Front Matter and Index (Mertins - Signal Analysis (Revised Edition)), страница 3

294Scaling function, 228, 237Scalogram, 215, 265, 289Schur algorithm, 131Schwarz inequality, 6Self-reciprocal kernels, 24Series expansions, 47general, 56orthogonal, 49Shannon wavelet, 230, 240Shapeadaptiveimage decomposition,193, 194Shape adaptive wavelet transform, 193,194Shift-invariance, 281Short-time Fourier transform, 196ff., 216discrete-time signals, 205perfect reconstruction, 204realizations using filter banks, 206reconstruction, 202reconstruction via series expansion,204spectral summation, 206Signal estimation, 113Signal spaces, lff.Signal-to-noise ratio, 207Singular value decomposition, 64, 67Smoothing kernel, 280separable, 284Soft thresholding, 263Span, 48Spectral estimation, 134-142Spectral factorization, 151Spectral subtraction, 207Spectral summation, 206Spectrogram, 201, 215, 265, 275, 283Speech analysis, 202Spline wavelets, 249Split-radix FFT, 91, 92Split-radix FHT, 97Stability condition, 221, 224Stationary process, 13STFT (see Short-time Fourier transform)Stochastic process (see Random process)Subband coding, 188Subsampling (see Downsampling)Subspace, 48Sum of subspaces, 48Symmetric bandpass, 40Symmetric reflection, 190Symmlets, 253Synthesis window, 202Temporal autocorrelation function, 269271Terz analysis, 226Thresholdinghard, 263soft, 263Tight frame, 225Time resolution, 199, 213, 286Time-frequency analysis, 196, 211, 269Time-frequency autocorrelation function, 267Time-frequency distributions, 265ff.affine-invariant, 289Choi-Williams, 288-291Cohen’s class, 281ff.general, 280Rihaczek, 288shift-invariant, 281ff.Zhao-Atlas-Marks, 288Time-frequency localization, 211, 216Time-frequency plane, 196, 198Time-frequency resolution, 198, 213Time-frequency window, 198, 213Time-scale analysis, 211, 214Toeplitz, 17Transform coding, 95Translation invariance, 214, 256Transmultiplexers, 195Tridiagonal matrix, 95Twiddle factors, 86, 92Two-scale relation, 233, 237IndexUnbiasednessfor deterministic parameters, 113for random parameters, 122of autocorrelation estimates, 133,136of spectral estimates, 136, 138, 140Uncertainty principle, 200, 265radar, 268, 269Unitary matrix, 65, 67, 70, 73, 105, 111Upsampling, 143, 144Vanishing moments, 243, 244Variance, 13Walsh functions, 56Walsh-Hadamard transform, 100Wavelet families, 247ff.Wavelet series, 223Wavelet transform, 210ff.analysis by multirate filtering, 232B trous algorithm, 256ff.biorthogonal, 224construction formulae, 238continuous-time signals, 210critical sampling, 224Daubechies wavelets, 252denoising, 263discrete (DWT), 197, 227ff.discrete-time signals, 255dual wavelet, 223dyadic, 219ff.dyadic sampling, 223ff.finite support, 245frame bounds, 224Haar wavelet, 229integral reconstruction, 217ff.linear phase, 247Mallat algorithm, 259Morlet wavelet, 260orthonormal, 224, 228, 236oversampling, 224, 258partition of unity, 241regularity, 244, 245semi-discrete reconstruction, 217ff.series expansion, 223ff.Shannon wavelet, 230317stability condition, 224synthesis by multirate filtering, 233tight frame, 225time-scale analysis, 214translation invariance, 256Welch method, 139, 140White noise processbandlimited, 19continuous-time, 18discrete-time, 19Whitening transforms, 111, 112, 130Wide-sense stationary processes, 14Wiener filters, 124Wiener-Hopf equation, 124Wiener-Khintchine theorem, 15Wigner distribution, 269ff.cross, 275discrete-time, 290linear operations, 279Moyal’s formula, 273, 276properties, 272pseudo-, 279Wigner-Ville spectrum, 292ff.Windowed signal, 197WindowsBartlett window, 133-135, 138, 141Blackman window, 140, 141Hamming window, 140, 141Hanning window, 140, 141Yule-Walker equations, 128, 141Zero padding, 137Zero-delay lifting, 177Zhao-Atlas-Marks distribution, 288%Transform, 75, 77-80.