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Glossary 1/f noise: A type of random noise that increases in amplitude at lower frequencies. It is widely observable in physical systems, but not well understood. See white noise for comparison.
Glossary 631Glossary1/f noise: A type of random noise that increasesin amplitude at lower frequencies. It is widelyobservable in physical systems, but not wellunderstood. See white noise for comparison.-3dB cutoff frequency: The division between afilter's passband and transition band. Defined asthe frequency where the frequency response isreduced to -3dB (0.707 in amplitude)."A" law: Companding standard used in Europe.Allows digital voice signals to be representedwith only 8 bits instead of 12 bits by making thequantization levels unequal. See mu law forcomparison.AC: Alternating Current. Electrical term for theportion of a signal that fluctuates around theaverage (DC) value.Accuracy: The error in a measurement (or aprediction) that is repeatable from trial to trial.Accuracy is limited by systematic (repeatable)errors. See precision for comparison.Additivity: A mathematical property that isnecessary for linear systems. If input a producesoutput p, and if input b produces output q, then aninput of a+b produces an output of p+q.Aliasing: The process where a sinusoid changesfrom one frequency to another as a result ofsampling or other nonlinear action. Usuallyresults in a loss of the signal's information. Amplitude modulation: Method used in radiocommunication for combining an informationcarrying signal (such as audio) with a carrierwave. Usually carried out by multiplying the twosignals. Analysis: The forward Fourier transform;calculating the frequency domain from the timedomain. See synthesis for comparison.Antialias filter: Low-pass analog filter placedbefore an analog-to-digital converter. Removesfrequencies above one-half the sampling rate thatwould alias during conversion.ASCII: A method of representing letters andnumbers in binary form. Each character isassigned a number between 0 and 127. Verywidely used in computers and communication. Aspect ratio: The ratio of an image's width to itsheight. Standard television has an aspect ratio of4:3, while motion pictures have an aspect ratio of16:9.Assembly: Low-level programming language thatdirectly manipulates the registers and internalhardware of a microprocessor. See high-levellanguage for comparison. Associative property of convolution: Written as:. This is(a[n] tb[n]) tc[n] ' a[n] t(b[n] tc[n])important in signal processing because it describeshow cascaded stages behave.Autocorrelation: A signal correlated with itself.Useful because the Fourier transform of theautocorrelation is the power spectrum of theoriginal signal. Backprojection: A technique used in computedtomography for reconstructing an image from itsviews. Results in poor image quality unless usedwith a more advanced method.BASIC: A high-level programming languageknown for its simplicity, but also for its manyweaknesses. Most of the programs in this bookare in BASIC.Basilar membrane: Small organ in the ear thatacts as a spectrum analyzer. It allows differentfibers in the cochlear nerve to be stimulated bydifferent frequencies. Basis functions: The set of waveforms that adecomposition uses. For instance, the basisfunctions for the Fourier decomposition are unityamplitude sine and cosine waves. The Scientist and Engineer's Guide to Digital Signal Processing632Bessel filter: Analog filter optimized for linearphase. It has almost no overshoot in the stepresponse and similar rising and falling edges.Used to smooth time domain encoded signals.Bidirectional filtering: Recursive method used toproduce a zero phase filter. The signal is firstfiltered from left-to-right, then the intermediatesignal is filtered from right-to-left.Bilinear transform: Technique used to map thes-plane into the z-plane. Allows analog filters tobe converted into equivalent digital filters. Binning: Method of forming a histogram whenthe data (or signal) has numerous quantizationlevels, such as in floating point numbers.Biquad: An analog or digital system with twopoles and up to two zeros. Often cascaded tocreate a more sophisticated filter design.Bit reversal sorting: Algorithm used in the FFTto achieve an interlaced decomposition of thesignal. Carried out by counting in binary with thebits flipped left-for-right.Blackman window: A smooth curve used in thedesign of filters and spectral analysis, calculatedfrom: ,0.42 &0.5cos(2Bn/M) %0.08cos(4Bn/M)where n runs from 0 to M.Brightness: The overall lightness or darkness ofan image. See contrast for comparison.Butterfly: The basic computation used in theFFT. Changes two complex numbers into twoother complex numbers. Butterworth filter: Separates one band offrequencies from another; fastest roll-off whilekeeping the passband flat; can be analog ordigital. Also called a maximally flat filter.C: Common programming language used inscience, engineering and DSP. Also comes in themore advanced C++.Carrier wave: Term used in amplitudemodulation of radio signals. Refers to the highfrequency sine wave that is combined with a lowerfrequency information carrying signal.Cascade: A combination of two or more stageswhere the output of one stage becomes the inputfor the next. Causal signal: Any signal that has a value ofzero for all negative numbered samples. Causal system: A system that has a zero outputuntil a nonzero value has appeared on its input(i.e., the input causes the output). The impulseresponse of a causal system is a causal signal.Central Limit Theorem: Important theorem instatistics. In one form: a sum of many randomnumbers will have a Gaussian pdf, regardless ofthe pdf of the individual random numbers. Cepstrum: A rearrangement of "spectrum." Usedin homomorphic processing to describe thespectrum when the time and frequency domainsare switched.Charge coupled device (CCD): The light sensorin electronic cameras. Formed from a thin sheet ofsilicon containing a two-dimensional array of lightsensitive regions called wells.Chebyshev filter: Used for separating one bandof frequencies from another. Achieves a fasterroll-off than the Butterworth by allowing ripple inthe passband. Can be analog or digital.Chirp system: Used in radar and sonar. Animpulse is converted into a longer duration signalbefore transmission, and compressed back into animpulse after reception. Circular buffer: Method of data storage used inreal time processing; each newly acquired samplereplaces the oldest sample in memory.Circular convolution: Aliasing that can occur inthe time domain when frequency domain signalsare multiplied. Each period in the time domainoverflows into adjacent periods.Circularity: The appearance that the end of asignal is connected to its beginning. This ariseswhen considering only a single period of aperiodic signal.Classifiers: A parameter extracted from andrepresenting a larger data set. For example: sizeof a region, amplitude of a peak, sharpness of anedge, etc. Used in pattern recognition.Closing: A morphological operation defined as anerosion operation followed by a dilation operation.Cochlea: Organ in the ear where sound inconverted into a neural signal. Cochlear nerve: Nerve that transmits audioinformation from the ear to the brain. Coefficient-of-variation (CV): Common way of Glossary 633stating the variation (noise) in data. Defined as:100% × standard deviation / mean.Commutative property of convolution: Writtenas: . a[n] tb[n] ' b[n] ta[n]Companding: An "s" shaped nonlinearity allowsvoice signals to be digitized using only 8 bitsinstead of 12 bits. Europe uses "A" law, while theUnited States uses the mu law version.Complex conjugation: Changing the sign of theimaginary part of a complex number. Oftendenoted by a star placed next to the variable.Example: if , then .A ' 3 %2j A(' 3 &2jComplex DFT: The discrete Fourier transformusing complex numbers. A more complicated andpowerful technique than the real DFT. Complex exponential: A complex number of theform: . They are useful in engineering andea %bjscience because Euler's relation allows them torepresent sinusoids.Complex Fourier transform: Any of the fourmembers of the Fourier transform family writtenusing complex numbers. See real Fouriertransform for comparison.Complex numbers: The real numbers (used ineveryday math) plus the imaginary numbers(numbers containing the term j, where ).j ' &1Example: .3 %2jComplex plane: A graphical interpretation ofcomplex numbers, with the real part on the x-axisand the imaginary part on the y-axis. This isanalogous to the number line used with ordinarynumbers.Composite video: An analog television signalthat contains synchronization pulses to separatethe fields or frames.Computed tomography (CT): A method used toreconstruct an image of the interior of an objectfrom its x-ray projections. Widely used inmedicine; one of the earliest applications of DSP.Old name: CAT scanner.Continuous signal: A signal formed fromcontinuous (as opposed to discrete) variables.Example: a voltage that varies with time. Oftenused interchangeably with analog signal. Contrast: The difference between the bright-nessof an object and the brightness of the background.See brightness for comparison. Converge: Term used in iterative methods toindicate that progress is being made toward asolution ("The algorithm is converging") or that asolution has been reached ("The algorithm hasconverged"). Convolution integral: Mathematical equationthat defines convolution in continuous systems;analogous to the convolution sum for discretesystems. Convolution kernel: The impulse response of afilter implemented by convolution. Also known asthe filter kernel and the kernel.Convolution sum: Mathematical equationdefining convolution for discrete systems.Cooley and Tukey: J.W. Cooley and J.W. Tukey,given credit for bringing the FFT to the world ina paper they published in 1965. Correlation: Mathematical operation carried outthe same as convolution, except a left-for-right flipof one signal. This is an optimal way to detect aknown waveform in a signal.Cross-correlation: The signal formed when onesignal is correlated with another signal. Peaks inthis signal indicate a similarity between theoriginal signals. See also autocorrelation.Cutoff frequency: In analog and digital filters,the frequency separating the passband from thetransition band. Often measured where theamplitude is reduced to 0.707 (-3dB).CVSD: Continuously Variable Slope Deltamodulation, a technique used to convert a voicesignal into a continuous binary stream. DC: Direct Current. Electrical term for theportion of the signal that does not change withtime; the average value or mean. See AC forcomparison.Decibel SPL: Sound Pressure Level. Log scaleused to express the intensity of a sound wave: 0dB SPL is barely detectable; 60 dB SPL is normalspeech, and 140 dB SPL causes ear damage. Decimation: Reducing the sampling rate of adigitized signal. Generally involves low-passfiltering followed by discarding samples. Seeinterpolation for comparison.Decomposition: The process of breaking a signalinto two or more additive components. Often refersspecifically to the forward Fourier transform, The Scientist and Engineer's Guide to Digital Signal Processing634breaking a signal into sinusoids.Deconvolution: The inverse operation ofconvolution: if , find givenx[n] th[n] ' y[n] x[n]only . Deconvolution is usuallyh[n] and y[n]carried out by dividing the frequency spectra.Delta encoding: A broad term referring totechniques that store data as the differencebetween adjacent samples. Used in ADC, datacompression and many other applications.Delta function: A normalized impulse. Thediscrete delta function is a signal composed of allzeros, except the sample at zero that has a value ofone. The continuous delta function is similar, butmore abstract.Delta-sigma: Analog-to-digital conversionmethod popular in voice and music processing.Uses a very high sampling rate with only a singlebit per sample, followed by decimation.Dependent variable: In a signal, the dependentvariable depends on the value of the indepen-dentvariable. Example: when a voltage changes overtime, time is the independent variable and voltageis the dependent variable.Difference equation: Equation relating the pastand present samples of the output signal with pastand present samples of the input signal. Alsocalled a recursion equation.Dilation: A morphological operation. Whenapplied to binary images, dilation makes theobjects larger and can combine disconnectedobjects into a single object. Discrete cosine transform (DCT): A relative ofthe Fourier transform. Decomposes a signal intocosine waves. Used in data compression. Discrete derivative: An operation for discretesignals that is analogous to the derivative forcontinuous signals. A better name is the firstdifference. Discrete Fourier transform (DFT): Member ofthe Fourier transform family dealing with timedomain signals that are discrete and periodic.Discrete integral: Operation on discrete signalsthat is analogous to the integral for continuoussignals. A better name is the running sum.Discrete signal: A signal that uses quantizedvariables, such as a digitized signal residing in acomputer.Discrete time Fourier transform (DTFT):Member of the Fourier transform family dealingwith time domain signals that are discrete andaperiodicDithering: Adding noise to an analog signalbefore analog-to-digital conversion to prevent thedigitized signal from becoming "stuck" on onevalue. Domain: The independent variable of a signal.For example, a voltage that varies with time is inthe time domain. Other common domains are thespatial domain (such as images) and thefrequency domain (the output of the Fouriertransform). Double precision: A standard for floating pointnotation that used 64 bits to represent eachnumber. See single precision for comparison. DSP microprocessor: A type of microprocessordesigned for rapid math calculations. Often has apipeline and/or Harvard architecture. Also calleda RISC. Dynamic range: The largest amplitude a systemcan deal with divided by the inherent noise of thesystem. Also used to indicate the number of bitsused in an ADC. Can also be used withparameters other than amplitude; see frequencydynamic range.Edge enhancement: Any image processingalgorithm that makes the edges more obvious.Also called a sharpening operation.Edge response: In image processing, the outputof a system when the input is an edge. Thesharpness of the edge response is often used as ameasure of the resolution of the system.Elliptic filter: Used to separate one band offrequencies from another. Achieves a fast roll-offby allowing ripple in the passband and thestopband. Can be used in both analog and digitaldesigns.End effects: The poorly behaved ends of afiltered signal resulting from the filter kernel notbeing completely immersed in the input signal.Erosion: A morphological operation. Whenapplied to binary images, erosion makes theobjects smaller and can break objects into two ormore pieces. Euler's relation: The most important equation incomplex math, relating sine and cosine waves with Glossary 635complex exponentials.Even/odd decomposition: A way of breaking asignal into two other signals, one having evensymmetry, and the other having odd symmetry.Even order filter: An analog or digital filterhaving an even number of poles.False-negative: One of four possible outcomes ofa target detection trial. The target is present, butincorrectly indicated to be not present. False-positive: One of four possible outcomes ofa target detection trial. The target is not present,but incorrectly indicated to be present. Fast Fourier transform (FFT): An efficientalgorithm for calculating the discrete Fouriertransform (DFT). Reduces the execution time byhundreds in some cases.FFT convolution: A method of convolvingsignals by multiplying their frequency spectra. Sonamed because the FFT is used to efficiently movebetween the time and frequency domains.Field: Interlaced television displays the even linesof each frame (image) followed by the odd lines.The even lines are called the even field, and theodd lines the odd field. Filter kernel: The impulse response of a filterimplemented by convolution. Also known as theconvolution kernel and the kernel.Filtered backprojection: A technique used incomputed tomography for reconstructing an imagefrom its views. The views are filtered and thenbackprojected.Finite impulse response (FIR): An impulseresponse that has a finite number of nonzerovalues. Often used to indicate that a filter is carriedout by using convolution, rather than recursion.First difference: An operation for discretesignals that mimics the first derivative forcontinuous signals; also called the discretederivative.Fixed point: One of two common ways thatcomputers store numbers; usually used to storeintegers. See floating point for comparison. Flat-top window: A window used in spectralanalysis; provides an accurate measurement of theamplitudes of the spectral components. Thewindowed-sinc filter kernel can be used. Floating point: One of the two common waysthat computers store numbers. Floating pointuses a form of scientific notation, where amantissa is raised to an exponent. See fixedpoint for comparison. Forward transform: The analysis equation of theFourier transform, calculating the frequencydomain from the time domain. See inversetransform for comparison.Fourier reconstruction: One of the methods usedin computed tomography to calculate an imagefrom its views.Fourier series: The member of the Fouriertransform family that deals with time domainsignals that are continuous and periodic.Fourier transform: A family of mathematicaltechniques based on decomposing signals intosinusoids. In the complex version, signals aredecomposed into complex exponentials. Fourier transform pair: Waveforms in the timeand frequency domains that correspond to eachother. For example, the rectangular pulse and thesinc function.Fovea: A small region in the retina of the eyethat is optimized for high-resolution vision. Frame: An individual image in a televisionsignal. The NTSC television standard uses 30frames per second. Frame grabber: A analog-to-digital converterused to digitize and store a frame (image) from atelevision signal. Frequency domain: A signal having frequency asthe independent variable. The output of theFourier transform.Frequency domain aliasing: Aliasing that occursoccurring in the frequency domain in response toan action taken in the time domain. Aliasingduring sampling is an example.Frequency domain convolution: Convolutioncarried out by multiplying the frequency spectraof the signals. Frequency domain encoding: One of two mainways that information can be encoded in a signal.The information is contained in the amplitude,frequency, and phase of the signal's componentsinusoids. Audio signals are the best example.See time domain encoding for comparison. The Scientist and Engineer's Guide to Digital Signal Processing636Frequency domain multiplexing: A method ofcombining signals for simultaneous transmis-sionby shifting them to different parts of the frequencyspectrum. Frequency dynamic range: The ratio of thelargest to the lowest frequency a system can dealwith. Analog systems usually have a much largerfrequency dynamic range than digital systems.Frequency resolution: The ability to distinguishor separate closely spaced frequencies. Frequency response: The magnitude and phasechanges that sinusoids experience when passingthrough a linear system. Usually expressed as afunction of frequency. Often found by taking theFourier transform of the impulse response.Fricative: Human speech sound that originates asrandom noise from air turbulence, such as: s, f,sh, z, v and th. See voiced for comparison.Full-width-at-half-maximum (FWHM): Acommon way of measuring the width of a peak ina signal. The width of the peak is measured atone-half of the peak's maximum amplitude. Fundamental frequency: The frequency that aperiodic waveform repeats itself. See harmonicfor comparison.Gamma curve: The mathematical function orlook-up table relating a stored pixel value and thebrightness it appears in a displayed image. Alsocalled a grayscale transform. Gaussian: A bell shaped curve of the generalform: . The Gaussian has many uniqueex2properties. Also called the normal distribution.Gibbs effect: When a signal is truncated in onedomain, ringing and overshoot appear at edges andcorners in the other domain. GIF: A common image file format using LZW(lossless) compression. Widely used on the worldwide web for graphics. See TIFF and JPEG forcomparison.Grayscale: image A digital image where eachpixel is displayed in shades of gray between blackand white; also called a black and white image. Grayscale stretch: Greatly increasing thecontrast of a digital image to allow the detailedexamination of a small range of quantizationlevels. Quantization levels outside of this rangeare displayed as saturated black or white.Grayscale transform: The conversion functionbetween a stored pixel value and the brightnessthat appears in a displayed image. Also called agamma curve. Halftone: A common method of printing imageson paper. Shades of gray are created by variouspatterns of small black dots. Color halftones usedots of red, green and blue. Hamming window: A smooth curve used in thedesign of filters and spectral analysis, calculatedfrom: , where n runs from0.54 & 0.46cos(2Bn/M)0 to M.Harmonics: The frequency components of aperiodic signal, always consisting of integermultiples of the fundamental frequency. Thefundamental is the first harmonic, twice thisfrequency is the second harmonic, etc. Harvard Architecture: Internal computer layoutwhere the program and data reside in separatememories accessed through separate busses;common in microprocessors used for DSP. SeeVon Neumann Architecture for comparison.High fidelity: High quality music reproduction,such as provided by CD players.High-level language: Programming languagessuch as C, BASIC and FORTRAN.High-speed convolution: Another name for FFTconvolution. Hilbert transformer: A system having the freq-uency response: Mag = 1, Phase = 90E, for allfrequencies. Used in communications systems formodulation. Can be analog or digital.Histogram equalization: Processing an image byusing the integrated histogram of the image as thegrayscale transform. Works by giving large areasof the image higher contrast than the small areas.Histogram: Displays the distribution of values ina signal. The x-axis show the possible values thesamples can take on; the y-axis indicates thenumber of samples having each value.Homogeneity: A mathematical property of alllinear systems. If an input produces anx[n]output of , then an input produces any[n] kx[n]output of , for any constant k.ky[n]Homomorphic: DSP technique for separatingsignals combined in a nonlinear way, such as bymultiplication or convolution. The nonlinear Glossary 637problem is converted to a linear one by anappropriate transform.Huffman encoding: Data compression methodthat assigns frequently encountered charactersfewer bits than seldom used characters. Hyperspace: Term used in target detection andneural network analysis. One parameter can begraphically interpreted as a line, two parameters aplane, three parameters a space, and more thanthree parameters a hyperspace.Imaginary part: The portion of a complexnumber that has a j term, such as 2 in . In3 %2jthe real Fourier transform, the imaginary part alsorefers to the portion of the frequency domain thatholds the amplitudes of the sine waves, eventhough j terms are not used.Impulse: A signal composed of all zeros exceptfor a very brief pulse. For discrete signals, thepulse consists of a single nonzero sample. Forcontinuous signals, the width of the pulse must bemuch shorter than the inherent response of anysystem the signal is used with.Impulse decomposition: Breaking an N pointsignal into N signals, each containing a singlesample from the original signal, with all theother samples being zero. This is the basis ofconvolution.Impulse response: The output of a system whenthe input is a normalized impulse (a deltafunction).Impulse train: A signal consisting of a series ofequally spaced impulses. Independent variable: In a signal, the depen-dent variable depends on the value of theindependent variable. Example: when a voltagechanges over time, time is the independentvariable and voltage is the dependent variable.Infinite impulse response (IIR): An impulseresponse that has an infinite number of nonzerovalues, such as a decaying exponential. Oftenused to indicate that a filter is carried out by usingrecursion, rather than convolution.Integers: Whole numbers: .þ &2, &1, 0, 1, 2, þAlso refers to numbers stored in fixed pointnotation. See floating point for comparison. Interlaced decomposition: Breaking a signal intoits even numbered and odd numbered samples.Used in the FFT. Interlaced video: A video signal that displaysthe even lines of each image followed by the oddlines. Used in television; developed to reduceflicker.Interpolation: Increasing the sampling rate of adigitized signal. Generally done by placing zerosbetween the original samples and using a low-passfilter. See decimation for comparison.Inverse transform: The synthesis equation of theFourier transform, calculating the time domainfrom the frequency domain. See forwardtransform for comparison.Iterative: Method of finding a solution bygradually adjusting the variables in the rightdirection until convergence is achieved. Used inCT reconstruction and neural networks. JPEG: A common image file format usingtransform (lossy) compression. Widely used onthe world wide web for graphics. See GIF andTIFF for comparison. Kernel: The impulse response of a filterimplemented by convolution. Also known as theconvolution kernel and the filter kernel.Laplace transform: Mathematical method ofanalyzing systems controlled by differentialequations. A main tool in the design of electriccircuits, such as analog filters. Changes a signalin the time domain into the s-domainLearning algorithm: The procedure used to finda set of neural network weights based on examplesof how the network should operate. Line pair: Imaging term for cycle. For example,5 cycles per mm is the same as 5 line pairs permm. Line pair gauge: A device used to measure theresolution of an imaging system. Contains aseries of light and dark lines that move closertogether at one end. Line spread function (LSF): The response of animaging system to a thin line in the input image.Linear phase: A system with a phase that is astraight line. Usually important because it meansthe impulse response has left-to-right symmetry,making rising edges in the output signal look thesame as falling edges. See also zero phase.Linear system: By definition, a system that hasthe properties of additivity and homogeneity. The Scientist and Engineer's Guide to Digital Signal Processing638Lossless compression: Data compressiontechnique that exactly reconstructs the originaldata, such as LZW compression. Lossy compression: Data compression methodsthat only reconstruct an approximation to theoriginal data. This allows higher compressionratios to be achieved. JPEG is an example.Matched filtering: Method used to determinewhere, or if, a know pattern occurs in a signal.Matched filtering is based on correlation, butimplemented by convolution. Mathematical equivalence: A way of usingcomplex numbers to represent real problems.Based on Euler's relation equating sinusoids withcomplex exponentials. See substitution forcomparison. Mean: The average value of a signal or othergroup of data.Memoryless: Systems where the current value ofthe output depends only on the current value of theinput, and not past values.MFLOPS: Million-Floating-Point-Operations-Per-Second; a common way of expressing computerspeed. See MIPS for comparison.MIPS: Million-Instructions-Per-Second; acommon way of expressing computer speed. SeeMFLOPS for comparison. Mixed signal: Integrated circuits that containboth analog and digital electronics, such as anADC placed on a Digital Signal Processor. Modulation transfer function (MTF): Imagingjargon for the frequency response. Morphing: Gradually warping an image from oneform to another. Used for special effects, such asa man turning into a werewolf. Morphological: Usually refers to simple non-linear operations performed on binary images,such as erosion and dilation.Moving average filter: Each sample in theoutput signal is the average of many adjacentsamples in the input signal. Can be carried out byconvolution or recursion.MPEG: Compression standard for video, such asdigital television. Mu law: Companding standard used in theUnited States. Allows digital voice signals to berepresented with only 8 bits instead of 12 bits bymaking the quantization levels unequal. See "A"law for comparison.Multiplexing: Combining two or move signalstogether for transmission. This can be carried outin many different ways. Multirate: Systems that use more than onesampling rate. Often used in ADC and DAC toobtain better performance, while using lesselectronics. Natural frequency: A frequency expressed inradians per second, as compared to cycles persecond (hertz). To convert frequency (in hertz) tonatural frequency, multiply by 2B.Negative frequencies: Sinusoids can be writtenas a positive frequency: , or a negativecos(Tt)frequency: . Negative frequencies arecos(&Tt)included in the complex Fourier transform, makingit more powerful.Normal distribution: A bell shaped curve of theform: . Also called a Gaussian.ex2NTSC: Television standard used in the UnitedStates, Japan, and other countries. See PAL andSECAM for comparison.Nyquist frequency, Nyquist rate: These termsrefer to the sampling theorem, but are used indifferent ways by different authors. They can beused to mean four different things: the highestfrequency contained in a signal, twice thisfrequency, the sampling rate, or one-half thesampling rate.Octave: A factor of two in frequency.Odd order filter: An analog or digital filterhaving an odd number of poles.Opening: A morphological operation defined asa dilation operation followed by an erosionoperation.Optimal filter: A filter that is "best" in somespecific way. For example, Wiener filters producean optimal signal-to-noise ratio and matchedfilters are optimal for target detection.Overlap add: Method used to break long signalsinto segments for processing.PAL: Television standard used in Europe. SeeNTSC for comparison. Glossary 639Parallel stages: A combination of two or morestages with the same input and added outputs. Parameter space: Target detection jargon. Oneparameter can be graphically interpreted as aline, two parameters a plane, three parametersa space, and more than three parameters ahyperspace.Parseval's relation: Equation relating the energyin the time domain to the energy in the frequencydomain. Passband: The band of frequencies a filter isdesigned to pass unaltered. Passive sonar: Detection of submarines and otherundersea objects by the sounds they produce.Used for covert surveillance. Phasor transform: Method of using complexnumbers to find the frequency response of RLCcircuits. Resistors, capacitors and inductorsbecome R, , and , respectively.&j/TC jTLPillbox: Shape of a filter kernel used in imageprocessing: circular region of a constant valuesurrounded by zeros.Pitch: Human perception of the fundamentalfrequency of an continuous tone. See timbre forcomparison. Pixel: A contraction of "picture element." Anindividual sample in a digital image.Point spread function (PSF): Imaging jargon forthe impulse response. Pointer: A variable whose value is the address ofanother variable.Poisson statistics: Variations in a signal's valueresulting from it being represented by a finitenumber of particles, such as: x-rays, light photonsor electrons. Also called Poisson noise andstatistical noise.Polar form: Representing sinusoids by theirmagnitude and phase: , where M isMcos(Tt % N)the magnitude and N is the phase. Seerectangular form for comparison.Pole: Term used in the Laplace transform and z-transform. When the s-domain or z-domaintransfer function is written as one polynomialdivided by another polynomial, the roots of thedenominator are the poles of the system, while theroots of the numerator are the zeros.Pole-zero diagram: Term used in the Laplaceand z-transforms. A graphical display of thelocation of the poles and zeros in the s-plane or z-plane. Precision: The error in a measurement orprediction that is not repeatable from trial to trial.Precision is determined by random errors. Seeaccuracy for comparison.Probability distribution function (pdf): Givesthe probability that a continuous variable will takeon a certain value. Probability mass function (pmf): Gives theprobability that a discrete variable will take on acertain value. See pdf for comparison.Pulse response: The output of a system when theinput is a pulse.Quantization error: The error introduced whena signal is quantized. In most cases, this resultsin a maximum error of ±½ LSB, and an rms errorof LSB. Also called quantization noise. 1/ 12Random error: Errors in a measurement orprediction that are not repeatable from trial totrial. Determines precision. See systematic errorfor comparison. Radar: Radio Detection And Ranging. Echolocation technique using radio waves to detectaircraft. Real DFT: The discrete Fourier transform usingonly real (ordinary) numbers. A less powerfultechnique than the complex DFT, but simpler. Seecomplex DFT for comparison.Real FFT: A modified version of the FFT. About30% faster than the standard FFT when the timedomain is completely real (i.e., the imaginary partof the time domain is zero). Real Fourier transform: Any of the members ofthe Fourier transform family using only real (asopposed to imaginary or complex) numbers. Seecomplex Fourier transform for comparison.Real part: The portion of a complex number thatdoes not have the j term, such as 3 in . In3 %2jthe real Fourier transform, the real part refers tothe part of the frequency domain that holds theamplitudes of the cosine waves, even though no jterms are present.Real time processing: Processing data as it isacquired, rather than storing it for later use. The Scientist and Engineer's Guide to Digital Signal Processing640Example: DSP algorithms for controlling echoes inlong distance telephone calls.Reconstruction filter: A low-pass analog filterplaced after a digital-to-analog converter.Smoothes the stepped waveform by removingfrequencies above one-half the sampling rate.Rectangular form: Representing a sinusoid bythe form: , where A is calledAcos(Tt) % B sin(Tt)the real part and B is called the imaginary part(even though these are not imaginary numbers).Rectangular window: A signal with a group ofadjacent points having unity value, and zeroelsewhere. Usually multiplied by another signal toselect a section of the signal to be processed. Recursion coefficients: The weighing valuesused in a recursion equation. The recursioncoefficients determine the characteristics of arecursive (IIR) filter.Recursion equation: Equation relating the pastand present samples of the output signal with thepast and present values of the input signal. Alsocalled a difference equation.Region-of-convergence: The term used in theLaplace and z-transforms. Those regions in the s-plane and z-planes that have a defined value. RGB encoding: Representing a color image byspecifying the amount of red, green, and blue foreach pixel.RISC: Reduced Instruction Set Computer, alsocalled a DSP microprocessor. A fewer number ofprogramming commands allows much higherspeed math calculations. The opposite is theComplex Instruction Set Computer, such as thePentium. ROC curve: A graphical display showing howthreshold selection affects the performance of atarget detection problem. Roll-off: Jargon used to describe the sharpness ofthe transition between a filter's passband andstopband. A fast roll-off means the transition issharp; a slow roll-off means it is gradual.Root-mean-square (rms): Used to express thefluctuation of a signal around zero. Often used inelectronics. Defined as the square-root of themean of the squares. See standard deviation forcomparison.Round-off noise: The error caused by roundingthe result of a math calculation to the nearestquantization level.Row major order: A pattern for converting animage to serial form. Operates the same asEnglish writing: left-to-right on the first line, left-to-right on the second line, etc. Run-length encoding: Simple data compressiontechnique with many variations. Characters thatare repeated many times in succession are replacedby codes indicating the character and the length ofthe run.Running sum: An operation used with discretesignals that mimics integration of continuoussignals. Also called the discrete integral.s-domain: The domain defined by the Laplacetransform. Also called the s-plane.Sample spacing: The spacing between sampleswhen a continuous image is digitized. Defined asthe center-to-center distance between pixels. Sampling aperture: The region in a continuousimage that contributes to an individual pixelduring digitization. Generally about the same sizeas the sample spacing.Sampling theorem: If a continuous signalcomposed of frequencies less than f is sampled at2f, all of the information contained in thecontinuous signal will be present in the sampledsignal. Frequently called the Shannon samplingtheorem or the Nyquist sampling theorem.SECAM: Television standard used in Europe.See NTSC for comparison. Seismology: Branch of geophysics dealing withthe mechanical properties of the earth.Separable: An image that can be represented asthe product of its vertical and horizontal profiles.Used to improve the speed of image convolution.Sharpening: Image processing operation thatmakes edges more abrupt. Shift and subtract: Image processing operationthat creates a 3D or embossed effect.Shift invariance: A property of many systems.A shift in the input signal produces nothingmore than a shift in the output signal. Meansthat the characteristics of the system do notchanging with time (or other independentvariable). [...]... many systems. A shift in the input signal produces nothing more than a shift in the output signal. Means that the characteristics of the system do not changing with time (or other independent variable). Glossary 633 stating the variation (noise) in data. Defined as: 100% × standard deviation / mean. Commutative property of convolution: Written as: . a[n] tb[n] ' b[n] ta[n] Companding: An "s"... 169-176 Spectral inversion. See under Filters Spectral response of the eye, 380-381 Spectral reversal. See under Filters, digital Speech digital recording, 6 generation, 6, 357, 364-368 recognition, 6-7, 364-368 Glossary 639 Parallel stages: A combination of two or more stages with the same input and added outputs. Parameter space: Target detection jargon. One parameter can be graphically interpreted as a line,... 348-350 spectral inversion, 270-272, 293 spectral reversal, 273-274 step response, 262-263, 265-267, 338 stopband (defined), 268 stopband attenuation, 268-269, 293-296 time domain parameters, 266-268 Glossary 641 Sigmoid: An "s" shaped curve used in neural networks. Signal: A description of how one parameter varies with another parameter. Example: a voltage that varies with time. Signal... Switched capacitor filter: Analog filter that uses rapid switching to replace resistors. Made as easy-to-use integrated circuits. Often used as antialias filters for ADC and reconstruction filters for DAC. Glossary 637 problem is converted to a linear one by an appropriate transform. Huffman encoding: Data compression method that assigns frequently encountered characters fewer bits than seldom used characters. . Glossary 63 1Glossary1 /f noise: A type of random noise that increasesin amplitude. audioinformation from the ear to the brain. Coefficient-of-variation (CV): Common way of Glossary 633stating the variation (noise) in data. Defined as:100% × standard