Question
Digital Signal Processing
2. Design a 3-tap FIR highpass filter with a cutoff frequency of 1,600Hz and a sampling rate of 8,000 Hz using a
a. rectangular window function
b. Hamming window function
Determine the transfer function and difference equation of the designed FIR system, and compute and plot the magnitude frequency response for Ω =0, π/4,π/2,3π/4 and π radians.

4.
Design a 5-tap FIR highpass filter with a cutoff frequency of 250 Hz and a sampling rate of 1,000 Hz using a
a. rectangular window function
b. Hamming window function
Determine the transfer function and difference equation of the designed FIR system, and compute and plot the magnitude frequency response for Ω =0, π/4,π/2,3π/4 and π radians.

8.
Consider an FIR highpass filter design with the following specifications:
Passband =0-1,500 Hz
Stopband = 2,000-4,000 Hz
Passband ripple = 0.02 dB
Stopband attenuation = 60 dB
Sampling rate = 8,000 Hz
Determine the following:
a. window method
b. length of the FIR filter
c. cutoff frequency for the design equation

9.
Consider an FIR bandpass filter design with the following specifications:
Lower cutoff frequency =1,500 Hz
Lower transition width = 600 Hz
Upper cutoff frequency = 2,300 Hz
Upper transition width = 600 Hz
Passband ripple = 0.1 dB
Stopband attenuation =50 dB
Sampling rate: 8,000 Hz
Determine the following:
a. window method
b. length of the FIR filter
c. cutoff frequencies for the design equation

10.
Consider an FIR bandstop filter design with the following specifications:
Lower passband = 0-1,200 Hz
Stopband = 1,600 - 2,000 Hz
Upper passband = 2,400 - 4,000 Hz
Passband ripple = 0.05 dB
Stopband attenuation = 60 dB
Sampling rate = 8,000 Hz
Determine the following:
a. window method
b. length of the FIR filter
c. cutoff frequencies for the design equation

29.
Design a 41tap bandpass FIR filter with lower and upper cutoff frequencies of 2,500Hz and 3,000 Hz, respectively, using the following window functions. Assume a sampling frequency of 8,000 Hz.
a. Hanning window function
b. Blackman window function.
List the FIR filter coefficients and plot the frequency responses for each design.

30.
Design a 41-tap band reject FIR filter with cutoff frequencies of 2,500 Hz and 3,000 Hz, respectively, using the Hamming window function. Assume a sampling frequency of 8,000 Hz. List the FIR filter coefficients and plot the frequency responses.
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        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        1.17mstwenty4_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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        1.21mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
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        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        • 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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        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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      • select * from `subjects` where `subjects`.`id` in (355)
        1.06mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
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        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 44825 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.04mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
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        Backtrace
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        Backtrace
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