Assignment #12

ECSE-2410 Signals & Systems Fall 2004 Due Tue 10/26/04

1(24). Consider the signals .

(a)(6) Sketch and its Fourier transform . Label axes and key values.

(b)(6) Sketch and . Label axes and key values.

(c)(3) Sketch . Label axes and key values.

(d)(3) Sketch . Label axes and key values.

(e)(3) Determine which of the signals , , , are bandlimited.

(f)(3) For signal , find the lowest sampling frequency that will permit reconstructing it from the sampled signal, i.e., find the Nyquist sampling rate.

2(16). A sampled signal is generated by sampling the original signal every 0.1 seconds as shown in the figure, where , with .

(a)(4) Sketch .

(b)(4) What is the sampling frequency in radians/sec. ?

(c)(4) What is the highest frequency (rad/sec) in the original signal ?

(d)(4) Is it possible to recover the original signal from the sampled signal ? Answer Yes or No and state why?

3(10). Two signals are multiplied as follows

where is the impulse train, , with sec.

(a)(5) Let the spectrum of be

Sketch the spectrum of , . Can be recovered from using lowpass filtering? Why or why not?

(b)(5) Repeat part (a) if the spectrum of is

and remains the same. Can be recovered from using lowpass filtering? Why or why not?

4(20). O&W 7.24

5(30). O&W 7.38