The English course "Digital signal processing" (DSP) gives an introduction into discrete-time signals and systems. It presents methods for analyzing discrete-time signals and systems. It also describes how to design systems and to process signals for solving practical problems.

1.

Introduction

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history of DSP, why DSP

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signals and systems

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difference between continuous-time and discrete-time sinusoidal signals, aliasing

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analog-to-digital conversion, sampling, Nyquist criterion, quantization

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digital-to-analog conversion

2.

Discrete-time signals and systems

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discrete-time signals, classification of signals

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discrete-time systems, classification of systems

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linear time-invariant and time-variant systems, impulse response, convolution, causality and stability, FIR and IIR systems

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linear constant-coefficient difference equation and its solution, non-recursive and recursive systems.

3.

The z-transform

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z-transform, region of convergence, inverse z-transform

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properties of the z-transform

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transfer function of an LTI system

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rational transfer function, poles and zeros, stability

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inversion of the z-transform, partial fraction expansion

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solving linear constant-coefficient difference equations using z-transform

4.

Frequency analysis of signals and systems

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Fourier series of continuous-time and discrete-time periodic signals

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Fourier transform of continuous-time and discrete-time non-periodic signals

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sampling theorem

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duality in Fourier series and Fourier transform, properties of the Fourier transform

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frequency analysis of discrete-time LTI systems, frequency response and its relation to the transfer function

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lowpass, highpass, bandpass, notch filter, comb filter, digital oscillator, linear phase FIR filter, allpass, minimum-phase filter

5.

The discrete Fourier transform

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Discrete Fourier transform (DFT)

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properties of DFT

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circular convolution

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filtering based on DFT

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fast Fourier transform (FFT)

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applications of FFT