DISCRETE-SIGNAL ANALYSIS AND DESIGN- P37

DISCRETE-SIGNAL ANALYSIS AND DESIGN- P37:Electronic circuit analysis and design projects often involve time-domainand frequency-domain characteristics that are difÞcult to work with usingthe traditional and laborious mathematical pencil-and-paper methods offormer eras. This is especially true of certain nonlinear circuits and sys-tems that engineering students and experimenters may not yet be com-fortable with.
Nội dung trích xuất từ tài liệu:
DISCRETE-SIGNAL ANALYSIS AND DESIGN- P37166 GLOSSARYIntermodulation. Two or more input signals combine in a nonlinear cir- cuit or device to create spurious output frequencies.Inverse discrete Fourier transform (IDFT). Converts the frequency domain X (k ) to the time domain x (n). DeÞned according to Bracewell.Inverse fast Fourier transform (IFFT). A high-speed alternative for the IDFT. A Mathcad function deÞned according to Bracewell.Laplace transform. Converts a function in the S -plane σ ± j ω domain to a function in the time domain. The inverse transform performs the opposite process.Mathcad. A personal computer program that performs a very wide range of mathematical calculations, either numerical or symbolic, in inter- active form.Mathcad program. A structured set of logical operations that perform branching, counting, and loop procedures in a Mathcad worksheet.Mathcad X-Y Trace. A Mathcad utility that displays x and y values on a Mathcad graph.Mathtype. A program from Design Science.com that is used to enter equations into a word-processing document.Multiplication. A math process such as “3 × 4 = 12” or “a × b = c.” Two types of multiplication are “sequence” and “polynomial.” Two proper- ties are “commutative” and “associative.”Multisim. A program from National Instruments Co. that aids in circuit and system simulation, using accurate device models and embedded test instruments and sophisticated graphing capabilities.Non-real-time analysis. The signal is stored in memory and the analysis is performed at the speed of the computer, not at the same rate as the signal itself.Normal distribution. The Gaussian probability density function of x from x = minus inÞnity to x = plus inÞnity. The cumulative distribution function CDF is the area under the curve from x min to x max .Odd symmetry. The two sides X (k ) and X (N − k ) of a phasor spectrum have opposite phase.One-sided sequence. A sequence in which all components are in the positive-frequency or positive-time domain. The sequence is construc- ted from the two-sided sequence. GLOSSARY 167Phase noise. Noise created by variations in phase of a signal. The rate of change of phase creates a phase noise power spectrum.Phase shift network. An RC op-amp or DSP network that performs a negative 90◦ phase shift and a constant amplitude over a desired (e.g., speech) bandwidth.Phasor. The complex exponential A exp ( ± jωt) is a phasor with ampli- tude A and zero average power. It can be at a positive or a negative frequency, depending on the sign of j . Two ± j phasors combine to produce a sine wave or a cosine wave at positive frequency.Planck’s constant. 6.63 × 10−34 joule-sec.Postdetection Þlter. After RF/IF-to-baseband conversion, a signal can be Þltered at baseband to improve the quality of the signal and can frequently improve signal-to-noise ratio.Power spectrum. In an X (k ) two-sided phasor spectrum, the collection of phasor values (real or complex) at (k) from 0 to N − 1 is a phasor spectrum. The combination of phasors at X (k ) and X (N − k ) form a voltage or current signal at frequency (k ). This signal has a power value, real (watts) or imaginary (vars), and a phase angle. The collection of the power values from 0 to N /2 − 1 is a positive-frequency (including dc) power spectrum.Power (average). The average value of the product of voltage v (t) and the current i (t). If the two are in phase, the power is maximum and realvalued. If they are 90◦ out of phase, the average power is zero. The power value in a circuit can have a real component (watts) and an imaginary component (vars) and can have a phase angle θ with respect to some reference point.Probability. A measure of the likelihood of an event. A tossed coin can be heads (50% probability) or tails (50% probability) for a large number of experiments.Programming. Mathcad allows special program structures to be placed on a Mathcad worksheet. These programs greatly expedite and simplify certain kind of calculations that are difÞcult otherwise.Pseudorandom. An event that is unpredictable in a short time interval but repeats at speciÞc longer time intervals. Each occurrence may have random properties.168 GLOSSARYRandom. An event that is unpredictable in time and frequency and amplitude.Real-time analysis. An analysis that is performed in the same time frame as the experiment that is being observed.Record averaging. A statistical averaging of many sets (records) of mea- surements of a noise-contaminated random signal.Record length. The number of observations or measurements, from 0 to N − 1, in a sequence.Sequence. A succession from 0 to N − 1 of values of a discrete signal in the time domain or frequency domain.Sine wave, cosine wave. A pair of phasors, one at positive frequency and one at negative frequency, combine to make a sine or cosine wave.Smoothing. The process of reducing the amplitude differences between adjacent samples of a discrete signal.Spectral leakage. The variation of the amplitude of a discrete spectrum line at an integer value of k ± a small deviation |ε|.Spectrum analyzer. An instrument used to view the spectrum of an RF signal on a CRT display.State variable. The state of a system is its values of time, amplitude, frequency, phase, and derivatives at time (n) and frequency (k ).Statistical analysis. The properties of a noisy signal must be determined by procedures that extract an average result that approximates the prop- erties of the noise-free signal.Steady-state sequence. A sequence from 0 to N − 1 that repeats forever in the time x (n) or frequency X (k ) domain. Each sequence consists of time, or frequency-varying components, possibly superimposed on a constant (dc) background. All transient ...