Designing Filters

The critical frequency, fcrit, for the filters that will be designed is the −3 dB frequency for the low-pass and high-pass filters, pole and/or zero for the shelving filters, and the center frequency for the all-pass filter.
The critical frequency is the experimenter’s birthday (sans year) in kHz for birthdays prior to July and the birthday divided by two for birthdays from July to December.
For instance, if the experimenter was born on May 24 the critical frequency is 5.24 kHz and if the experimenter was born on December 13 the critical frequency is 12.13/2 = 6.065 kHz.
1. Design a first order low-pass filter with a dc gain of 20db and a −3 dB frequency of f3 = fcrit.
2. Design a first order high-pass filter with a infinite frequency gain of 20dB and a −3 dB frequency of f3 = fcrit.
3. Design a first-order low-pass shelving filter with a pole frequency of fp = fcrit, a dc gain of 20dB,and an infinite frequency gain of 6dB.
4. Design a first-order high-pass shelving filter with a zero frequency of fz = fcrit, a dc gain of 6dB,and an infinite frequency gain of 20dB.
5. Design a first-order all pass filter with a phase shift of 90° at f.o = fcrit.

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