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Problems in Software Connect DataMatrix in Software Problems

5.11 Problems generate, create data matrix barcode none on software projects GS1 Standards Knowledge Centre (c) For G = 1 Software data matrix barcodes 00 and 1,000, tabulate the voltages at important points in your circuit after ve more passengers enter the elevator (total = 10) while the oor selector circuit is still set to the second oor. Describe any motion of the elevator relative to (b) above. (d) For G = 100 and 1,000, tabulate the voltages at important points in your circuit after all passengers get off the elevator while the oor selector circuit is still set to the second oor.

Describe any motion of the elevator relative to (c) above. (e) For G = 1,000, plot the voltages at important points in your circuit from time t = 0 to 100 s during the following events: t =0s the elevator is at rest with ve passengers at oor 2 t = 10 s ve more passengers instantaneously jump on t = 20 s the fourth oor is selected t = 30 s the elevator comes to rest t = 40 s all passengers instantaneously jump off t = 50 s the basement is selected t = 70 s the elevator comes to rest Assume that from rest, the elevator takes 1 s to accelerate to its limiting speed, and 1 s to decelerate to rest. 5.

36 Design a circuit for controlling a street light. The street light is to be turned on at night and turned off during the day. Components available are: r pin photodiode; r street light (200 V, 10 A); r electromechanical relay switch (an input of 10 V and 1 A is needed to close the switch, and an output of 200 V and 10 A is needed to light the street light); r additional components as needed, but keep it simple.

(a) Sketch your design, showing and labeling all essential components and interconnections. (b) List voltages at key points in the circuit at night. (c) List voltages at key points in the circuit during the day.

(d) Describe three important common-sense considerations for mounting the pin photodiode. 5.37 The convolution a(t) of two functions b(t) and c(t) is de ned as:.

a(t) = b(t) c(t) =. b(t)c(t t ) dt Also de ne a unit rectangle waveform r (t): r (t) = 1 for 0.5 < t < +0.5, r (t) = 0 otherwise (a) Sketch the convolution a(t) of b(t) = r (t) and c(t) = (t 1).

(b) Sketch the convolution a(t) of b(t) = r (t) and c(t) = + (t 2k) k= . Data analysis and control (c) Compute t he convolution a(t) of b(t) = r (t) and c(t) = r (t). The result should be a familiar function shown in the Course Reader and encountered in Laboratory Exercise 21. (d) Using the Fourier transform of r (t) (Example 5.

13) and the Fourier convolution theorem, compute the Fourier transform of a(t) = r (t) r (t). 5.38 You have been asked to help design a Doppler ultrasound system for measuring the speed of approaching vehicles on a highway.

The system sends a continuous tone of 100-kHz sound waves in a well-de ned direction and there is a receiver alongside that receives the Doppler-shifted echo. Your part in the project is to design the sampling and signal processing hardware and software, starting from the echo receiver. r The Doppler-shifted frequency is given by f = f (1+v/vs ) where v is the (1 v/vs ) speed of the approaching vehicle and vs is the speed of sound in air (assume 300 m/s).

r To simplify and speed your calculations, use the approximation f f (1 + 2v/vs ). r Assume that the echo receiver signal is the sum of 0.1-V p p echo and an unavoidable 10-V p p primary 100-kHz tone that leaks into the echo receiver.

r The echo circuit has wide-band ampli cation with white noise, so you decide to use a low-pass eight-pole Butterworth anti-aliasing lter that effectively accepts frequencies below f 1 and rejects frequencies above 2 f 1 , where f 1 is a frequency of your choosing. r Your system samples at frequency f s , takes M samples (where M is a power of 2), performs the FFT, and must be able to determine the speed of an approaching vehicle between 3 and 60 m/s to an accuracy of 0.3 m/s.

Answer the following: (a) What are the echo frequencies for vehicle speeds of 3, 30 (67 mph), 30.3, and 60 m/s (134 mph) (b) How long must your sampling window be to distinguish 30 m/s from 30.3 m/s clearly (c) How can you reduce the spectral leakage from the 10-V p p 100-kHz primary onto the 0.

1-V p p echo frequency (d) Considering the maximum signal frequency (corresponds to 60 m/s) and the white noise in the echo receiver circuit, what value of f 1 does your low-pass lter require (e) Considering the value of f 1 from (d) above, and that the lter rejects frequencies above 2 f 1 , what is the minimum sampling frequency that prevents the aliasing of white noise between f 1 and 2 f 1 into frequencies below f 1 (f) How many samples will you take for each measurement of vehicle speed (g) Sketch all FFT magnitudes versus frequency index for a vehicle speed of 30 m/s. You will need to use a vertical axis labeled in powers of 10. Provide.

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