Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

PROBLEMS

Delta Functions

1.1

(a) Find the area of g(x) on :

(1.84)

(b) Find a general expression for h(x) on :

(1.85)

1.2

(a) Convolve the following functions:

(1.86)

(b) Repeat (a) for

(1.87)

1.3

(a) Find an expression for in terms of two delta functions. (b) Show that is identical to the rectangle function.

1.4

(a) Convolve the following two functions:

(1.88)

(b) Repeat (a) for

(1.89)

where is the discrete unit-step function.

1.5 The Dirac delta function can be modeled using ...