The basics of DSP for use in intelligent sensor applications: Part 2

Creed Huddleston

July 6, 2010

Creed Huddleston

High-pass Filters
A complement to the low-pass filter is the high-pass filter, which passes only high-frequency signal components and blocks the low-frequency ones. In the idealized high-pass filter of Figure 2.11 below, the passband starts at 1500 Hz and continues to all higher frequencies.

Note that the bandwidth in this case is infinite since all frequencies starting with the passband are included in the filter.

Figure 2.11. Idealized High-pass Filter with Passband Starting at 1500 Hz

Since we just stated that no real-world signal has infinite bandwidth, why would we want to use a filter that seems to assume that condition? In some cases, the signal we’re measuring is an inherently AC signal; by the nature of the system anything below a certain frequency is obviously noise because no valid signal components exist below that frequency.

An example of this might be the auditory response of the human ear, which is sensitive only to frequencies in the range of 20 Hz to about 20 kHz. Anything below 20 Hz is of no practical value and can be treated as noise.

Bandpass Filters
A bandpass filter is essentially the combination of a high-pass filter and a low-pass filter in which the passband of the high-pass filter starts at a lower frequency than the bandwidth of the low-pass filter, as shown in Figure 2.12 below. Here we see that the filter will pass frequencies between 750 Hz and 1500 Hz while blocking all others.

Figure 2.12. Idealized Bandpass Filter

Bandpass filters are used whenever the designer wants to look at only a particular frequency range. A very common example of this is the tuner in a radio, in which the tuner uses a bandpass filter with a very narrow passband to isolate the signal from an individual radio station.

With the tuner, the goal is to pass the signal from the station of interest as clearly as possible while simultaneously attenuating the signals of all other stations (presumably at lower or higher frequencies) to the point where they are inaudible.

Bandpass filters are also commonly used to look at the strength of the signal in certain passbands of interest. DTMF detectors use this principle to determine what key a person has pressed on their touchtone phone.

In a DTMF system, each key is represented by a combination of two and only two frequencies that have no common harmonics. These two frequencies always have one component from a group of four low-frequency values and a second component from a group of four high-frequency values, as is shown in Table 2.1 below.

Table 2.1. DTMF Tone Combinations

Basically, to be a valid DTMF tone, each of the two frequency components needs to be within about 1.5% of their nominal value, and the difference in signal strength between the two components (known as “twist”) must be less than 3 dB.

Using a bandpass filter for each of the eight frequency components plus one for the overall signal bandwidth, a detector can examine the outputs of each filter to determine that only two frequency components are active at any given time, that the two components are a valid combination (one from the low-frequency group and one from the high-frequency group), and that their relative strength is acceptable.

Bandstop Filters
The bandstop, or notch, filter can be viewed as the complement to the bandpass filter in much the same way that the high-pass filter is the complement of the low-pass filter.

Whereas bandpass filters allow only a relatively narrow band of frequencies to pass, bandstop filters sharply attenuate a narrow band of frequencies and leave the rest relatively untouched. Figure 2.13 below shows an example of a bandstop filters.

Figure 2.13. Idealized Bandstop Filter

By far the greatest application of bandstop filters is in the reduction of powerline noise centered around 50 Hz or 60 Hz (depending on location). In many applications, the 50-Hz or 60-Hz power signal will couple into the sensing circuitry and, unfortunately, the power signal’s frequency often is in the midst of the frequency spectrum for the signal of interest.

A simple low-pass or high-pass filter that would exclude all frequencies above or below the power frequency would attenuate the desired signal too much in such cases, so designers try to remove only the frequency components right around that of the power.