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{a(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence
$$y\left( n \right) = \frac{1}{N}\sum\limits_{r = 0}^{N - 1} {x\left( r \right)} x\left( {n + r} \right)$$      is
Which of the following is expressed by the given equation Y = β0 + β1X + Ɛ which shows a real-valued dependent variable Y is modeled as function of a real-valued independent variable X plus noise?
Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
1. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued.
2. The complex Fourier series coefficients of x(3f) are {3ak} where k is integer valued.
3. The fundamental angular frequency of x(3t) is 6π rad/s.
For the three statements above, which one of the following is correct?
If X(k) is the N-point DFT of a sequence x(n), then circular time shift property is that N-point DFT of x((n-l))N is X(k)e-j2πkl/N.
If X(k) is the N-point DFT of a sequence x(n), then what is the DFT of x*(n)?
There is a hint in this question and a statement is given later. Carefully read the excerpts provided and determine the statement based on that episode. The current Australian team has lost three of their last five Test series. They lost their last two Test series, one of which was against Pakistan, which is not considered to be a strong team now. Australia's two best batsman, Steve Smith and David Warner are currently suspended and their absence has weakened the Australian team. There is a lot of dissatisfaction and introspection about how their national team plays in Australia, how they show aggression on the field, how they do not show respect to the team against them, and neglecting the media at the most, and focusing only on winning only, the discussion on the future of the game is ongoing. There are. Australian cricket never reached such a low level. This is the best opportunity to knock them into their own house. In other words, if this India could not beat Australia in Australia in this series, then it would prove that the campaign around this team is only the same: the propaganda. Legislation: The current Australian team won two of the last five Tests they played. Choose the right one from the next option A - The statement is completely true. B - Statement is most true. C - There is no definitive definition based on C-statement. D- Statement is completely false.
Consider with respect to HusserI's concept of phenomena.
1. Phenomena is a substantial unity that has real properties, real parts and real changes.
2. Phenomena is no substantial unity, that has no real parts and no real changes.
3. Phenomena has no nature, but only essence.
4. Phenomena have no essence, but only nature.
In real valued function and complex valued function, time is _______________
Given below are four statements- (p) The second principal focus of a lens is the position of the object, real or virtual whose image is at infinity. (q) The second principal focus of a lens is the position of the image, real or virtual whose object is at infinity. (r) The first principal focus of a lens is the position of the object, real or virtual whose image is at infinity. (s) The first principal focus of a lens is the position of the image, real or virtual whose object is at infinity.  Examine the above statements and find which among then are correct. 
Consider the following statements in case of reverted gear train: 1. The direction of rotation of the first and the last gear is the same. 2. the direction of rotation of the first and the last gear is opposite. 3. The first and the last gears are on the same shaft. 4. The first and the last gears are on separate but co-axial shafts. Which of these statements is/are correct?