6. The Discrete Fourier Transform (DFT)――10 hours

6.1 Four Fourier Transform Pairs

? Representation of periodic sequences: the discrete Fourier series ? Properties of the DFS ? The Fourier transform of periodic signals ? Sampling the Fourier transform ? Fourier representation of finite-duration sequences: the discrete Fourier transform ? Properties of the DFT ? Linear convolution using the DFT time → continuous discrete ↓

Fourier transform

x(t)?12?discrete-time Fourier transform

Aperiodic

?????X(j?)ej?td???j?tx[n]?12??2?0X(ej?)ej?nd? ???j?ncontinuous

X(j?)??x(t)e????dt?X(ej?)?n????x[n]e discrete

Fourier series Discrete Fourier transform periodic

xp(t)?Ck?1Tk????Cek??jk?0t1N?1?nk x[n]??X[k]WNNk?0X[k]??x[n]Wn?0N?1nkN?T0xp(t)e?jk?0t ↑

aperiodic periodic ← frequency

6.2 Representation of Periodic Sequences: The Discrete Fourier Series

6.4 The Discrete Fourier Transform

9

6.5 Circular Convolution of Two Finite-Length Sequences

6.6 Linear Convolution Using the Discrete Fourier Transform

7. Computation of the Discrete Fourier Transform――3 hours

? Decimation-in-Time FFT Algorithms ? Decimation-in-Frequency FFT Algorithms 7.1 Decimation-In-Time FFT Algorithms

7.2 Decimation-In-Frequency FFT Algorithms

8. Digital Filters Design based on Matlab――6 hours

The Filter Design and Analysis Tool (FDATool) is a powerful user interface for designing and analyzing filters. FDATool enables you to quickly design digital FIR or IIR filters by setting filter performance specifications, by importing filters from your MATLAB workspace, or by directly specifying filter coefficients. FDATool also provides tools for analyzing filters, such as magnitude and phase response plots and pole-zero plots. FVTool, which can be launched from FDATool, provides a separate window for analyzing filters. You can use FDATool as a convenient alternative to the command line filter design functions.

8.1 Filter Design Methods---IIR and FIR

8.2 Filter Design and Analysis Tool

8.3 Analyzing the Filter

8.4 Converting the Filter Structure

8.5 Exporting a Filter Design

8.6 Saving and Opening Filter Design Sessions

10