger than the end of the frequency spectrum.
As arbitrary signals have frequency content that extends out to infinity, you cannot increase the sampling rate to infinity. The other option is to choose a suitable maximum frequency that you need to sample. This brings us to the second point You should use an anti-aliasing filter to remove all frequency content greater than the Nyquist frequency.
This second point should illustrate the advantage of an anti-aliasing filter. Many image sensors might struggle to cope with that high frequency pattern and produce strange bands of colour or odd stripes in your images. For years, anti-aliasing filters came standard on all digital SLRs, but in recent years — pioneered by Nikon in its entry-level DSLRs — manufacturers have begun removing the anti-aliasing filter from the image sensor.
Common questions answered. Over the last few years the pixel count of digital cameras has gone up significantly so that they can resolve much more detail. No one wants this distortion, of course, but because editing raw files gives you so much flexibility, any unwanted colour patterns can usually be removed at the post-processing stage.
Manufacturers have gambled — and rightly so — that photographers want the option to record more detail at the expense of spending a little more time on the computer editing.
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