ecen4763.notes.37

ecen4763.notes.37 - in the frequency domain (describe the...

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1 ECEN 4763: Introduction to Digital Signal Processing Fall 2009 Lecture 37: Friday, November 13, 2009 Discrete Fourier Transform, Part VI 1. Using the DFT to estimate the CTFT 2. Examples
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2 Discrete Fourier Transform, Part VI 1. Using the DFT to estimate the CTFT 2. Examples
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3 Yes, this answer does indeed make sense!
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6 Freq. resolution due to DFT Freq. resolution due to windowing Width of window’s DTFT
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7 Summary of CTFT estimation via the DFT 1. How does X(k) relate to X(Ω)? 2. What are the sources of corruption in our estimation? Aliasing due to undersampling in time Limited frequency resolution due to chunk-based analysis Spectral leakage
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8 Discrete Fourier Transform, Part VI 1. Using the DFT to estimate the CTFT 2. Examples Final exam question, Fall 2006
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10 Final exam question, Fall 2006
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12 Second prelim exam questions, Fall 2007
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13 Second prelim exam questions, Fall 2007 Second prelim exam questions, Fall 2007
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14 Second prelim exam questions, Fall 2007 If we perform linear interpolation of DT samples, what does the DT filter look like
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Unformatted text preview: in the frequency domain (describe the general shape)? Answer : Linear convolution is performed by convolving the time-domain signal with a DT triangle filter. In frequency, we multiply the signals DTFT with a periodic sinc 2 . Why is it so easy to compute the DTFS of a sinusoid? Answer : The DTFS of a sinusoid is non-zero only at the frequency of the sinusoid. Thus, there will be only two non-zero DTFS coefficients, and these can be computed via observation. How many samples of a CT signal do we need to resolve spectral features that are 10 Hz apart? Answer : We need at least 2 f s / 10 samples. How do we perform linear convolution via the DFT? Answer : We perform the following steps: (1) zero-pad both signals to length N 1 + N 2 1, where N 1 and N 2 are the lengths of the two signals; then (2) compute the DFT of each zero-padded signal; then (3) multiply the DFTs; and the (4) perform an inverse DFT of the product....
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ecen4763.notes.37 - in the frequency domain (describe the...

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