To append zero values on the end of an array. Used when taking an FFT of an array whose length is not a whole power of two when the algorithm requires a power-of-two array size. Also, used to avoid circular convolution errors (See FFT).
See COHERENCE, PARTIAL.
Analysis of signals (information) that occur in a known, usually restricted bandwidth. Normally applies to frequency domain analysis which does not include zero. (See BASEBAND ANALYSIS, FREQUENCY DOMAIN.)
A frequency domain "averaging" method which saves the highest response measured in each quantized increment during a specified time internal or number of spectral averages. The resultant spectrum is a composite of the highest spectral values measured during the averaging process (See FREQUENCY DOMAIN).
PEAK LEVEL HOLD (OVERALL LEVEL)
A frequency domain measurement where a series of spectra are compared as to overall level (total power in band of interest, usually rms) and the spectrum with the highest overall level is retained (See FREQUENCY DOMAIN, RMS) .
A frequency domain measurement where, in a series of spectral measurements, the one spectrum with the highest magnitude at a specified frequency is retained.
See CIRCULAR CONVOLUTION.
Term applied to a situation where the data being measured in a sampled data system is exactly periodic (repeats an integer number of times) within the frame length. It results in a leakage-free measurement in digital analysis instrumentation if a rectangular window is used. Real signals are typically not periodic in the window unless sampling is synchronized to the data periodically.
A type of noise generated by digital measurement systems that satisfies the conditions for a periodic signal, yet changes with time so that devices under test respond as though excited in a random manner. When transfer function estimates are measured with this type of noise for the excitation, each individual measurement is leakage-free and, by ensemble averaging. the effects of system nonlinearities are reduced, thus providing benefits of both pseudo-random and true-random excitation.
A waveform which repeats itself over some fixed period of time.
The r repetitive characteristic of a signal. If the period is T (sec), then this results in a discrete frequency or line spectrum with energy only at frequencies spaced at 1/T (Hz) intervals.
The time displacement between two sinusoidal quantities measured relating
to the time of one complete cycle of the sinusoidal. The phase can be expressed
in degrees (or radians) where 360 degrees (or 
)
represents one complete cycle. A phase angle can also be defined as the angle,
A, given:
where x and y are the real and imaginary parts of a complex number.
The roots (possibly complex) of the denominator of a ratio of polynomials (possibly complex). They are used in continuous or discrete system transfer function analysis and describe the impulse response characteristics of systems. See ZEROS.
A function which varies as the square of a measured quantity. Power in this sense is not necessarily physical power.
POWER SPECTRAL DENSITY (PSD) FUNCTION. Also called the AUTO SPECTRAL DENSITY
A real-valued continuous function of frequency, presented with frequency on the horizontal axis and density on the vertical axis. which is a special case of a "cross-spectral density function" where the signal is compared with itself. The following is a method for measuring the PSD, which can lead to a definition of PSD: a signal is passed through a contiguous set of bandpass filters with an effective noise bandwidth B. The mean square output of each filter divided by the bandwidth B is measured with an effective averaging time T. A plot of this normalized mean square output as a function of the filter center frequencies is an estimate of the PSD. The PSD can be defined as the limit of this process where the time T is increased without limit and the bandwidth B is reduced to zero.
An equivalent definition is: the Fourier transform of the autocorrelation function. It is also the expected value of the squared magnitude of the Fourier transform of a sample time history divided by the effective (noise) filter bandwidth. Note that for a finite time history the value of the power spectral density can only be estimated. The statistical error and the effective filter shape are essential parts of that estimate.
An accumulation of data samples plotted as a function of an independent variable
of the samples, such as amplitude, and normalized for a specified integral
value is termed a histogram. For a time-varying function 
,
the probability density, 
,
can be defined as the limiting case of a histogram as:
where:
A term, , the probability
density function is also called the frequency function of a sample distribution.
To find the probability that a value falls within a specific range 
to 
, we integrate through
the range. Symbolically:
Since it is certain that every measurement must yield some real value, we must have
Note that the probability density function is always positive, being the derivative of the probability distribution function.
PROBABILITY DISTRIBUTION FUNCTION
The probability that the value of a variable 
is less than some specific 
as given by:
From the nonnegative character of the density function ,
we see that 
cannot decrease
with increasing 
; and also,
that 
In a digital Fourier analysis system, the improvement in signal-to-noise ratio between periodic components and broadband noise obtained by transformation to the frequency domain and observation in that domain. The effect is caused by the noise power being spread out over all frequencies while the discrete signal power remains constant at fixed frequencies. Doubling the number of frequency resolution lines provides 3 dB of processing gain; i.e., the noise floor will appear to be reduced by 3 dB in each cell (See FOURIER TRANSFORM).