Application Notes

Glossary of Filtering Terms

Aliasing

A phenomenon that occurs during digital sampling (including A/D conversion) when a high-frequency signal or noise is converted by the sampling process to a false lower frequency below half the sampling rate.

 

Attenuation Slope

For a low-pass filter, the slope of the gain vs. frequency curve in the region of rapidly increasing attenuation just above the cutoff frequency. Many filters have a gain in this region which is proportional to a negative power of frequency (i.e., linear on a log-log graph), so the slope is commonly expressed in decibels per octave, which indicates the number of decibels increase for each doubling of frequency. Most anti-alias filters have attenuation slopes ranging from 45 to 120 dB/octave. At 120 dB/octave, a disturbing input at a frequency of 1.7 times cutoff is attenuated by over 80 dB. That is, a 1-volt disturbance is reduced to 100 mV, completely eliminating the disturbing signal for most purposes.

 

DC Offset

The shift in the DC level of the signal. DC offset can be as much as 150 to 200 mV in some filters, or as little as a fraction of a millivolt in other filters.

Droop

A monotonic decrease in passband gain with frequency. If present, it typically is included in the gain or ripple specification. See Gain Error and Passband Ripple.

 

Gain Error

The difference between the specified and actual passband gains. For typical filters, the gain error can be as high as a few percent. It can refer to frequencies far below cutoff only or to the whole passband. If a "ripple" is stated or if the term "DC gain error" is used, the gain error probably refers to low frequencies. If not, it likely refers to most or the entire passband and includes the ripple.

 

Group Delay

The time delay through the filter for a pulse of sine waves. If the group delay is non-uniform and varies with the sine-wave frequency, the time-domain response to a sharp input-signal change may show overshoot or ringing. At any sine-wave frequency, the filter group delay is the derivative of the filter phase shift with respect to frequency: delay = d(phase shift) / d(frequency). Thus, a perfectly uniform group delay is equivalent to a perfectly linear phase response. See also Phase Linearity.

 

Harmonic Distortion

The amount of distortion introduced by slight non-linearities in the amplifiers of a filter circuit. This will vary drastically with signal amplitude and to some extent with frequency as well. For peak-to-peak amplitudes of, say 80% of the full voltage range, typical distortion levels may be around 0.005% to 0.05% at mid-frequencies. For levels closer to full scale, the distortion increases; for lower levels, it usually decreases.

 

Low-Pass Filter

A filter that ideally passes unchanged all slower frequency components from DC to the filter cutoff and totally eliminates faster components above that point. In real filters, the transition has a finite slope instead of being discontinuous, and the attenuation at high frequencies is not infinite. See Attenuation Slope and Stopband Attenuation.

 

Noise and Interference

Unwanted electrical signals that can come from the data acquisition system itself or from such external sources as 50Hz or 60 Hz pickup, broadcasting stations, and mechanical vibrations.

 

Nyquist Frequency

The frequency at one-half the sampling rate.

 

Nyquist Theorem

A mathematical theorem stating that a band-limited input signal can be recovered without distortion if it is sampled at a rate of at least twice the highest frequency component of interest within the signal.

 

Passband Ripple

The variation in gain over the passband; when the gain-vs.-frequency response appears rippled instead of flat. Typical filters can have 1 or 2% ripple over most of the passband. If passband frequencies near the cutoff are included, the ripple can be significantly greater.

 

Phase Linearity

The linearity of a plot of phase shift vs. frequency, the response of which should be a straight line. (See also Group Delay). However, in practice, a filter designed for phase linearity can have passband phase linearity as low as a fraction of a degree, while other filters can have non-linearities so great that the group delay changes by a factor as high as 2 or 3 over the passband.

 

Stopband Attenuation

For a low-pass filter, the attenuation at all frequencies above where the gain vs. frequency response has finished its rapid falloff. Typically 75 to 100 dB.

 

Wideband Noise

In a filter specification, the random noise generated by a filter over a band equal to or greater than the passband. This is often a large part of the total wideband noise at the filter output. Typical high-quality filters like the AAF-1 series introduce 60 to 150 microvolts RMS of wideband noise. Unlike for resistor noise, changing the filter passband does not greatly change the total wideband RMS value for switched-capacitor filter noise.

PHONE (714) 850-9984        FAX (714) 850-9987       E-MAIL productinfo@alligatortech.com

---

[ HOME | US & WORLDWIDE SALES OFFICES | APPLICATION ASSISTANCE | TECH SUPPORT | SEARCH ]

(c)1997 Alligator Technologies