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# ENME351_additional-example - than 1 also satisfy 3 N needs...

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ENME351 Additional Examples Haijun Liu October 20, 2009 Given the following signal y ( t ) = 4 sin (8 πt ) + 2 sin (20 πt ) + 3 sin (42 πt ) determine an appropriate sample rate and sample size that provides minimal spectral leakage. The sample size needs to be a multiple power of 2. 1. The Nyquist theorem requires the sampling frequency f s to satisfy: f s 2 f m = 2 × 21 = 42 Hz 2. To avoid spectral leakage, the sample period needs to be an integer multiple of the signal period: Nδt = m 1 T 1 = m 2 T 2 = m 3 T 3 Or N f s = m 1 f 1 = m 2 f 2 = m 3 f 3 where m 1 , m 2 , and m 3 needs to be integers. Substituting the frequencies of the three components in the signal, we have Γ = N f s = m 1 4 = m 2 10 = m 3 21 It can be found out that the smallest value of Γ is 1. Other integers that are larger

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Unformatted text preview: than 1 also satisfy. 3. N needs to be a multiple power of 2. Satisfying the three conditions above, the minimum values for sampling rate and sample size are: f s = 64 Hz, N = 64(Γ = 1) Other possibilities include: f s = 64 Hz, N = 256(Γ = 4) f s = 128 Hz, N = 128(Γ = 1) See Figure 1 for their amplitude spectrum. 1 5 10 15 20 25 30 35 1 2 3 4 5 Frequency (Hz) Amplitude (a) f s = 64 Hz,N = 64 5 10 15 20 25 30 35 1 2 3 4 5 Frequency (Hz) (b) f s = 64 Hz,N = 256 Figure 1: Amplitude spectrum. Note N = 256 gives better frequency resolution than N = 64. 2...
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