EE 435 Lect 31 Spring 2010

EE 435 Lect 31 Spring 2010 - EE 435 Lecture 31 Quantization...

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Unformatted text preview: EE 435 Lecture 31 Quantization Noise Absolute and Relative Accuracy Distortion Analysis ( ) 1- h m 1 mN N 2 A P m + = ( ) k = 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 = ( ) 1 N k S kT x = MAX P f N f = 2 N . 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 harmonic More importantly, substantial raise in the computational noise floor !!! (from over - 300dB to only -40dB) Errors at about the 6-bit level ! . Review from last lecture . FFT Examples Recall the theorem that provided for the relationship between the DFT terms and the Fourier Series Coefficients required 1. The sampling window be an integral number of periods 2. P SIGNAL N f f 2 N max > . Review from last lecture . Example If f SIG =50Hz and N P =20 N=512 P SIGNAL N f f 2 N max > f max < 640Hz . Review from last lecture . Example ) sin( . ) sin( . ) sin( t 14 5 t 2 5 t V IN + + = If f SIG =50Hz Consider N P =20 N=512 SIG f 2 = Recall 20log 10 (0.5)=-6.0205999 (i.e. a component at 700 Hz which violates the band limit requirement) . Review from last lecture . Effects of High-Frequency Spectral Components . Review from last lecture . Effects of High-Frequency Spectral Components . Review from last lecture . Effects of High-Frequency Spectral Components . Review from last lecture . Effects of High-Frequency Spectral Components Columns 1 through 7 -296.9507 -311.9710 -302.4715 -302.1545 -310.8392 -304.5465 -293.9310 Columns 8 through 14 -299.0778 -292.3045 -297.0529 -301.4639 -297.3332 -309.6947 -308.2308 Columns 15 through 21 -297.3710 -316.5113 -293.5661 -294.4045 -293.6881 -292.6872 -0.0000 Columns 22 through 28 -301.6889 -288.4812 -292.5621 -292.5853 -294.1383 -296.4034 -289.5216 Columns 29 through 35 -285.9204 -292.1676 -289.0633 -292.1318 -290.6342 -293.2538 -296.8434 f high =14fo . Review from last lecture . Effects of High-Frequency Spectral Components Columns 36 through 42 -301.7087 -307.2119 -295.1726 -303.4403 -301.6427 -6.0206 -295.3018 Columns 43 through 49 -298.9215 -309.4829 -306.7363 -293.0808 -300.0882 -306.5530 -302.9962 Columns 50 through 56 -318.4706 -294.8956 -304.4663 -300.8919 -298.7732 -301.2474 -293.3188 f high =14fo . Review from last lecture . Effects of High-Frequency Spectral Components f f 2 f sample alias = Columns 225 through 231 -296.8883 -292.8175 -295.8882 -286.7494 -300.3477 -284.4253 -282.7639-296....
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EE 435 Lect 31 Spring 2010 - EE 435 Lecture 31 Quantization...

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