b. The figure below shows a cross section through an insulated heated pipe which is made of steel (thermal conductivity, k = 45 W/m K) with an inner radius (r1) of 800 mm and an outer radius (r2) of 1300 mm. The pipe is coated with two layers of insulating materials, the first layer has a thickness of 200 mm and thermal conductivity, k =25.9 W/m K, the second layer has a thickness of 400 mm and the thermal conductivity, k = 35 W/m K. Air at Tf1 = 310 oC flows through the pipe and the convective heat transfer coefficient from the air to the outside has a value of h1 = 120 W/m2 K, The outside surface of the pipe is surrounded by air which is at 50 oC (Tf2) and the convective heat transfer coefficient on this surface has a value of h2 = 90 W/m2 K. Calculate, (a) the thermal resistance (b) the heat transferred (c) temperature T1, T2, T3 and T4 (d) comment on your results.

## b. The figure below shows a cross section through an insulated heated pipe which is made of steel (thermal conductivity, k = 45 W/m K) with an inner radius (r1) of 800 mm and an outer radius (r2) of 1300 mm. The pipe is coated with two layers of insulating materials, the first layer has a thickness of 200 mm and thermal conductivity, k =25.9 W/m K, the second layer has a thickness of 400 mm and the thermal conductivity, k = 35 W/m K. Air at Tf1 = 310 oC flows through the pipe and the convective heat transfer coefficient from the air to the outside has a value of h1 = 120 W/m2 K, The outside surface of the pipe is surrounded by air which is at 50 oC (Tf2) and the convective heat transfer coefficient on this surface has a value of h2 = 90 W/m2 K. Calculate, (a) the thermal resistance (b) the heat transferred (c) temperature T1, T2, T3 and T4 (d) comment on your results.

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The Achulles tension force of Ft = 650 N is mobilized when the man tries to stand on his toes. As this is done , each of his feet is subjected to a reactive force of Nf = 400 N. Part A) determine the direction of the resultant moment produced by Ft and Nf about the ankle joint A. Part B) determine the magnitude of the resultant moment produced by Ft and Nf about the ankle joint A

## The Achulles tension force of Ft = 650 N is mobilized when the man tries to stand on his toes. As this is done , each of his feet is subjected to a reactive force of Nf = 400 N. Part A) determine the direction of the resultant moment produced by Ft and Nf about the ankle joint A. Part B) determine the magnitude of the resultant moment produced by Ft and Nf about the ankle joint A

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!

## 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!

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