- A linear time-invariant system has the gain and phase responses plotted below.
- Compute the output signal if the input signal is: (i) cos(100t); (ii) 7+3cos(100t+20°).
- Compute the
*input*signal if the*output*signal is: (i) cos(100t); (ii) 7+3cos(100t+20°).

Note that gain is in*decibels*, phase is in*degrees*, and frequency is in*radians/second*.

- A periodic signal with period T=3 has Fourier series amplitudes c
_{n}and phases ø_{n}in radians:**n**0 1 2 3 4 5 6 7 8 9 10 **c**_{n}6.3 5.4373 2.9302 1.9832 1.4954 1.1992 1.0005 0.8581 0.7511 0.6677 0.6010 **ø**_{n}0 -1.1425 -1.3709 -1.4646 -1.5208 -1.5616 -1.5946 -1.6231 -1.6488 -1.6726 -1.6951 **Plot**the sum of the first 11 terms of the Fourier series. What function is this approximating?

- A linear system has gain function of the form: GAIN(w)=B/(w²+A²); PHASE(w)=0.

Here w is angular frequency in radians/second and A and B are*unknown constants*.

The response of the system to 3cos(2t)+5cos(8t) is 15cos(2t)+10cos(8t).**Compute A and B**.

- HINT: Use symmetry to cut your work in half, since this is an even function.
- Compute the Fourier series expansion of the triangle wave shown below.

- This signal is passed through a "brick-wall" low-pass filter, which passes

with no effect all frequencies below 2 Hz and rejects all frequencies above 2 Hz.

**Plot**the output using Matlab. Explain why the corners have been rounded.

"A chicken is an egg's way of making another egg"--Anonymous- Compute the Fourier series expansion of the triangle wave shown below.

Attach a printout of the Matlab computer code you used to generate