ELEC212 Chapter 10 Fourier AnalysisUsing DFT

ELEC212 Chapter 10 Fourier AnalysisUsing DFT - Fourier...

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1 The Hong Kong University of Science and Technology Department of Electronic and Computer Engineering ELEC 212 Chapter 10 Fourier Analysis of Signals Using the DFT 2 09-10 Fall ELEC 212 Fourier Analysis using the DFT Fourier Analysis of Signals using the DFT ± Major application: analyzing the frequency content of continuous-time signals ± Windowing is necessary since the input to the DFT must be finite duration ± The effect in the frequency domain is a convolution ± The window length L usually less than or equal to the DFT length N ± V [ k ] corresponds to equally space samples of the DTFT of v [ n ] 3 09-10 Fall ELEC 212 Fourier Analysis using the DFT Fourier Analysis of Signals using the DFT CTFT of input signal CTFT of anti-aliasing filter CTFT of signal at output of anti-aliasing filter DTFT of discrete-time sequence DTFT of discrete-time window sequence DTFT (and DFT) of discrete- time sequence after windowing 4 09-10 Fall ELEC 212 Fourier Analysis using the DFT Fourier Analysis of Signals using the DFT-Example 10.1
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5 09-10 Fall ELEC 212 Fourier Analysis using the DFT DFT Analysis of Sinusoidal Signals - Windowing ± In analyzing sinusoidal signals using the DFT, windowing and spectral sampling have an important effect ± Windowing smears or broadens the impulses in the theoretical Fourier representation, it reduces the ability to resolve sinusoidal signals ± Leakage: The component at one frequency leaks into the vicinity of another component due to the spectral smearing introduced by the windowing ± Leakage mainly depends on the shape and length of the window – Increasing the length of DFT (by zero padding) cannot reduce the leakage 6 09-10 Fall ELEC 212 Fourier Analysis using the DFT Example 10.3 ± Consider a sampled continuous-time signal consisting of the sum of two sinusoidal components ± The Fourier Transform of the windowed sequence is ± DTFT of windowed sequence consists of DTFT of window, replicated at discrete- time frequencies ± ω 0 and ± 1 and scaled by one-half of the amplitudes of the
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This note was uploaded on 03/27/2011 for the course ELEC 212 taught by Professor Prof.matthewmckay during the Spring '11 term at HKUST.

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ELEC212 Chapter 10 Fourier AnalysisUsing DFT - Fourier...

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