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What is the fundamental period of the below signal? You need to find the fundamental frequency of e and e 5 separately. The fundamental period of [n] is the least common multiple of the se two numbers.
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4 days ago
Signals and systems
Fundamental period calculation
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Define signal y(t) = %∞ k=−∞ x(0.5t − 10k), where x(t) = e−2t t ≥ 1 0 t < 1 (a) Determine the constant a such that the signal x(−2t +a) is borderline anticausal. (b) Is the signal y(t) periodic? If so, determine the period Ty. If not, explain why y(t) is not periodic.
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4 days ago
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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1.35: Given x1(t) = cos (t), x2(t) = sin(πt), and x3(t) = x1(t)+x2(t). (a) Determine the fundamental periods T1 and T2 of signals x1(t) and x2(t). (b) Show that x3(t) is not periodic, which requires T3 =k1T1 =k2T2 for some integers k1 and k2. (c) Determine the powers Px1 , Px2, and Px3 of signals x1(t), x2(t), and x3(t).
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4 days ago
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Consider the signal x(t) shown in Fig. P1.1-10. Outside the interval shown, x(t) is zero. Determine the signal energy E[x(t)].
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Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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In Fig. P1.2-3, express signals x1(t), x2(t), x3(t), x4(t), and x5(t) in terms of signal x(t) and its time-shifted, time-scaled, or time-reversed versions
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Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Exa) Calculate the output 𝒚𝒌of LTID system with the following input, 𝒙𝒌, and impulse response, 𝒉𝒌 𝑥𝑛=(0.4)^𝑛*𝑢[𝑛] ℎ𝑛=(0.8)^𝑛*𝑢[𝑛]
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hwmadeeasy
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6 days ago
Signals and systems
discrete convolution
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Determine the DTFT of the following signal 𝑥𝑛=4(1/2)^𝑛*𝑢(𝑛)
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6 days ago
Signals and systems
DTFT calculation
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Write the state equations for the series RLC circuit shown in Fig. 1.45, using the inductor current q1(t) and the capacitor voltage q2(t) as state variables. Express every voltage and current in this
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saicharan414
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October 12, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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6 Determine the power and the rms value for each of the following signals: (a) 5+10 cos(100t +π/3) (b) 10 cos(100t +π/3)+16 sin(150t +π/5) (c) (10+2 sin 3t) cos 10t (d) 10 cos 5t cos 10t (e) 10 sin 5t cos 10t (f) ejαt cosω0t
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October 12, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Figure P1.1-7 shows a periodic 50% duty cycle dc-offset sawtooth wave x(t) with peak amplitude A. Determine the energy and power of x(t).
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hwmadeeasy
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October 12, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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If the inductor voltage vL(t) is taken as the output, show that the RLC circuit in Fig. 1.34 has an input–output equation of (D2 +3D+2)vL(t) = D2x(t).
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hwmadeeasy
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October 12, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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If the capacitor voltage vC(t) is taken as the output, show that the RLC circuit in Fig. 1.34 has an input–output equation of (D2 +3D+2)vC(t) = 2x(t)
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hwmadeeasy
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October 12, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Find the power of the periodic signal x(t) shown in Fig. P1.1-4. Find also the powers and the rms values of: (a) −x(t) (b) 2x(t) (c) cx(t) Comment
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saicharan414
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October 11, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Show that an everlasting exponential e−at is neither an energy nor a power signal for any real value of a. However, if a is imaginary, it is a power signal with power Px = 1 regardless of the value of a.
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saicharan414
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October 11, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Show that the energies of the signals in Figs. 1.3a, 1.3b, 1.3c, and 1.3d are 4, 1, 4/3, and 4/3, respectively. Observe that doubling a signal quadruples the energy, and time-shifting a signal has no effect on the energy. Show also that the power of the signal in Fig. 1.3e is 0.4323. What is the rms value of signal in Fig. 1.3e?
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saicharan414
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October 11, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Show that if ω1 = ω2, the power of x(t) = C1 cos(ω1t +θ1)+C2 cos(ω2t +θ2) is [C1 2 +C2 2 + 2C1C2 cos(θ1 −θ2)]/2, which is not equal to the Ex. 1.2b result of (C1 2 +C2 2)/2.
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hwmadeeasy
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October 11, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Show that the system described by the following equation is linear: dy(t)/ dt +t 2 y(t) = (2t +3)x(t)
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hwmadeeasy
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October 10, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Find the energies of the signals illustrated in Fig. P1.1-1. Comment on the effect on energy of sign change, time shifting, or doubling of the signal. What is the effect on the energy if the signal is multiplied by k?
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hwmadeeasy
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October 10, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Show that the signal shown in Fig. 1.18 can be described as x(t) = (t −1)u(t −1)−(t −2)u(t −2)−u(t −4)
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saicharan414
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October 6, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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Show that (a) (t 3 +3)δ(t) = 3δ(t) (b) ‘ sin t 2 − π 2 (δ(t) = −δ(t) (c) e−2t δ(t) = δ(t) (d) ω2 +1 ω2 +9 δ(ω −1) = 1 5 δ(ω −1)
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hwmadeeasy
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October 6, 2021
Signals and systems
linear systems and signals 3rd ed b.p.lathi chapter 1
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