= k) of Problem 3 Design a causal, linear phase, low pass filter (cutoff = 0c...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
= k) of Problem 3 Design a causal, linear phase, low pass filter (cutoff = 0c and gain length 3 using the optimization (CAD) method discussed in lecture 20 by following the steps outlined below. h(n) = bod(n) + b₁d(n − 1) + bod(n − 2) (a) Show that the mean square error (bo, b₁; K, 0c) is given by k²0c 2kb1 + (262 +6²) -- sinec -sin20c ㅠ πT (b) Show that the values of bo and b₁ that minimize the mean square error e(bo, b₁; K, 0c) are given by €(bo, b₁; k, 0c) = k k 4π -sinec π Make sure that you verify that the Jacobian J for the above values of bo and b₁ gives a minimum, i.e., J> 0. bo = -sin20 and b₁ kbo π = = (c) Plot the normalized magnitude H(0)| and phase ZH(0) for cutoff c π/4. (To plot the normalized magnitude, divide |H(0)| by |H(0)|max.) On the |H(0)| plot, show also the normalized ideal low pass filter magnitude with cutoff at c. Comment on the magnitude and phase response of the designed filter. = (d) Plot the normalized magnitude |H(0)| and phase ZH(0) for cutoff Oc π/2. On the |H(0)| plot, show also the normalized ideal low pass filter magnitude with cutoff at 0c. Com- ment on the magnitude and phase response of the designed filter. (e) Plot the normalized magnitude | H(0)| and phase ZH(0) for cutoff 0e = 3π/4. On the H(0) plot, show also the normalized ideal low pass filter magnitude with cutoff at 0c. Comment on the magnitude and phase response of the designed filter. = k) of Problem 3 Design a causal, linear phase, low pass filter (cutoff = 0c and gain length 3 using the optimization (CAD) method discussed in lecture 20 by following the steps outlined below. h(n) = bod(n) + b₁d(n − 1) + bod(n − 2) (a) Show that the mean square error (bo, b₁; K, 0c) is given by k²0c 2kb1 + (262 +6²) -- sinec -sin20c ㅠ πT (b) Show that the values of bo and b₁ that minimize the mean square error e(bo, b₁; K, 0c) are given by €(bo, b₁; k, 0c) = k k 4π -sinec π Make sure that you verify that the Jacobian J for the above values of bo and b₁ gives a minimum, i.e., J> 0. bo = -sin20 and b₁ kbo π = = (c) Plot the normalized magnitude H(0)| and phase ZH(0) for cutoff c π/4. (To plot the normalized magnitude, divide |H(0)| by |H(0)|max.) On the |H(0)| plot, show also the normalized ideal low pass filter magnitude with cutoff at c. Comment on the magnitude and phase response of the designed filter. = (d) Plot the normalized magnitude |H(0)| and phase ZH(0) for cutoff Oc π/2. On the |H(0)| plot, show also the normalized ideal low pass filter magnitude with cutoff at 0c. Com- ment on the magnitude and phase response of the designed filter. (e) Plot the normalized magnitude | H(0)| and phase ZH(0) for cutoff 0e = 3π/4. On the H(0) plot, show also the normalized ideal low pass filter magnitude with cutoff at 0c. Comment on the magnitude and phase response of the designed filter.
Expert Answer:
Answer rating: 100% (QA)
To design the causal linear phase low pass filter of length 3 using the optimization CAD method lets ... View the full answer
Related Book For
Digital Signal Processing
ISBN: ?978-0133737622
3rd Edition
Authors: Jonh G. Proakis, Dimitris G.Manolakis
Posted Date:
Students also viewed these accounting questions
-
Show that the mean square error s2 = SSE/ k (n - l) for the analysis of variance in a one-way classification is an unbiased estimate of a2.
-
WACC Calculations D/A E/A rdebt requity tax rate WACC 0.600 0.400 6% 30% 25% 14.70%
-
By trail-and-error design a third-order low pass filter with cutoff frequency at 0 = /9 radians/sample interval. Start your search with (a) z1 = z2 = z3 = 0, p1 = r, p2.3 = rejk, r = 0.8 (b) r = 0.9,...
-
Prove that point B in Figure 18.1 is not Pareto effi cient. Food Fo FB OA Abner E C B Contract curve UAB UBB MB -Medicine Z Belinda Mo Figure 18.1 Edgeworth Box for Exchange; Pareto Efficient Points...
-
During Christmastime, when the publics holdings of currency increase, what defensive open market operations typically occur? Why?
-
Refer to Exercise 10.7. a. Place a 99% confidence interval on the proportion of false negatives produced by the test. b. Is there substantial evidence (a = .01) that the test produces less than 2%...
-
Of all the events that occur each day, how would you describe those that are recorded in a firm's accounting records? LO11
-
The following information is available for Lowry Company. Instructions (a) Compute cost of goods manufactured. (b) Prepare an income statement through gross profit. (c) Show the presentation of the...
-
113_22se2 ... > Quizzes > Quiz B The acceleration function (in m/s2) and intitial velocity for a particle moving along a line is given by a(t) = -6t - 22, v(0) = -10, 0
-
Larry Power started a new business in the name of Power Electrical on October 1, 2020. During October, a number of activities occurred and the following totals resulted at October 31, 2020 (shown in...
-
Analyze each of the characteristics in considering the indicated test for dependency as a qualifying child or qualifying relative. In the last two columns, after each listed test (e.g., gross...
-
You opened a savings account five years ago and deposited $500 at that time. The following year, you added another $400 to the account. You did not add any more money until today when you deposited...
-
Bethany company forecast November sales to be 80,000 units. Each unit requires three pounds of material, which costs $2.50 per pound, and 30 minutes of direct labor time. Direct laborers earn $12.00...
-
The Ski Trip Probability The ski club you belong to is off on another trip. This time you invite 2 of your friends to join. You are excited and very hopeful the three of you will be assigned to the...
-
Analyse how cryptocurrencies as a digital asset could play an important role (or not) in the current global economy. Current global economy, in this context, is referring to phenomenon such as the...
-
Bodacious Corporation produced 100 units of Product AA. The total standard and actual costs for materials and direct labor for the 100 units of Product AA are as follows:...
-
Listen What is the preimage of A B A B A
-
One study found that the elderly who do not have children dissave at about the same rate as the elderly who do have children. What might this finding imply about the reason the elderly do not dissave...
-
Show that the system in figure isequivalent. rsin un (n) x(n) rcos wp rcos un -rsin un (n) y(n) 2rcos an
-
Consider an FIR system with the following system function:? H(z) = (1 ? 0.8 e j?/2 z -1 )(1 ? 0.8 e- j?/2 z -1 ) (1 ? 1.5 e j?/4 z -1 ) (1 ? 1.5 e- j?/4 z -1 ) (a) Determine all systems that have the...
-
Recall that the Fourier transform of x(t) = e j0 is X(j) = 2( 0 ) and the Fourier transform of: (a) Determine the Fourier transform Y( j ) of Y( t ) = p( t ) e j0t And roughly sketch |Y(j)| versus...
-
Estimation of mean by sampling Jupiter Corporation collects daily information on the number of differential assemblies produced by its employees. The following data have been collected during the...
-
Sample size and estimation error The management of Carelli Farms has taken a random sample of the number of bushels of corn meal used weekly in its cattle feed lot. The sample of 30 items has a mean...
-
Sample size needed to estimate mean Refer to the data in Problem 22-12 for Jupiter Corporation's production of differential assemblies. Management wants to estimate the mean of the population by...
Study smarter with the SolutionInn App