LECTURE 4 4-15 Copyright  1998, Texas Instruments Incorporated All Rights Reserved A Practical Example AMPLITUDE OF X 1 =  1 2 +j 2 =  2 X 0 =x 0 + x 2 + x 1 +x 3 X 1 =x 0 –x 2 + -j(x 1 –x 3 ) = 1–0 + -j(0–1) = 1 + j X 2 =(x 0 + x 2 ) – (x 1 + x 3 ) = (1 + 0) - (0 + 1) = 0 X 3 =(x 0 –x 2 )– -j (x 1 –x 3 ) = (1–0)– -j(0–1) = 1– j = 1 + 0 + 0 + 1 = 2 FFT Conversion SAMPLED AT 10kHz T s = 100 uS 1 NT s =F = x k = {1,0,0,1} Amplitude Time 0 1 2 (nT s ) 0 12 3 Time Domain Amplitude Frequency 1 2 kHz  Frequency Domain 03122 0-2.52.55.0-5.0 Frequency Spacing
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