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Unformatted text preview: 1 && ECE 306 Sampling of Analog Signals Quantization of ContinuousAmplitude Signals & && && Sampling of Analog Signals Example: a. Find the minimum sampling rate required to avoid aliasing. b. If , What is the discretetime signal after sampling? c. If , What is the discretetime signal after sampling? d. What is the frequency F of a sinusoidal that yields sampling identical to obtained in part c? a The minimum sampling rate is ( ) 3cos100 a x t t = Solution: 100 = 50 Hz F = 2 100Hz s F F = = and the discretetime signal is ( ) ( ) 3cos 3cos 3cos2 100 1 100 2 a x n x nT n n n = = = = 200 s F Hz = 75 s F Hz = 2 && Sampling of Analog Signals b and in part in (c). Hence Solution: If , the discretetime signal is 200 s F Hz = ( ) 3cos 3cos 3cos2 100 1 200 2 4 x n n n n = = = c If , the discretetime signal is 75 Hz s F = 2 100 4 1 ( ) 3cos 3cos 3cos 2 3cos2 3 3 75 3 x n n n n n = = = & = d For the sampling rate , 75 Hz s F = 75 s F fF f = = 1 3 f = 75 25Hz 3 F = = ( ) 3cos2 3cos50 a y t Ft t = = So, the analog sinusoidal signal is && The Sampling Theorem We must have some information about the analog signal especially the frequency content of the signal, to select the sampling period T or sampling rate F s . For example A speech signal goes below around 20Khz. A TV signal is up to 5Mhz. Any analog signal can be represented as sum of sinusoids of different amplitudes, frequencies, and phases. 1 ( ) cos(2 ) N a i i i i x t A Ft = = + where N the number of frequency components. Suppose that Nth frequency do not exceed the largest frequency max F max i F F < 3 && The Sampling Theorem To avoid the aliasing problem, is selected so that...
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This note was uploaded on 03/11/2008 for the course ECE 306 taught by Professor Aliyazicioglu during the Winter '08 term at Cal Poly Pomona.
 Winter '08
 Aliyazicioglu
 Aliasing

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