Filter Terminologies

Brief definitions of terms related to filter design:
Convolution
Neighborhood operation in which each output pixel is a weighted sum of neighboring input
pixels. Image processing operations implemented with convolution include smoothing,
sharpening, and edge enhancement.
Correlation
Neighborhood operation in which each output pixel is a weighted sum of neighboring input
pixels. Correlation is closely related mathematically to convolution.
Bandwidth - few terms in signal processing have more definitions than this one. We'll define
bandwidth as the frequency width of the passband of a filter. For a low-pass filter, the bandwidth
is equal to the cutoff frequency. For a bandpass filter, the bandwidth is typically defined as the
frequency difference between the upper and lower -3 dB points.
Attenuation - an amplitude loss, usually measured in dB, incurred by a signal after passing
through a filter.
Cascaded filters - the implementation of a filtering system where multiple individual filters are
connected in series. That is, the output of one filter drives the input of the following filter.
Center Frequency (fo) - the frequency lying at the midpoint of a bandpass filter.
Cutoff Frequency - the upper passband frequency for low-pass filters, and the lower passband
frequency for highpass filters. A cutoff frequency is determined by the -3 dB point of a filter
magnitude response relative to a peak passband value.
Decibels (dB) - a logarithmic unit of attenuation, or gain, used to express the relative voltage or
power between two signals. For filters we use decibels to indicate cutoff frequencies (-3 dB) and
stopband signal levels (-20 dB)
Digital filter- computational process, or algorithm, transforming a discrete sequence of numbers
(the input) into another discrete sequence of numbers (the output) having a modified frequency
domain spectrum. Digital filtering can be in the form of a software routine operating on data
stored in computer memory or can be implemented with dedicated digital hardware.
Filter Coefficients - the set of constants, also called tap weights, used to multiply against
delayed signal sample values within a digital filter structure. Digital filter design is an exercise in
determining the filter coefficients that will yield the desired filter frequency response. For an FIR
filter, the filter coefficients are, by definition, the impulse response of the filter.
Filter Order - a number describing the highest exponent in the numerator or denominator of the
z-domain transfer function of a digital filter. For FIR filters, there is no denominator in the
transfer function and the filter order is merely the number of taps used in the filter structure. For
IIR filters, the filter order is equal to the number of delay elements in the filter structure.
Generally, the larger the filter order, the better the frequency magnitude response performance of
the filter.
Frequency Magnitude Response - a frequency domain description of how a filter interacts with
input signals.
Impulse Response - a digital filter's time domain output sequence when the input is a single
unity-valued sample (an impulse) preceded and followed by zero-valued samples. Using perhaps
the most powerful principle in signal processing, we can say that a linear digital filter's frequency
domain response can be calculated by taking the discrete Fourier transform of the filter's time
domain impulse response.
Linear Phase Filter- a filter that exhibits a constant change in output phase angle as a function
of frequency. The resultant filter phase plot vs frequency is a straight line. As such, a linear
phase filter's group delay is a constant. In order to preserve the integrity of their informationcarrying
signals, linear phase is an important criteria for filters used in communication systems.
Phase Response - the difference in phase, at a particular frequency, between an input sinewave
and the filter's output sinewave at that frequency. The phase response, sometimes called phase
delay, is usually depicted by a curve showing the filter's phase shift vs frequency.
Ripple - Ripple refers to fluctuations (measured in dB) in the passband, or stopband, of a filter's
frequency magnitude response curve.
Rolloff - a term used to describe the steepness, or slope, of the filter response in the transition
region from the passband to the stopband.
Transfer Function - a mathematical expression of the ratio of the output of a filter over the
input of the filter. Given the transfer function we can determine the filter's frequency magnitude
and phase responses.
Transition Region - the frequency range between the passband and the stopband of a filter.
Passband - that frequency range over which a filter passes signal energy.
Stopband - that band of frequencies attenuated by a digital filter