1-Verify the following:8(n) = u(n) – u(n – 1)and find af such thatи(п) — 2и(п — 1) — У арб(п — k)k=02) Take u(n) as the unit step function. Sketch the following signals.- w(n) = u(n) – u(n – 6). ( This is called a window function.)-0 (n) cos (π /4)cos (πη/4)- y(n) = v(n) . w(n)- x(n) = y(-n + 3). Use two different approaches so as to verify your result.%3D3) Take u(n) as the unit step function. Sketch the following signals.-в(m) — 2(и(п + 1) — и(п — 3)).-v1 (n) = v(n)+ v(-n)- v2(n) = v(n) – v(-n)Discuss the symmetrical properties of vi and v2. Write v(n) in terms of vi and v2.

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Answered: 1-Verify the following: 6 (п) — и(п) —…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Suppose that a continuous-time sinusoid x(t) = 4 cos(1800pi*t+ pi/3) is sampled with a sampling frequency of fs, producing the discrete-time signal x[n] = x(n/fs).1. Find a value of fs so that x[n] = 4cos(0.4pi*n−pi/3).2. Find a value of fs so that x[n] = 2 for all n.3. Find a value of fs so that x[n] = 2(−1)^n
Question 3 A communication channel has a bandwidth of 100 kHz. This channel is to be used for transmission of an analog source m(t), where |m(t)|<1, whose bandwidth is 4 kHz. The power content of the message signal is 0.1 W. (a) If an FM system is employed and the whole channel bandwidth is utilized, determine the required modulation index. (b) Determine the ratio of the output SNR of an FM system used in part (a), to the output SNR of a conventional AM system (DSB-LC) with a modulation index of 0.85. Express the SNR ratio in dB.
Using MatLab, plot the signal x(t) = 10*cos(800*pi*t + pi/4). Use 5 samples per period and plot 3 periods using equations for each variable that are derived from the frequency, f, instead of hard-coding numbers where possible. Explain and/or annotate each of the parameters from x(t) = A*cos(w*t + phi) in the code.
It is easy to demonstrate that amplitude modulation satisfies the superposition principle, whereas angle modulation does not. To be specific, let m1 (t) and m2 (t) represent two message signals and let u1(t) and u2(t) represent the corresponding modulated versions.a) Show that when the combined message signal m1(t) + m2(t) DSB modulates a carrier Ac cos 2πfct, the result is the sum of the two DSB amplitude-modulated signals u1(t) + u2(t). b) Show that if m1(t) + m2(t) frequency modulates a carrier, the modulated signal is not equal to u1(t) + u2(t). A DSB-SC modulated signal is demodulated by applying it to a coherent detector.Evaluate the effect of a frequency error ∆f in the local carrier frequency of the detector, measured with respect to the carrier frequency of the incoming DSB-SC signal.b) For the case of a sinusoidal modulating wave, show that because of this frequency error, the demodulated signal exhibits beats at the error frequency. Illustrate you answer. There…
It is easy to demonstrate that amplitude modulation satisfies the superposition principle, whereas angle modulation does not. To be specific, let m1 (t) and m2 (t) represent two message signals and let u1(t) and u2(t) represent the corresponding modulated versions. a) Show that when the combined message signal m1(t) + m2(t) DSB modulates a carrier Ac cos 2πfct, the result is the sum of the two DSB amplitude-modulated signals u1(t) + u2(t). b) Show that if m1(t) + m2(t) frequency modulates a carrier, the modulated signal is not equal to u1(t) + u2(t). It is easy to demonstrate that amplitude modulation satisfies the superposition principle, whereas angle modulation does not. To be specific, let m1 (t) and m2 (t) represent two message signals and let u1(t) and u2(t) represent the corresponding modulated versions. a) Show that when the combined message signal m1(t) + m2(t) DSB modulates a carrier Ac cos 2πfct, the result is the sum of the two DSB amplitude-modulated signals u1(t) +…
1) Calculate the bandwidth and baud rate for an FSK signal with mark frequency 34 kHz, space frequency 26 kHz, and input bit rate 2 kbps. Use the calculator for bandwidth. 1.1) Using a table of Bessel functions, determine the minimum bandwidth for the FSK signal. Remember that the significant bands are taken for those with amplitude > 1%. As the table is normalized (Jo=1 at most), the significant sidebands are those with amplitude > 0.01)
Assuming that an oscilloscope displays a Vmax of 5.22V and Vmin of 1.33V. Calculate the percentage of modulation. Three (3) AM broadcast stations are spaced at 18 kHz, beginning at 73 kHz. Each station is allowed to transmit modulating up to 6 kHz. Compute for the upper and lower sidebands of each station and plot it in the frequency domain. Given a Vmax of 7.45V and a modulation index of 0.691, calculate for Vmin. A station is given a carrier frequency of 88 kHz. Having a modulating frequency of 12 kHz, compute for the upper and lower sidebands of the station.
Design an Armstrong indirect FM modulation to generate an FM signal with carrier frequency 97.3 MHz and Δf=10.24KHz . A NBFM generator of fc1=20 KHz and Δf=5 Hz is available . only frequency doublers can be used as multipliers. Additionally, a local oscillator with adjustable frequency 400 and 500 KHz is readily available for frequency mixing.
As an engineer, you are required to generate an FM signal using a single tone sinusoidal signal of frequency, fm with the modulation index of 1.5. Sketch the frequency spectrum of the FM signal and determine the total power contained in the frequency range fc-2 fm to fc + 2 fm - given the carrier voltage is 12 V and the load resistor is 1202
solve only question 1.b 1.a) Calculate the bandwidth and baud rate for an FSK signal with mark frequency 34 kHz, space frequency 26 kHz, and input bit rate 2 kbps. Use the calculator for bandwidth. 1.1 Using a table of Bessel functions, determine the minimum bandwidth for the FSK signal from the previous problem (Problem 1.a). Remember that the significant bands are taken for those with amplitude > 1%. Since the table is normalized (Jo=1 at most), the significant sidebands are those with amplitude > 0.01). -- Indications: In your answer, place the result without the units and expressed in kilohertz
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1. Given an analog signal x(t)=10 cos(2π.5500t)+5 cos(2π.7500t) is sampled at a rate of 8,000 Hz, a. Sketch the spectrum of the sampled signal up to 20 kHz; b. Sketch the recovered analog signal spectrum if an ideal low pass filter with a cutoff Frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal; c. determine the frequency/frequencies of aliasing noise.

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1-Verify the following: 6 (п) — и(п) — и (п — 1) and find ag such that и(п) — 2и(п — 1) — У арб(п — k) k=0