Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!
MAE 241 – Homework 1 Page 1 of 3 MAE 241 – Spring 2019 – Homework 1 Administered 1/11/2019 – Due 11PM, Sunday 1/19/2019 to Gradescope Problem 1 – Review of units The Phoenix with a mass of 400 kg was a spacecraft used for exploration of Mars. Determine the weight of the Phoenix, in N, for the following situations: a. On the surface of Mars where the acceleration of gravity is 3.73 m/s2. b. On Earth where the acceleration of gravity is 9.81 m/s2. Problem 2 – review of chemistry A closed system consists of 0.4 kmol of octane (C8H18) occupying a volume of 2 m3. Determine: a. The weight of the system, in N. b. The molar-based specific volume, in m3/kmol. c. The mass-based specific volume, and m3/kg. Let g = 9.81 m/s2. Problem 3 – review of chemistry A closed vessel having a volume of 2.0 liter holds 2.0 x 1022 molecules of carbon dioxide gas. Determine: a. The number of moles, in kmol b. The mass of CO2 present, in kg and. c. The molar specific volume, in m3/kmol d. The specific volume of the CO2, in m3/kg. Hint: use Table A-1 of your textbook for molecular mass. Problem 4 – Quasistatic Equilibrium The figure below shows a gas contained in a vertical piston–cylinder assembly. A vertical shaft whose cross-sectional area is 0.8 cm2 is attached to the top of the piston. Determine the magnitude, F, of the force acting on the shaft, in N, required if the gas pressure is 300 kPa. The masses of the piston and attached shaft are 30 kg and 0.5 kg, respectively. The piston diameter is D = 10 cm. The local atmospheric pressure is 100 kPa. The piston moves smoothly and slowly at constant velocity in the cylinder and g = 9.81 m/s2. MAE 241 – Homework 1 Page 2 of 3 Problem 5– Measurement of Pressure a. For the tank shown in the figure below derive an expression to compute the Length, L, of the column of fluid as a function of density of the fluid in the manometer, 𝜌, and the atmospheric pressure, Patm. b. Determine the value of L when the manometer liquid is water and the tank contains a gas at a pressure of 1.5 bar. A barometer indicates the local atmospheric pressure is 750 mmHg. You also know that the density of water is 997 kg/m3 and the density of mercury is 13.59 g/cm3. Let g = 9.81 m/s2. Problem 6 – Gage pressure measurement A pressure gage mounted at the inlet to an air compressor indicates that the gage pressure is 60.0 kPa. The absolute pressure of the at the exit of the compressor is 5.5 times the absolute pressure at the inlet. The atmospheric pressure is 1.01 bar. What is the absolute pressure of the gas at the inlet and what is the gage pressure of the gas at the exit? Problem 7 – Unit conversions Perform the following unit conversions. Please do not use an on-line unit converter since this problem is given to you as practice in preparation for what you need to be proficient in: a. 170.8 in3 to L b. 1089.438 ft-lbf to kJ c. 140.0 hp to kW d. 1400.0 lb/h to kg/s e. 41.1488 lbf/in2 to kPa f. 3500.0 ft3/min to m3/s g. 105.0 mile/h to km/h h. 1.4 ton (=2000 lbf) to N Problem 8 – Newton’s second law Estimate the magnitude of the force, in lbf, exerted on a 20-lb goose in a collision of duration 1.5 x 10−3 s with an airplane taking off at 150 miles/h. Assume the bird’s velocity is zero before the collision. MAE 241 – Homework 1 Page 3 of 3 Problem 9 – Temperature conversions On January 3, 2019, in Flagstaff, AZ, the lowest temperature was 14oF at 5 AM and the highest 44oF at 4 PM. a. Express these temperatures in oR, K and oC. b. Determine the temperature change in oF, oR, oC and K from morning low to afternoon high. c. What is the relationship between the temperature changes in oF and oR? d. What is the relationship between the temperature changes in oC and K? Problem 10 – Ideal gas law application A closed deformable system consisting of 2 lb of air undergoes a process during which the relation between pressure and volume is defined by the mathematical expression PVn = Constant. The process begins with P1 = 20 lbf/in2, V1 = 15 ft3 and ends with P2 = 100 lbf/in2. The value of n = 1.3. Determine: a. The final volume, V2, in ft3 b. The specific volume at states 1 and 2, in ft3/lb. c. Use the ideal gas law as you learned in your chemistry course to determine the initial temperature, in °F. Hint: if you need the molecular mass of air please use Table A-1 or A-1E.
2. Problem 7.2 The flyback converter of Figure 7.2a has an input of 48V, and output of 30V, a duty ratio of 0.45, and a switching frequency of 25kHz. the load resistor is 15Ω. a. Determine the transformer turns ratio b. Determine the transformer magnetizing inductance Lm such that the minimum inductor current is 25% of the average.
Problem 6.15 The boost converter of Fig 6-6 has the following parameters: Vs=20V, D=0.6, R=12.5Ω, L=65μH, C=200μF, and switching frequency = 40kHz. a. Determine the output voltage. b. Determine the average, maximum, and minimum inductor current. c. Determine the output voltage ripple. d. Dermine the average current in the diode.
Problem 6.7 A buck converter has an input of 60V and an output fo 25V. The load resistor is 9Ω, the switching frequency is 20-kHz, L=1mH, and C=200μF. a. Determine the duty ratio. b. Determine the average, peak, and rms inductor current. c. Determine the average source current. d. Determine the peak and average diode current.