Sheet 1 - assignment on even and odd signals PDF

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assignment on even and odd signals...

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Sheet 1 P1. For x (t) indicated in Figure 1, sketch the following: (a) (b) (c) (d)

x(-t) x(t + 2) x(2t + 2) x(1 - 3t)

Figure 1

P2. For x (t) indicated in Figure 2, sketch the following: (a) (b) (c) (d)

x(t - 2) x(2t) x(0.2t) x(-t) x(t)

1

-1

0

2

Figure 2 P3. For x (t) indicated in Figure 3, sketch the following: (a) x(3t) (b) x(-t) (c) x(2t + 3)

t

x(t)

1

-2

0

2

t 4

-1

Figure 3 P4. For x (t) indicated in Figure 4, sketch the following: (a) Even components for x(t) (b) Odd components for x(t) x(t)

1

-1

0

1

-1

Figure 4 P5. For a discrete – time signal x [n] shown Figure 5, (1) Sketch and carefully label each of the following signals: (a) x[n – 2] (b) x[4 - n] (c) x[2n] (2) What difficulty arises when try to define a signal as x [n/2].

Figure 5

2

t

P6. For each of the following signals (a - f), determine whether it is even, odd, or neither.

P7. Consider the signal y[n] in Figure 6.

Figure 6

(a) Find the signal x[n] such that Ev{x[n]} = y[n] for n > 0, and Od (x[n]} = y[n] for n < 0. (b) Suppose that Ev{w[n]} = y[n] for all n. Also assume that w[n] = 0 for n < 0. Find w[n]....