A filter used to remove the signals whose frequencies exceed one half the
sample rate 
. Ideal filters
are not realizable so that the cutoff frequency, transition band, and out-of-band
rejection need to be considered.
One of a collection of algorithms for computing discrete Fourier transforms (DFTs) in an optimum fashion. The fast Fourier transform (FFT) algorithm reduces the number of complex multiplications required to compute the transform. This is accomplished by factoring the weighted trigonometric summations required in the computation of the discrete Fourier transform into a sequence of shorter weighted summations by taking advantage of the periodicities and symmetries of the periodic weighting factors and of the transform itself.
A filter used to remove the signals whose frequencies exceed one half the
sample rate . Ideal filters
are not realizable so that the cutoff frequency, transition band, and out-of-band
rejection need to be considered.
A filter which passes all signal information between two cutoff frequencies and sharply attenuates all signal information outside that range.
A filter which attenuates all information between two cutoff frequencies and passes all signal information outside that range.
An efficient stable filter characterized by excellent phase linearity at the expense of sharpness of cutoff and passband flatness. Commonly used for shock and other transient waveform phenomenon and often referred to as a linear phase filter.
A filter having flat passband and moderately sharp cutoffs, but also moderately nonlinear phase response. Commonly used for acquisition of data from random processes.
Similar to the Butterworth filter, it achieves faster rolloff near cutoff, but at the expense of significant passband ripple and a nonlinear phase response.
A weighted sum that can be defined as
where:
If all the weights 
are zero,
the filter is called a nonrecursive filter. If one or more of the weights
are nonzero, the filter is
called a recursive filter. If any of the weights 
are nonzero for 
, the filter
is said to be nonrealizable since future values of the input samples, 
,
will be required. If all the filter weights
are zero for , the filter
is said to be realizable. If we define a digital unit impulse as:
where, 
is the sampling interval,
then the response of a digital filter to this impulse is called the impulse
response of the filter. The impulse response for any nonrecursive filter will
be finite for any finite 
.
Hence, nonrecursive filters are sometimes called finite impulse response filters.
Recursive filters are called infinite impulse response filters because the
impulse responses are not necessarily finite.
A low-pass filter with maximally linear phase response at the expense of sharpness of cutoff and passband flatness. Commonly used for shock and other transient waveform phenomenon (See FILTER, LOW-PASS).
A filter which passes all signal information above the cutoff frequency, and sharply attenuates everything below that frequency.
A filter which passes all signal information below the cutoff frequency, and sharply attenuates everything above that frequency.
See FILTER, DIGITAL.
The tendency of nonlinear phase filters to exhibit lightly damped oscillatory outputs in response to an impulsive input.
The peak-to-peak variation, in 
,
of the gain of the filter in the passband.
The best straight line fit to the slope of the filter transmissibility characteristic
in the transition band, usually expressed in
per octave.
The difference in frequency between the filter cutoff frequency and the point at which the gain reaches the first peak of the out-of-band ripple.
FILTER TRANSMISSIBILITY CHARACTERISTIC (FILTER SHAPE)
The magnitude of the frequency response function of a filter relating the output to the input of the filter.
FINITE IMPULSE RESPONSE FILTER
See FILTER, DIGITAL.
A number represented in such a way that the binary or decimal point is fixed with respect to one end of the numerals.
A set of numbers represented in memory by their mantissa and 2 common exponents for the block of numbers. Often used in FFTs to make better use of the memory word size when the incoming data consist of small integers. (See FFT).
A technique for representing data values as a digital word. Each datum is divided into four fields: mantissa, mantissa sign, base ten, or base two exponent and exponent sign. Frequently, a floating point value will use two or more computer words. The precision to which values can be represented is determined by a number of bits allotted to the mantissa field and the dynamic range by the number of bits in the exponent field.
Equal to half the sampling frequency, above which higher signal frequencies are folded or aliased back into the analysis band.
A bilateral transformation typically used to convert quantities from time domain to frequency domain and vice versa, usually derived from the Fourier integral of a periodic function when the period grows without limit, often expressed as a Fourier transform pair. In the classic sense, a Fourier transform takes the form of:
where:
In the discrete or sampled sense (See DFT), this can be expressed as:
where:
(See INVERSE FOURIER TRANSFORM, TIME DOMAIN, FREQUENCY DOMAIN, DFT, DFT - l , FAST FOURIER TRANSFORM.)
Discrete set of elements (numbers) representing a time or frequency
domain function. The numerical size of the element set is called the frame,
block, or record size and is generally a power of 2, such as 64, 128, 256,
etc. The term frame length, or block length, is used to describe the length
of the element set in seconds or milliseconds and is equal to 
where
is the frame size and 
is the sampling interval (See TIME DOMAIN,
FREQUENCY DOMAIN, MEMORY
LENGTH).
See MECHANICAL IMPEDANCE/ MOBILITY.
Term used to describe the operation of an analyzer or processor which operates continuously at a fixed rate, not in synchronism with some external reference event, Analyzers, processors and computing systems are often thought to be operating in a triggered, block synchronous, or free running mode of operation.
See FREQUENCY INCREMENT.
Any parameter which is expressed as a function of frequency.
See PROBABILITY DENSITY FUNCTION.
The spacing between frequency components obtained by performing a discrete
Fourier transform operation on a sequence of time samples, which in turn have
a sampling interval 
:
where:
The frequency range (bandwidth) over which the performance of the device remains within acceptable limits. Typical analyzers have selectable ranges. As applied to analyzers it usually refers to upper frequency limit of analysis, considering zero as the lower analysis limit (See ZOOM ANALYSIS).
A property of a physically realizable stable linear system expressed as a
function of the frequency 
;
defined as the Fourier transform of the impulse response function. Several
of its important properties are:
where 
and 
are the Fourier transform of the output and input to the system,
where 
are the cross spectral
density between the output and input and the auto spectral density of the
input. For a noise-free linear system,
where 
are the auto spectral
density functions of the output and input to the system,
where 
are the gain and phase
of the response of the system to a sinusoidal input at the frequency 
.
The frequency response function is a special case of the transfer function
where the transfer function
is evaluated along the line 
.
The frequency response function can replace the transfer function with no loss of useful information.
A mathematical concept, A variable 
is said to be a single-valued function of 
,
for a certain range of values of 
,
if to each value of , one
and only one value of is
assigned. In this case, is
termed the independent variable and ,
the dependent variable. The set of values over which the function 
is defined is known as the domain of .
The set of values taken on by
is known as the range of .
The lowest frequency periodic component present in a complex waveform. At least one complete period of a signal must be present for it to qualify as the fundamental.
