Consider the analog signal given as: f (t) = 3 + sin(1500 t) + sin(4000t) Design
ID: 2082883 • Letter: C
Question
Consider the analog signal given as: f (t) = 3 + sin(1500 t) + sin(4000t) Design a digital filter such that only the frequency component sin(1500t) is passed and the rest are suppressed. Use a chebyshev type l filter with 2 dB for the maximum allowable ripple in the passband. Clearly show how you arrived at a proper sampling time, cut of frequencies of the filter, and the order of filter. Plot the magnitude response of the filter as well as the original signal, f(t), and it filtered version using your designed filter. Include the Matlab work (script, not print out of the entire Matlab workspace/command window) with your handout (that is I need a script that I can run to verify your work).Explanation / Answer
Solution When there are several forces involved it is sometimes easier to immediately collect all i components then all j components, i.e. resolve horizontally then vertically. 40 o 80 25 o 45 15 o 10 Resolving horizontally: 25 cos 10 40 cos 80 15 cos 45 = 7.068 Resolving vertically: 40 sin80 15 sin 45 25 sin 10 = 24.445 Therefore the resultant has magnitude 7.0682 + 24.4452 = 25.45 = 25 (2 s.f.) acting at an angle of tan1 24.445 7.068 = 73.87 = 74 (2 s.f.) above the positive x-axis. Notes 1. It is not always necessary to resolve in the directions of i and j, see leaflets 2.6/ 2.7 (Forces at an Angle/ Motion on a Slope). 2. The method is also applicable to work in three dimensions, as each force can be resolved into i, j and k components. Exercises 1. Consider two forces of magnitudes 20 N and 16 N acting on a particle, as shown in diagram 1. What is the magnitude and direction of the resultant force? 2. Consider two forces of magnitudes 26 N and 28 N acting on a particle, as shown in diagram 2. What is the magnitude and direction of the resultant force? 3. For the set of forces shown in diagram 3, what is the magnitude and direction of the resultant force? 4. For the set of forces shown in diagram 4, what is the magnitude and direction of the resultant force? 20 o 15 o 70 16 diagram 1 28 o 35 o 30 26 diagram 2 12 o 75 12 o 75 14 o 75 diagram 3 4 6 12 o 20 o 20 3 d