5.8 Frequency measurement. Consider a 50-point signal consisting of three sinuso
ID: 2292008 • Letter: 5
Question
5.8 Frequency measurement. Consider a 50-point signal consisting of three sinusoidal components r(n) :: Al sin(wi n) + A2 sin(Wyn) + A3 sin(Wyn) Suppose you want to use windowing and the FFT to estimate the frequen cies of the sinusoidal components from the data (you do not know the frequencies). For which of the following two signals is the estimation of the frequencies more difficult? (MATLAB is not required for this problem.) A) r(n) 10 sin(0.31 ? n) + 11 sin(0.32t n) + 9 sin(0.33r n) B) x(n) 0.01 sin(0.2? n) + 0.011 sin(0.5mn) + 0.012 sin(0.Srn). Clearly explain your answer.Explanation / Answer
Hello,
Please find the answer attached below. If the answer has helped you please give a thumbs up rating. Thank you and have a nice day!
The estimation of the frequencies in signal A will be more difficult than that in signal B. The reason is that even though the amplitudes of the signals in A are high enough, the frequency components in the signal do not have frequencies which are far aprt from each other. w1 = 0.31pi, w2 = 0.32pi and so on. Any miscalculations on windowing can lead to an erronoeous conclusion. For better resolution, we may need to have a large number of samples (greater than the 50 samples given in this question)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.