glossary of filter terms

Definitions (in alphabetical order) related to the characteristics of analog lowpass filters (LPF). With a little imagination they can be modified to include responses of highpass (HPF), bandpass (BPF), and bandstop (BSF) filters.

anti-alias filter

to convert a lowpass analog signal to digital format the first requirement is to sample (determine) the magnitude of the analog signal at regular intervals (the sampling rate). These magnitudes are then converted to digital words. Nyquist has shown that the original analog signal can be recovered from these samples, without distortion, provided that the sampling rate is at least twice that of the bandwidth of the original signal (both these are measured in the same units, typically Hertz).

If the signal bandwidth is too great, by the above criterion, there will be distortion. This is referred to as aliasing distortion.

Thus, for a given sampling rate, the analog signal must be confined to a defined bandwidth. The filter which defines this bandwidth has a lowpass characteristic. Its purpose is to prevent aliasing distortion, and so is defined as an anti-aliasing filter..
~~~~~ go back with your browser back button. If lost, go home

approximation

a mathematical definition of the desired transfer function. Typically expressed as a rational polynomial, from which can be obtained a set of poles and zeros in the s-plane.

An approximation can be achieved in many ways, including:

• synthesis: which I think of as being pure pencil and paper work, ending up with a solution in precise mathematical form
• CAD: which is what I have done, and which could never be done with pencil and paper alone; a computer is essential.

~~~~~ go back with your browser back button. If lost, go home

allpass equalizer

a circuit added in cascade with a filter having a characteristic, which, when combined with that of the filter, produces an overall ' flat ', or equiripple group delay characteristic. Its job is made harder (higher order required) if the group delay characteristic of the filter has a large 'spike' in it. This will typically (always?) occur at the passband edge, and is particularly severe in the case of an elliptic filter.

The term 'allpass' implies that the amplitude response of the equalizer is constant - it passes all frequencies equally - and so there is no modification to the amplitude response of the filter.
~~~~~ go back with your browser back button. If lost, go home

biquad

short for biquadratic. Refers to a transfer function defined by the ratio of two quadratic terms. It also refers to the electronic circuit which can realize the transfer function defined by this.
~~~~~ go back with your browser back button. If lost, go home

design

a loosely defined term which covers the whole field of filter production. A design would begin with a specification , and be followed by the approximation and realization.
~~~~~ go back with your browser back button. If lost, go home

equiripple

a response is said to be equiripple if it oscillates, with frequency, equally above and below a mean value. Typically applies to responses within the passband of a filter. The stopband response of an elliptic filter is also referred to as being equiripple, but this is not strictly according to the above definition.
~~~~~ go back with your browser back button. If lost, go home

flat (response)

a response is said to be 'flat' when it varies only minimally from being constant with frequency over a specified range (bandwidth). See equiripple above.
~~~~~ go back with your browser back button. If lost, go home

group delay

the negative rate of change of phase with frequency. Expressed in seconds.
~~~~~ go back with your browser back button. If lost, go home

group delay ripple

the peak-to-peak delay variation over the 'flat' region of the group delay characteristic. Expressed in seconds.
~~~~~ go back with your browser back button. If lost, go home

normalization

the technique of frequency scaling. Simplifies filter comparisons. The frequency responses are scaled to place the upper edge of the passband at unit frequency. In most cases (for mathematical convenience, if nothing else) the frequency is given in radians/sec. Remember w radian/s is equivalent to 2.pi.f Hz (where f is in Hertz).
~~~~~ go back with your browser back button. If lost, go home

order (of a filter)

relates to the 'size', or complexity, of a filter, in terms of the number of poles in the transfer function. A biquadratic is of order 2, and a real pole of order 1.
~~~~~ go back with your browser back button. If lost, go home

passband

the frequency region in which there is little signal attenuation. For a LPF this extends from DC to the start of the transition band (referred to as the corner of the passband).
~~~~~ go back with your browser back button. If lost, go home

passband ripple

the peak-to-peak gain variation within a passband. Usually expressed in decibels (dB).
~~~~~ go back with your browser back button. If lost, go home

phase response

the relationship between the input and output signals of a filter is complex. In particular, the phase relationship between these two signals varies with frequency. If the variation is linear with frequency, then each frequency component will suffer the same time delay in passing through the filter. This is desirable, for example, if waveform fidelity is important; it is of little consequence for the transmission of speech signals.
~~~~~ go back with your browser back button. If lost, go home

quadrature phase splitter

a quadrature phase splitter - QPS - is a pair of networks with complementary phase characteristics. With a common input the two output signals are of constant amplitude but differ in phase by 90 degrees. These can be configured to generate a single sideband signal.
~~~~~ go back with your browser back button. If lost, go home

realization

the physical entity whose transfer function matches as closely as possible that of the filter approximation.
~~~~~ go back with your browser back button. If lost, go home

response

typically shorthand for frequency response.
~~~~~ go back with your browser back button. If lost, go home

slotband

regulatory organizations such as CCITT, FCC, Austel, etc, provide clients with spectrum 'slots'. The regulatory definition of a slot may be fairly involved, but, in simple terms, it is equivalent to specifying an allowed band for transmission, within which the user is free to exploit the resource as s/he wishes, and to ensure extremely low levels of leakage outside the limits. In terms of specifying a filter characteristic it means the band limit is determined by the stop frequencies for a bandpass filter, or from DC to the start of the stopband for a lowpass filter. Thus it is the sum of the passband plus transition band(s).
~~~~~ go back with your browser back button. If lost, go home

specification

A specification for a filter usually starts out by defining the amplitude/frequency characteristic of the transfer function. It may also include in addition some requirements of (or constraints upon) one or other of the group delay, phase response, pulse response, and so on. These requirements are conveniently described in terms of a specification mask
~~~~~ go back with your browser back button. If lost, go home

specification mask

filter responses are conveniently specified in terms of specification masks. Any filter whose response will fit within the mask is deemed to meet the specification. A typical specification mask, for the amplitude response of a lowpass filter, is shown in the Figure below.

Although any filter whose response will fit within the mask is a candidate, one generally understands that it is the filter of the lowest order which is deemed to meet the specification.

a lowpass specification mask.

~~~~~ go back with your browser back button. If lost, go home

steepening

the technique of adding imaginary zeros (finite frequency zeros) to allpole stages of a lowpass filter to 'steepen' the amplitude response. This technique does not influence the group delay response.
~~~~~ go back with your browser back button. If lost, go home

stopband attenuation

the minimum attenuation of signal energy in the stopband, relative to that of the passband. Usually expressed in decibels (dB).
~~~~~ go back with your browser back button. If lost, go home

transition band

the frequency region between the upper edge of the passband and the beginning of the stopband.
~~~~~ go back with your browser back button. If lost, go home

transition band ratio

the ratio of the frequencies of the upper edge and the lower edge of the transition band. The smaller this is the 'sharper' the filtering characteristic is said to be.

At any time use your browser back button to return to where you came from, else go home.