Express e in terms of a frequency domain integral

Assignment Help Project Management

Reference no: EM131279008

Suppose we are given a real and finite-energy (but otherwise arbitrary) DT signal w[n], with associated DTFT W(ejΩ). We want to approximate w[n] by another real, finite-energy DT signal y[n] that is bandlimited to the frequency range |Ω| jΩ) is zero for |Ω| ≥ π/4. Apart from this constraint on its bandwidth, we are free to choose y[n] as needed to get the best approximation. Suppose we measure the quality of approximation by the following sumof-squared-errors criterion:

Our problem is then to minimize E by appropriate choice of the bandlimited y[n], given the signal w[n]. This problem leads you through to the solution.

(a) Express E in terms of a frequency-domain integral on the interval |Ω| jΩ) - Y(ejΩ).

(b) Write your integral from (a) as a sum of integrals, one over each of the ranges -π/4 ≤ Ω ≤ π/4, π/4 ≤ Ω jΩ) needs to be picked in order to minimize E, and what the resulting minimum value of ε is.

(c) Using your result in (b), write down an explicit formula for the y[n] that minimizes ε, expressing this y[n] as a suitable integral involving W(ejΩ).

Reference no: EM131279008

Questions Cloud

What is discounting and how is it related to compounding : What is discounting? How is it related to compounding? - What are the three techniques for solving lump sum discounting problems?

Why does an investment have an opportunity cost rate : How does the present value of an amount to be received in the future change as the time is extended and as the interest rate increases?

Determine the maximum allowable input : Suppose the input differential signal applied to a bipolar differential pair must not change the transconductance (and hence the bias current) of each transistor by more than 10%. From Eq. (10.58), determine the maximum allowable input.

Obtain an explicit time domain expression for the output : If you were allowed to determine the value of H(s) for only a single value of s, which value of s would you pick in order to obtain an explicit time-domain expression for the output y(t) corresponding to the above input?

Express e in terms of a frequency domain integral : Express E in terms of a frequency-domain integral on the interval |Ω| jΩ) - Y(ejΩ).- write down an explicit formula for the y[n] that minimizes ε, expressing this y[n] as a suitable integral involving W(ejΩ).

How much total work is done on the box : A person is pulling a box across a horizontal floor at a constant speed of 1.8 m/s.The string the person is using to pull the box makes an angle of 28.0° relative to horizontal. The box has a mass of 4.60 kg and the tension in the string is 13.6N...

Determine the loop gain and prove that the feedback is posit : An adventurous student replaces the NMOS source follower in Fig. 12.90 with a PMOS common-source stage (Fig. 12.91). Unfortunately, the amplifier does not operate well.

What is this distance in meters : A sports car moving at constant speed travels 150 m in 4.00 s. If it then brakes and comes to a stop while decelerating at a rate of 6.0 m/s2. How long does it take to stop?

How the operon helps microbe survive and possibly thrive : Describe an operon, the regulatory proteins, the cellular process and the molecules being "sensed". Include details about the orientation of the genes and the promoter/operator sequences or activator binding site. Provide details about the repressor/..

User Account

All Pages