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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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Scenario: You are to design synchronous and asynchronous circuits that will allow the following requirements to be met. Tasks: 1. Packet number checking A synchronous sequential machine is to have a single input line and a single output line. The circuit is to receive messages of 4-bit words coded in binary (least significant bit first). The purpose of the circuit is to detect whether the number coming in is a prime number (divisible by only itself and 1). Thus, the output is to become 1 whenever a 4-bit word does represent a valid prime number. At the end of each word the machine is to return to the reset starting state. Steps: 1) Draw a State Diagram (Mealy) and check for redundancies 2) Then assign binary State Identifiers. 3) Make a Next State Truth Table (NSTT) 4) Select a bistable type 5) Determine expressions for the bistable inputs 6) Determine expressions for the outputs 2. Monitoring System A monitoring system sends 1s positive going pulses to a device to ensure that it is operating correctly. The device will respond by lowering its normally high line as soon as it receives the pulse then raising the line again within the 1s if working correctly. If the device line doesn’t respond correctly or respond at all then an alarm must occur. 1) Carry out a design for the asynchronous system that will realise the requirements up to the point where internal conditions are designated to the lines in the merged table. 2) Explain what the designer would have to do to ensure the system was hazard free and the output was as short as possible.

## Scenario: You are to design synchronous and asynchronous circuits that will allow the following requirements to be met. Tasks: 1. Packet number checking A synchronous sequential machine is to have a single input line and a single output line. The circuit is to receive messages of 4-bit words coded in binary (least significant bit first). The purpose of the circuit is to detect whether the number coming in is a prime number (divisible by only itself and 1). Thus, the output is to become 1 whenever a 4-bit word does represent a valid prime number. At the end of each word the machine is to return to the reset starting state. Steps: 1) Draw a State Diagram (Mealy) and check for redundancies 2) Then assign binary State Identifiers. 3) Make a Next State Truth Table (NSTT) 4) Select a bistable type 5) Determine expressions for the bistable inputs 6) Determine expressions for the outputs 2. Monitoring System A monitoring system sends 1s positive going pulses to a device to ensure that it is operating correctly. The device will respond by lowering its normally high line as soon as it receives the pulse then raising the line again within the 1s if working correctly. If the device line doesn’t respond correctly or respond at all then an alarm must occur. 1) Carry out a design for the asynchronous system that will realise the requirements up to the point where internal conditions are designated to the lines in the merged table. 2) Explain what the designer would have to do to ensure the system was hazard free and the output was as short as possible.

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Perception checking – 1000 words Apply the perception checking process to at least 3 different individuals Write a paper including each of the following in some way: (They need not be in this order) A brief description or outline of the basic steps in the perception checking process A detailed description of your experience in at least 1 of the applications of the process A brief mention of the other applications A summary of how it worked for you–what you learned and how you think it might apply in your life As with all writing assignments in this class, Write using the active voice wherever possible Develop a good structure with opening and closing statements and supporting material Pay attention to spelling, grammar, sentence and paragraph structure Write in the most interesting way you can

## Perception checking – 1000 words Apply the perception checking process to at least 3 different individuals Write a paper including each of the following in some way: (They need not be in this order) A brief description or outline of the basic steps in the perception checking process A detailed description of your experience in at least 1 of the applications of the process A brief mention of the other applications A summary of how it worked for you–what you learned and how you think it might apply in your life As with all writing assignments in this class, Write using the active voice wherever possible Develop a good structure with opening and closing statements and supporting material Pay attention to spelling, grammar, sentence and paragraph structure Write in the most interesting way you can

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