Questions and Answers of Signals and Systems

In wireless communications, the effects of multi-path significantly affect the quality of the received signal. Due to the presence of buildings, cars, etc. between the transmitter and the receiver
Consider the sampling signalwhich we will use in the sampling of analog signals later on.(a) Plot Î´T(t). Findand carefully plot it for all t. What does the resulting signal ss(t)
When defining the impulse or Î´(t) signal the shape of the signal used to do so is not important. Whether we use the rectangular pulse we considered in this Chapter or another pulse, or
(a) Consider the periodic signals x1 (t) = 4cos(πt) and x2(t) = −sin(3πt +π/2). Find the periods T1 of x1 (t) and T2 of x2 (t) and determine if x(t) = x1 (t) + x2(t) is periodic. If so,
Signal energy and RC circuit€”The signal x(t) = eˆ’ˆ£tˆ£is defined for all values of t.(a) Plot the signal x(t) and determine if this signal is finite
Consider the triangular train of pulses x(t) in Figure 1.23.(a) Carefully plot the derivative of x(t), y(t) = dx(t)/dt.(b) Can you computeIf so, what is it equal to? If not, explain why not.(c)
For a complex exponential signal x(t) =2ej2πt(a) Suppose y(t) = ejπt, would the sum of these signals z(t) = x(t) + y(t) be also periodic? If so, what is the fundamental period of z(t)?(b) Suppose
A periodic signal can be generated by repeating a period.(a) Find the function g(t), defined in 0 ‰¤ t ‰¤ 2 only, in terms of basic signals and such that when repeated
Consider the signal x(t) in Figure 1.21.(a) Plot the even-odd decomposition of x(t), i.e., find and plot the even xe(t) and the odd xo(t) components of x(t).(b) Show that the energy of a
Let x(t) = t[u(t) − u(t −1)], we would like to consider its expanded and compressed versions.(a) Plot x(2t) and determine if it is a compressed or expanded version of x(t).(b) Plot
A signal x(t) is defined as x(t) = r(t + 1) ˆ’ r(t) ˆ’2u(t) + u(t ˆ’ 1).(a) Plot x(t) and indicate where it has discontinuities. Compute y(t) = dx(t)/dt and plot
The signalcan be written as x(t) = ˆ£tˆ£p(t).(a) Carefully plot x(t) and define p(t), then find y(t) = dx(t)/dt and carefully plot it.(b) Calculateand comment on how your
Is it true that (if not true, give correct answer)(a) for any positive integer k(b) for a periodic signal x(t) of fundamental period T0for any value of t0? Consider, for instance, x(t)
Consider the periodic signal x(t) = cos(2Ω0t) + 2 cos(Ω0t),−∞ < t < ∞, and Ω0 = π. The frequencies of the two sinusoids are said to be harmonically related.(a) Determine the
Consider a circuit consisting of a sinusoidal source vs(t) = cos(t) u(t) connected in series to a resistor Rand an inductor L and assume they have been connected for a very long time.(a) Let R =
Do reflection and time-shifting commute? That is, do the two block diagrams in Figure 1.20 provide identical signals, i.e., is y(t) equal to z(t)? To provide an answer to this consider the signal
The following problems relate to the symmetry of the signal:(a) Consider a causal exponential x(t) = eˆ’t u(t). i. Plot x(t) and explain why it is called
Consider a finite support signal x(t) = t, 0 ≤ t ≤1, and zero elsewhere.(a) Plot x(t +1) and x(−t +1). Add these signals to get a new signal y(t). Do it graphically and verify your results

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