Digital Signal Processing 2. Given an analog signal x(t)=5 cos⁡(...

Question
Digital Signal Processing
2.
Given an analog signal
x(t)=5 cos⁡(2π.2,500t)+2 cos⁡(2π.3,200t), for t≥0,
sampled at a rate of 8,000 Hz,
a. sketch the spectrum of the sampled signal up to 20 kHz;
b. sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal.

8. Assuming a continuous signal is given as
x(t)=10 cos⁡(2π.5,000t)+5 sin⁡(2π.7,500t), for t≥0, sampled at a rate of 8,000 Hz,
a. sketch the spectrum of the sampled signal up to 20 kHz;
b. sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff
frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal;
c. determine the frequency/frequencies of aliasing noise

14.
Given a DSP system in which a sampling rate of 8,000 Hz is used and the anti-aliasing filter is a Butterworth lowpass filter with a cutoff frequency 3.2 kHz, determine the order of the Butterworth lowpass filter required to make the percentage of aliasing level at the cutoff frequency less than 10%.

28. Assuming that a 8-bit ADC channel accepts analog input ranging from -2.5 to 2.5 volts, determine the following:
a. number of quantization levels;
b. step size of the quantizer or resolution;
c. quantization level when the analog voltage is 1.5 volts;
d. binary code produced by the ADC;
e. quantization error
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        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        1.1mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        1.12mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
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        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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        Backtrace
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      • select * from `subjects` where `subjects`.`id` in (355)
        990μstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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        • 23. app/Repositories/HomeworkLibraryRepository.php:39
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        1.04mstwenty4_siteHomeworkLibrary.php#260
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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