Obtain the sum of the squares of values, Mathematics

This question is in the form of an exercise and questions designed to give you more insight into signal processing. On the Moodle site for the module there is an EXCEL file called "FFT_exercise_2012". The first column contains the numbers 1 to 32. Then there is a column representing a "random time series", i.e. a digitised signal. The next eight columns are sine waves and cosine waves in pairs. The first pair is the fundamental based on 32 samples, i.e. one complete cycle. Then there are the second harmonics, and the third harmonics. The graphs for each of the digitised functions have been created to help you visualise these standard functions.

The time series given to you is the exact sum of a mean value plus a different multiple of each of these 8 sine and cosine components plus one further mystery harmonic. Your main task is to find these 10 values. But there are some initial tasks to help you think through how to find the values.

(a) Generate the columns on the EXCEL spreadsheet you will need for sin1, cos1, sin2, cos2, ... , sin4, cos4. Please note that the EXCEL function SIN(value) requires the value to be in radians. Also the EXCEL function PI() will give ??to lots of significant figures.

(b) Obtain the sum of the squares of values in each of the sine and cosine columns using EXCEL. What values do you obtain?

(c) What is the mean value of the random time series?

(d) What are the amplitudes of the 8 sinusoidal components that added to the mean make up the time series? Produce a table corresponding to sin1, cos1, sin2, cos2, etc.

(e) What is the amplitude of the mystery harmonic component and which component is it? Use the notation sin or cos plus a harmonic number, e.g. sin5, cos6, etc.

Posted Date: 3/25/2013 1:20:57 AM | Location : United States

Related Discussions:- Obtain the sum of the squares of values, Assignment Help, Ask Question on Obtain the sum of the squares of values, Get Answer, Expert's Help, Obtain the sum of the squares of values Discussions

Write discussion on Obtain the sum of the squares of values
Your posts are moderated
Related Questions
Find the number of zeros of the polynomial from the graph given. (Ans:1)

Determine the height of the Washington Monument to the nearest tenth of a meter. a. 157.8 m b. 169.3 m c. 170.1 m d. 192.2 m c. The height of the monument is the add

If ABCD isaa square of side 6 cm find area of shaded region

(a) The generating function G(z) for a sequence g n is given by G(z) = 1 - 2z/(1 + 3z)3 Give an explicit formula for g n . (b) For the sequence gn in the previous part co

Assume A and B are symmetric. Explain why the following are symmetric or not. 1) A^2 - B^2 2) (A+B)(A-B) 3) ABA 4) ABAB 5) (A^2)B

Multiply following and write the answers in standard form.  (a) 7 i ( -5 + 2 i )  (b) (1 - 5 i ) ( -9 + 2 i ) Solution (a) Thus all that we have to do is distribu

Can you explain why is the steepness of a curve partially calculated by the units of measurement?

determine the equation that represent the following lines be sure to define your variable and show all of your work

Area of the equilateral triangle: Given : D, E, F are the mind points of BC, CA, AB. R.T.P. : We have to determine the ratio of the area of of triangle DEF and triangle AB