(section 1471x) discrete time signals and systems · eel 3135 (section 1471x) discrete-time signals...
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EEL 3135EEL 3135(Section 1471X)(Section 1471X)
DiscreteDiscrete--Time Signals and SystemsTime Signals and Systems
Lecture 9Lecture 9
Prof. Jian Li
Dept. of Electrical and Computer EngineeringUniversity of Florida,Gainesville, FL 32611
Office: 437 EBPhone: 352-392-2642 Email: [email protected]
Dept. of ECE 3
DTFT ReviewDTFT Review
Fourier Synthesis (Inverse Fourier Transform)
Fourier Analysis (Fourier Transform)
Periodicity
Discrete Signal Periodic Spectra
Dept. of ECE 4
Discrete Fourier Transform (DFT)Discrete Fourier Transform (DFT)
Periodic Discrete Signal Discrete Periodic Spectra
Sampling will make x[n] periodic!
N-Point DFT Pair
Synthesis
Analysis
Dept. of ECE 6
MATLAB for DFTMATLAB for DFT
Number of frequency samples
XX = XX = fftfft((xxxx, N);, N);
Input sequence of length L < N
---- xx xx first zerofirst zero--padded to length Npadded to length N---- NN--pointpoint DFT is next computedDFT is next computed---- FFT is a fast way of computing DFTFFT is a fast way of computing DFT
Dept. of ECE 7
FFTFFT
Computations ofComputations ofDFT ( )DFT ( )vs. FFTvs. FFT( ( ))
N = # of PointsN = # of PointsN = Power of 2N = Power of 2
Dept. of ECE 8
Spectrum AnalysisSpectrum Analysis
Frequency content Frequency content of a signal is often a of a signal is often a function of timefunction of time
Not very informative
Dept. of ECE 9
SpectrogramSpectrogram
--ShortShort--time time (windowed)(windowed)Fourier Fourier transformtransform
Dept. of ECE 10
Spectrogram ExampleSpectrogram Example
--Frequency vs. time Frequency vs. time --GrayGray--level for level for intensityintensity
Dept. of ECE 11
Resolution in SpectrogramResolution in Spectrogram
OriginalResolution in time Resolution in time and frequency and frequency always in conflictalways in conflict
Good freq resolution
Good time resolution
Dept. of ECE 12
AssignmentsAssignments
Finish Lectures 1 – 8 Assignments
Read Chapter 9 as much as possible
Play with demos etc. on your CD
Enjoy your new knowledge on signals and systems
Apply your new knowledge
Update me with your achievements in life!