This page contains a brief index to the lecture notes for EE 4773/6773: Introduction to Digital Signal Processing.

• Lecture 01: Lecturer introduction, an overview of the course (Sects. 1.1-1.3)

• Lecture 02: Student introductions, an overview of the course project (Sects. 1.1-1.3)

• Lecture 03: The Sampling Theorem, why DSP, a basic DSP system, basic signal classifications, normalized frequency, motivation for the sampling theorem (Sects. 1.4,1.5)

• Lecture 04: Basic definitions, elementary signals, classification of signals, important properties and operations, signal flow graphs, and classification of systems - static, time-invariant, linearity, and causality (Sects. 2.1,2.2)

• Lecture 05: Analysis of LTI systems, representation of signals as impulse trains, discrete convolution, properties of convolution, causality, stability, classification as FIR vs. IIR (Sect. 2.3)

• Lecture 06: Difference equations, constant-coefficient difference equations, the characteristic equation, implementation of discrete-time systems, FIR and IIR realizations (Sects. 2.4,2.5)

• Lecture 07: correlation of discrete-time signals, crosscorrelation and autocorrelation, normalized correlation, properties of correlation functions (Sects. 2.6,2.7)

• Lecture 08: Definition of the z-transform, region of convergence, the inverse z-transform, example, relationship to the Fourier transform, and the complex cepstrum (Sect. 3.1)

• Lecture 09: Properties of the z-transform, more examples (Sect. 3.2)

• Lecture 10: A surprise!, poles and zeroes, effects on causal signals, and transfer functions of LTI systems (Sect. 3.3)

• Lecture 11: the inverse z-transform, power series expansions, partial fraction expansions, z-transform of a sinewave (Sect. 3.4)

• Lecture 12: The one-sided z-transform, the shifting property, the final value theorem, and application to difference equations with initial conditions (Sect. 3.5)

• Lecture 13: Response of rational system functions, response of systems with non-zero initial conditions, causality and stability, multiple order poles, the Schur-Cohn Stability test, reflection and predictor coefficients, stability of second order systems (Sects. 3.6,3.7)

• Lecture 15: The Fourier series of continuous time signals, the power density spectrum, the Fourier transform, the energy density spectrum, Parseval's relation (Sect. 4.1)

• Lecture 16: The Fourier Series for discrete-time signals, the power density spectrum, the Fourier transform, convergence, energy density spectrum (Sect. 4.2)

• Lecture 17: Properties of the Fourier transform (Sect. 4.3)

• Lecture 18: Frequency-domain characteristics of LTI systems, steady-state and transient responses (Sect. 4.4)

• Lecture 19: Ideal filters, a table contrasting continuous and discrete signals, the concept of bandwidth, lowpass filtering, frequency ranges of common signals (Sect. 4.5)

• Lecture 20: Invertibility, minimum-phase systems, FIR systems as all-zero filters, system identification and deconvolution, homomorphic deconvolution (Sects. 4.6,4.7)

• Lecture 21: Frequency-domain sampling, reconstruction, frequency-domain interpolation, the DFT as a linear transform (Sect. 5.1)

• Lecture 22: Relationship of the DFT to other transforms, time-domain windowing, better windows (Sect. 5.1)

• Lecture 23: The system function for LTI systems, the frequency response function, interconnection of LTI systems, correlation functions and power spectra (Sect. 5.1)

• Lecture 24: Properties of the DFT, symmetry, circular convolution, using the DFT for linear filtering (Sect. 5.2)

• Lecture 25: Causality, dimensions of the digital filter design problem, design of linear-phase filters, the Kaiser window method (Sect. 5.3)

• Lecture 26: Computation of the frequency response, first-order poles and zeros, complex-conjugate pairs, a geometric interpretation (Sect. 5.4)

• Lecture 27: Efficient computation of the DFT, computational complexity, divide and conquer approaches (Sect. 6.1)

• Lecture 28: The Radix-2 FFT, decimation in time and frequency, DFTs of two real sequences, quantization properties (Sect. 6.2)

• Lecture 29: Structures for the realization of discrete-time systems, direct form implementations, frequency sampling structures (Sects. 7.1,7.2)

• Lecture 30: Lattice implementations of FIR systems, matrix formulations and two-port networks, conversions between FIR and lattice filters (Sect. 7.2)

• Lecture 31: IIR direct-form structures, transposed structures, cascade-form structures, parallel-form structures, lattice and ladder structures, implementation of discrete-time systems (Sect. 7.3,7.4)

• Lecture 33: State-space descriptions, solutions of the state-space equations, relationships between I/O and state-space, state-space analysis in the Z-domain (Sect. 7.5)

• Lecture 34: Representation of numbers, analysis of sensitivity to quantization errors, limit cycles, statistical characterization of quantization effects (Sects. 7.6-7.9)

• Lecture 35: Zeros of a linear phase filter, design of linear phase filters using windows, design by frequency sampling, optimum equiripple linear-phase FIR filters, the Parks-McLellan algorithm (Sect. 8.1)

• Lecture 36: Design of IIR filters from analog prototypes, design by the approximation of derivatives, impulse invariance, the bilinear transform (Sect. 8.2)

• Lecture 37: Analog prototypes (Butterworth, Chebyshev, Elliptic, and Bessel), a comparison (Sect. 8.2)

• Lecture 38: Frequency transformations, design methods based on least-squares methods (Sects. 8.3,8.4)

• Lecture 39: Pole/zero design of lowpass filters, lowpass to highpass transformation, digital resonators, notch filters, comb filters, all-pass filters (Sects. 8.4,8.5)

• Lecture 40: Weiner filters, frequency domain design of IIR filters (Sect. 8.5)

• Lecture 41: The Sampling Theorem, Sin(x)/x interpolation, the Bandlimited Sampling Theorem (Sect. 9.1)

• Lecture 42: A/D converters, sample and hold, quantization and coding, analysis of quantization errors, oversampling, sigma-delta modulation (Sect. 9.2)

• Lecture 44: D/A conversion, sample and hold, first-order hold, linear interpolation with delay (Sect. 9.3)

• Lecture 46: Multirate signal processing, signal interpolation, interpolation/decimation by a ratio of integers (Chapter 10)