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Unformatted text preview: EE 435 Lecture 30 Spectral Performance – Windowing Distortion Analysis ( ) 1 h m 1 mN Χ N 2 A P m ≤ ≤ + = ( ) k Χ = THEOREM: If N P is an integer and x(t) is band limited to f MAX , then and for all k not defined above where is the DFT of the sequence f = 1/T, and ( ) 1 N k k Χ − = ( ) 1 N k S kT x − = MAX P f N f = • 2 N ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ .• • • • • Review from last lecture .• • • • • Question: How much noise is in the computational environment? Environmental Noise Observation: This noise is nearly uniformly distributed The level of this noise at each component is around 310dB .• • • • • Review from last lecture .• • • • • Question: How much noise is in the computational environment? Assume A k = 310 dB for N k ≤ ≤ 20 A k kDB 10 A = A kdB =20log10A k 5 . 15 20310 k 10 10 A − = ≅ A N A V A A 1 N 1 k 2 k RMS Noise, k = − = = ≅ ∑ fV 18 10 8 . 1 10 512 A N V 14 5 . 15 RMS Noise, = • = = ≅ − − Note: This computational environment has a very low total computational noise and does not become significant until the 45bit resolution level is reached !! .• • • • • Review from last lecture .• • • • • Considerations for Spectral Characterization FFT Length DFT REF k n / 2 n+1 X A 3•2 2 ¡ 1 12 3 2 QUANT E LSB REF n X X + = • ¡ Substituting for E QUANT , obtain This value for A k thus decreases with the length of the DFT window .• • • • • Review from last lecture .• • • • • Considerations for Spectral Characterization • Tool Validation • FFT Length • Importance of Satisfying Hypothesis NP is an integer Bandlimited excitation • Windowing .• • • • • Review from last lecture .• • • • • Observations • Modest change in sampling window of 0.01 out of 20 periods (.05%) still results in a modest error in both fundamental and...
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This note was uploaded on 01/31/2012 for the course EE 345 taught by Professor Geiger during the Fall '11 term at Iowa State.
 Fall '11
 GEIGER

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