Chapter 5 Week 6 DTFT Intro for Wednesday - 6 may

Chapter 5 Week 6 DTFT Intro for Wednesday - 6 may - EE341

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EE 341 Discrete Time Linear Systems – Week 6 Spring 2011 Supplement Page 1 Motivating Example for the Discrete-Time Fourier Transform (DTFT) In the plots below, we propose to design an “ideal” lowpass filter in the frequency domain, by defining 1 [] ,0 1 5 Hk k  , as shown below. The corresponding time-domain impulse response 1 hn , is the 16- point ( N = 16) invese DFT of 1 . The next few pages address the question: Why is 1 not an ideal lowpass filter? -3 -2 -1 0 1 2 3 0 0.2 0.4 0.6 0.8 1 Frequency (radians per second) Amplitude H 1 [k] - 16 point DFT frequency response 0 5 10 15 0 0.2 0.4 Time index h 1 [n] - 16 point time-domain impulse response
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EE 341 Discrete Time Linear Systems – Week 6 Spring 2011 Supplement Page 2 Although the filter is 16 points long, we will have to zero-pad its impulse response in order to implement linear convolution. Suppose we have a signal [] x n that we wish to filter, and it is 1000 points long. Then a DFT size of 1024 is more than sufficient for linear convolution.
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Chapter 5 Week 6 DTFT Intro for Wednesday - 6 may - EE341

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