## Digital Signal ProcessingCovers the analysis and representation of discrete-time signals and systems, including discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform. Emphasis is placed on the similarities and distinctions between discrete-time and continuous-time signals and systems. Also covers digital network structures for implementation fo both recursive (infinite impulse response) and nonrecursive (finite impulse response) digital filters with four videocassettes devoted to digital filter design for recursive and nonrecursive filters. Concludes with a discussion of the fast Fourier transform algorithm for computation of the discrete Fourier transform. |

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Page 76

In particular, with the input and output satisfying the difference equation Mi Ni M,

N* 2 2a*rX»« - k, n - r) =2 J.bkAm - k,n - r) (2.63) k=0 r-0 *-0 r=0 and

z-transform to both sides of Eq. (2.63) it follows, using the properties in Table 2.2,

...

In particular, with the input and output satisfying the difference equation Mi Ni M,

N* 2 2a*rX»« - k, n - r) =2 J.bkAm - k,n - r) (2.63) k=0 r-0 *-0 r=0 and

**applying**thez-transform to both sides of Eq. (2.63) it follows, using the properties in Table 2.2,

...

Page 338

In addition to

sequence in terms of its real part on the unit circle, it can also be

certain conditions, to specify the z-transform of a sequence in terms of its

magnitude ...

In addition to

**applying**this argument to specifying the z-transform of a causalsequence in terms of its real part on the unit circle, it can also be

**applied**, undercertain conditions, to specify the z-transform of a sequence in terms of its

magnitude ...

Page 539

11.2 Estimates of the Autocovariance The concepts introduced in the previous

section can be

a random process. Again we assume a stationary random process {*„}, - oo < n ...

11.2 Estimates of the Autocovariance The concepts introduced in the previous

section can be

**applied**in studying estimators for the autocovariance sequence ofa random process. Again we assume a stationary random process {*„}, - oo < n ...

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### Contents

DISCRETETIME SIGNALS AND SYSTEMS | 6 |

FLOW GRAPH AND MATRIX REPRESENTA | 136 |

DIGITAL FILTER DESIGN TECHNIQUES | 195 |

Copyright | |

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### Common terms and phrases

analog filter applied approximation arithmetic assume autocorrelation autocovariance causal cepstrum chapter circular convolution coefficients complex cepstrum complex logarithm computation consider continuous-time corresponding defined denote depicted in Fig derived determine difference equation digital filter digital signal processing discrete Fourier transform discussed error example exponential expressed FFT algorithm finite finite-duration sequence finite-length sequence FIR system first-order fixed-point fixed-point arithmetic floating-point frequency response H(eia Hilbert transform implementation impulse response input integral inverse length linear phase linear shift-invariant system linear system lowpass filter magnitude minimum-phase multiplication node noise sources noise-to-signal ratio obtain output noise parameters passband periodic sequence periodogram poles and zeros polynomial power spectrum Problem properties quantization random process random variables realization region of convergence representation represented result samples second-order sequence x(n Show shown in Fig spectrum estimate stopband system function techniques theorem truncation two-dimensional unit circle unit-sample response variance z-plane z-transform