This lecture covers rearrangements of the basic decimation-in-frequency algorithm and discuss the relation between decimation-in-time and decimation-in-frequency through the transposition theorem. It also covers more general arbitrary radix FFT algorithms.

Lecture 20: Computation of the discrete Fourier transform, part 3

This lecture discusses interpretation of the FFT flow graph and bit-reversed data ordering. It also discusses other decimation-in-time FFT algorithms by rearranging the flow graph and the decimation-in-frequency FFT algorithm.

Lecture 19: Computation of the discrete Fourier transform, part 2

This lectures covers different methods of computation of the discrete Fourier transform, including direct computation, successive decimation of the sequences, the decimation-in-time form of the FFT algorithm, and basic butterfly computation.

Lecture 18: Computation of the discrete Fourier transform, part 1

This lecture discusses the basic FIR filter design methods: windows, frequency sampling, and equi-ripple design.

Lecture 17: Design of FIR digital filters

This lecture gives examples of digital LPF design using impulse invariance and bilinear transformation on Butterworth filters, and compares the resulting designs.

Lecture 16: Digital Butterworth filters

This lecture introduces more techniques of digital filter design, including the bilinear transformation and algorithmic design procedures. It also discusses frequency warping introduced by the bilinear transformation.

Lecture 15: Design of IIR digital filters, part 2

This lecture introduces techniques of digital filter design, including transformation of analog filters to digital filters, approximation of derivatives by differences, and impulse invariant design procedures. It discusses the flaws and advantages of each.

Lecture 14: Design of IIR digital filters, part 1

This lecture covers direct form FIR filters, efficient implementation of FIR filters with linear phase, frequency sampling structure, and the effects of parameter-quantization in digital filter implementation.

Lecture 13: Network structures for finite impulse response (FIR)

This lecture covers basic network structures for IIR filters, direct cascade and parallel form, canonic structures, the transposition theorem for digital networks, and the resulting transposed forms.

Lecture 12: Network structures for infinite impulse response (IIR) systems

This lecture introduces block diagram presentation of difference equations, linear-signal flow graphs, flow graph representation of difference equations, and matrix representation of digital networks. It also discusses computability of digital networks.

Lecture 11: Representation of linear digital networks

This lecture covers circular convolution of finite length sequences. It discusses interpretation of circular convolution as linear convolution followed by aliasing, and describes implementation linear convolution by means of circular convolution.

Lecture 10: Circular convolution

This lecture includes more demonstrations of sampling and aliasing with a sinusoidal signal, sinusoidal response of digital filters, dependence of frequency response on sampling period, and the periodic nature of the frequency response of a digital filter.

Lecture 9: The discrete Fourier transform

This lecture introduces the Fourier series representation of sequences and describes how to determine the Fourier series coefficients. It also discusses properties of Fourier series.

Lecture 8: The discrete Fourier series

This lecture covers geometric determination of frequency response from pole-zero patterns in the z-plane. It also covers properties of z-transforms: scaling, differentiation, shifting, and convolution, ands gives examples of derivations of such properties.

Lecture 7: z-Transform properties

This lecture discusses and gives examples of the following methods of implementing the inverse z-transforms: the inspection method, power series, partial fraction expansion, and contour integration.

Lecture 6: The inverse z-transform

This lecture covers the z-transform and discusses its relationship with Fourier transforms. It also discusses relationship of the region of convergence to poles, zeros, stability, and causality.

Lecture 5: The z-transform

This lecture covers generalization of the frequency response representation of sequences and the inverse Fourier transform relation. It also covers the properties of and the relationship between continuous-time and discrete-time Fourier transforms.

Lecture 4: The discrete-time Fourier transform

This lecture covers stability and causality for discrete-time systems, systems described by linear constant-coefficient difference equations, and the frequency response of linear time-invariant systems.

Lecture 3: Discrete-time signals and systems, part 2

This lecture gives definitions of the unit sample, unit step, and exponential and sinusoidal sequences. It also gives definitions and representations of linear time-invariant discrete-time systems, and discusses properties of discrete-time convolution.

Lecture 2: Discrete-time signals and systems, part 1

This lecture provides an overview of the course and discusses some of the applications of digital signal processing.

Lecture 1: Introduction

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Digital Signal Processing

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