Describe the advantage of using the blackman-tukey method

Reference no: EM133017694

Question 1
You results using the DFT alone are inadequate so you decide to try to improve them.
(a) Why might you choose to apply a window to your data before performing the DFT?

(b) Given that one of the main reasons for applying a window when estimating the power spectrum is to decrease spectral leakage which of these windows would be the best option?

(d) If you use all of your data to calculate the autocorrelation what would be the length of the window and what frequency resolution would you obtain if you used the triangular window when estimating your power spectrum? Give your frequency resolution to 4 significant figures

(e) If you instead wanted to obtain a quality factor of 50 what would be the frequency resolution obtained? Give your frequency resolution to 4 significant figures

(f) Given that the quality factor of the estimate obtained by the standard periodogram is always Q = 1. Describe the advantage of using the Blackman-Tukey method.

Question 2

(a) If you want a frequency resolution of 0.1 Hz is it possible to also have a time res- olution of 0.5 seconds?

(b) If you have a window of 0.5s how many samples would there be?

(c) If the "frame rate" that is the number of DFTs which are calculated for each sec- ond of input signal is 25, how many samples is the window advanced by between each DFT?

(d) Which of the above methods would improve the frequency resolution of your spec- trogram? Explain your answer

(e) What are f0 and β?

(f) Using your answers to part (a) what would be the heart rate at 1 minute?

(g) What is the short time energy at 1 minute? Calculate your answer to 3 decimal places

(h) What is the short time energy at 3 minutes 15 seconds? (To 3 decimal places)

(i) How do your values compare? Is the short time energy an appropriate measure in this case? Think about what type of signal the cosine is

Attachment:- Problem Sheet.rar

Reference no: EM133017694

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