So what can we do? A bit of background information and then a solution. They published a theorem that explained the need to sample a real-world signal at more than two times the highest-frequency component present in a signal of interest. Q: So I need a low-pass filter to remove unwanted signals above 1 kHz. But how do I describe it to a supplier? When you have a sine wave, frequency equals bandwidth. Assume we have a bit ADC and the signal will span the entire 0- to 2. Low-pass analog filters have a characteristic slope, or roll-off, that shows how much signals get attenuated as frequency increases.
And engineers usually specify a filter cut-off frequency fc ; the point at which signal attenuation becomes -3 decibels dB. This information often appears on a Bode plot of attenuation in decibels dB vs. This Bode plot uses a logarithmic scale for frequency. Courtesy of the Wikimedia Commons. To simplify the mathematics of filter design, I recommend the free FilterLab filter-design software from Microchip Technology.
It lets people examine several filter types and their characteristics based on the characteristics they need. I have used the software to create filters and the following examples come from FilterLab.
FilterLab also can produce a schematic diagram of a filter with the characteristics you select. To properly filter the Hz test signal before it reaches an ADC we want no attenuation at Hz, and a steep attenuation of signals above that frequency. The figure below provides a FilterLab plot of attenuation vs. Here is the schematic diagram for the Butterworth filter described above:.
A: Before you determine a sample rate, look at the resolution of the ADC used to digitize the signal. A bit ADC has a resolution of 1 part in , which we express in decibels with the equation:. Need help? Contact Support. Welcome to our premium content library! First Name: required First name is required and must be a string. To motivate this, let us listen to the effect of aliasing for three different kinds of signals. We take an original audio signal and perform a downsampling operation, for example to save bandwidth.
Naturally, higher frequencies in the signal cannot be represented accurately with a too low sampling rate, so the downsampled audio does not sound as "bright" as the original. 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. An anti-aliasing filter is just a low pass filter with the cutoff frequency i. This filter cuts out any higher order frequency content in the input signal as any frequencies higher than the Nyquist frequency would be aliased.
With these frequencies removed from the signal, the ADC can now sample the remaining harmonic content without creating false low-frequency errors. Anti-aliasing filters are typically designed as higher order active filters using a low-noise op-amp. The goal is to design the filter with unity gain across the pass band and to set the -3 dB cutoff frequency to be set precisely equal to the Nyquist frequency, which in turn is half your intended sampling rate.
If you are using an adjustable ADC, always set the -3 dB cutoff to correspond to the Nyquist frequency for the smallest sampling frequency you intend to use in your system. Anti-aliasing filter design is all about engineering the transfer function for an active filter.
This can be as simple as selecting a wideband op-amp and wiring a low pass RC filter to the non-inverting input. A slightly more advanced design is to use higher order filtering as this will provide stronger rolloff beyond the -3 dB point in a Bode plot. An example is shown below.
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