Digital Signal Processing: Assignment 1:

1. Let x[n] belongs C where n belongs to Z. What is the value of  x[7.5]?
a. (x[7]+x[8])/2
b. 0
c. Undefined
d. sqrt(x[7].x[8])

Ans: c

2. Let x(t) = 1-mod(t) for mod(t) <=1
                 = 0, mod(t) > 1.
Which of the following is the discrete-time sequence that results when sampling x(t) at a time interval
of 0.25 sec?

Ans: b; sigma(k=-4 to 4)(1-mod(k)/4)delta(n-k)

3. Which of the following is the correct definition of the unit impulse function?

Ans: a; delta(t) = 0 for all t not equal to 0 and integral {delta(t)}=1 from limits -inf to +inf

4. An affine transform of the independent variable takes the form at+b in the CT case and Mn+N
in the DT case. Let y(t) be obtained from x(t) through an affine transform of x(t); y[n] is similarly obtained from . In which of the following cases can we recover the original signal from its affine-transformed version?

a. CT signals
b. DT signals
c. Both CT and DT signals
d. None of the above

Ans: a

5. Let x[n]=3-3 sigma(k =-7 to inf) delta[n-3-k]=A u[Bn+C] where A,B,C belongs to Z. The unknown constants are:

a. A=-3
b. B=1
c. C=-5
d. All of the above

Ans: d