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milestone_2_task_1 [2023/01/15 00:33] scott [Pass Off] |
milestone_2_task_1 [2023/01/18 15:18] (current) scott Figure scale |
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| As you know, the laser tag system supports 10 players each with an assigned frequency in the range of 1.4 - 4.2 kHz. If the receiver is being illuminated or 'hit' by a laser tag gun then the sampled signal will consist of both a square wave at a particular frequency and noise. The system needs to analyze the received signal to determine whether the sampled signal contains a 'hit' by a laser tag gun. As the shooting gun gets farther away from the receiver, the amplitude of the square wave signal from the shooting gun gets smaller. Since the noise amplitude stays the same, this corresponds to a lower SNR, and it gets harder to distinguish the signal from the noise. This figure shows a square wave added to a random noise signal: | As you know, the laser tag system supports 10 players each with an assigned frequency in the range of 1.4 - 4.2 kHz. If the receiver is being illuminated or 'hit' by a laser tag gun then the sampled signal will consist of both a square wave at a particular frequency and noise. The system needs to analyze the received signal to determine whether the sampled signal contains a 'hit' by a laser tag gun. As the shooting gun gets farther away from the receiver, the amplitude of the square wave signal from the shooting gun gets smaller. Since the noise amplitude stays the same, this corresponds to a lower SNR, and it gets harder to distinguish the signal from the noise. This figure shows a square wave added to a random noise signal: | ||
| - | {{ :square_example.jpg?400 |}} | + | {{ :square_example.jpg?600 |}} |
| It will be easy for you to see the square wave in the close range signal, when the SNR is high. However, for longer-range signals, it will just look like noise even though there is a square wave embedded in the signal. The beauty of your signal processing system will be in its ability to detect a hit in the noisy received signal even at relatively large ranges. | It will be easy for you to see the square wave in the close range signal, when the SNR is high. However, for longer-range signals, it will just look like noise even though there is a square wave embedded in the signal. The beauty of your signal processing system will be in its ability to detect a hit in the noisy received signal even at relatively large ranges. | ||
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| {{:lab5_fall2018.pdf|Lab #5 from ECEN 380}} | {{:lab5_fall2018.pdf|Lab #5 from ECEN 380}} | ||
| - | {{::filter_design_notes.pdf|Supplementary filter design handout from Dr. Rice}} | + | {{::filter_design_notes.pdf|Supplementary filter design handout}} |
| We are going to be using an Infinite Impulse Response (IIR) digital filter. Wikipedia has a description of this type of filter ([[http://en.wikipedia.org/wiki/Infinite_impulse_response]]). You should read through this description. The IIR digital filter is characterized by two sets of coefficients called a and b. | We are going to be using an Infinite Impulse Response (IIR) digital filter. Wikipedia has a description of this type of filter ([[http://en.wikipedia.org/wiki/Infinite_impulse_response]]). You should read through this description. The IIR digital filter is characterized by two sets of coefficients called a and b. | ||
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| You should create a frequency domain plot for each of the bandpass filters and overlay them on the same plot. The result should look similar to the following. | You should create a frequency domain plot for each of the bandpass filters and overlay them on the same plot. The result should look similar to the following. | ||
| - | {{ :m_2_1_1.jpg?400 |}} | + | {{ :m_2_1_1.jpg?600 |}} |
| The horizontal axis should be in frequency and cover the entire allowable frequency band (0<f<5kHz). | The horizontal axis should be in frequency and cover the entire allowable frequency band (0<f<5kHz). | ||
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| Plot the output of the filter command (operating on your square wave signal) for each of the 10 bandpass filters. The following plot shows the output of the first 4 bandpass filters when the square wave input has a frequency of 1471 Hz (the frequency for player 1): | Plot the output of the filter command (operating on your square wave signal) for each of the 10 bandpass filters. The following plot shows the output of the first 4 bandpass filters when the square wave input has a frequency of 1471 Hz (the frequency for player 1): | ||
| - | {{ :filtered2.jpg?400 |}} | + | {{ :filtered2.jpg?600 |}} |
| You can see from this plot that filters 2, 3, and 4 attenuate the signal a lot compared to filter 1 (look at the amplitudes of each filtered signal). The output of filter 1 has a much higher amplitude. If you zoom in on the output of filter 1 you should be able to see that the square wave was changed into a sine wave by the filter. (Do you understand why this happens? Remember that the square wave signal contains a sinusoid at the fundamental frequency, as well as higher frequency harmonics that give it a square shape. Our bandpass filter effectively takes out the higher harmonic frequencies that make it a square wave, leaving only the sinusoid at the fundamental frequency!) | You can see from this plot that filters 2, 3, and 4 attenuate the signal a lot compared to filter 1 (look at the amplitudes of each filtered signal). The output of filter 1 has a much higher amplitude. If you zoom in on the output of filter 1 you should be able to see that the square wave was changed into a sine wave by the filter. (Do you understand why this happens? Remember that the square wave signal contains a sinusoid at the fundamental frequency, as well as higher frequency harmonics that give it a square shape. Our bandpass filter effectively takes out the higher harmonic frequencies that make it a square wave, leaving only the sinusoid at the fundamental frequency!) | ||
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| Your resulting bar graph produced using the square wave with the frequency for player 1 should look like this: | Your resulting bar graph produced using the square wave with the frequency for player 1 should look like this: | ||
| - | {{ :power.jpg?400 |}} | + | {{ :power.jpg?600 |}} |
| You should produce 10 of these plots, one for each of the 10 player frequencies. | You should produce 10 of these plots, one for each of the 10 player frequencies. | ||
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| ===== Pass Off ===== | ===== Pass Off ===== | ||
| - | **The following items need to be shown to the TAs.** | + | The following items need to be shown to the TAs for pass off: |
| - | - Frequency response plot of the 10 filters overlaid in both linear and decibel scales {{ :m_2_1_1.jpg?400 |}} | + | - Frequency response plot of the 10 filters overlaid in both linear and decibel scales {{ :m_2_1_1.jpg?600 |}} |
| - | - Plots of total power of 200 ms long square wave through each filter (There should be 10 of these plots corresponding to a square wave for each of the player frequencies.) {{ :power.jpg?400 |}} | + | - Plots of total power of 200 ms long square wave through each filter (There should be 10 of these plots corresponding to a square wave for each of the player frequencies.) {{ :power.jpg?600 |}} |
| - | - List of filter coefficients for each of the 10 bandpass filters | + | - List of filter coefficients (with at least 17 significant digits) for each of the 10 bandpass filters |
milestone_2_task_1.1673767995.txt.gz · Last modified: 2023/01/15 00:33 by scott
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