Complex numbers are crucial in ultrasound imaging to represent both the amplitude and phase of the sound wavesused to create images of internal tissues and organs.Express the following complex numbers in polar form (reje with -π < 0 ≤ π).Z₁ = (1 + 2j)/(1 - 2j)Z₂ = (1 + j)ejπ/6-) Demonstrate that the derivative of a sinusoidal function yields the same result when calculated usingcomplex exponentials. Consider the waveformy(t)=sin(200лt + л/4)representing the signal driving an ultrasound transducer. First, calculate the time derivative of this waveform(dy/dt). Then, express y(t) in terms of complex exponentials and take the derivative. Did you obtain the sameresult?

Answered: Complex numbers are crucial in…

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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1. Suppose that MATLAB is used to plot a sinusoidal signal. The following MATLAB code generates the signal and makes the plot. Draw a sketch of the plot that will be done by MATLAB. Determine the amplitude (A), phase ($), and period of the sinusoid and label the period on your plot. dt = 0.001; tt = = .05 dt : .15; Fo = 8; Z sqrt (2) * (1-j); xx = real( Z*exp( 2j*pi*Fo*tt ) ); plot tt, XX ), grid title( 'SECTION of a SINUSOID' ), xlabel('TIME (sec)')
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4) The function sin x (which you may remember from Calculus 1 limits) is important in signal processing and electrical engineering, and is known as the "sinc" function, often abbreviated as just sinc(x). Find § sinc(x) dx. Then, approximate ſ sinc(x) dx using the first five terms of the appropriate series.
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A sinusoidal function has a frequency of 3 , a maximum value of 15 , a minimum value of -3, and a y-intercept of 6 . Which function could be the function described?
All answer is only in form of magnitude. USE 4 DECIMAL PLACES *A pure inductance is connected to a 150 V, 1 Hz supply, and the apparent power of the circuit is 300 VA. Find the value of the inductance *What is the RMS current of a trapezoidal wave with 1 A max? *A circuit consisting of a resistor in series with a capacitor takes 100 watts at a power factor of 0.1 from a 100 V, 60 Hz supply. Find the current flowing
Question 5 Given the two sinusoidal waveforms, f(t) = -50coswt - 30sinwt and g(t) =55coswt - 15sinwt Find the amplitude of f(t) %3D
A voltage is applied across the terminals of an inductor. The voltage is a 2.5 kHz sinusoidal voltage with zero phase angle and a maximum amplitude of 5mV. This voltage is applied across the terminals of the inductor, and the resulting steady-state current has a maximum amplitude of 314.2µA. a) What is the frequency of the current in radians per second? b) What is the phase angle of the current? c) What is the impedance, ZL, of the inductor? d) What is the inductance, L, of the inductor in mH? e) What is the inductive reactance, XL, of the inductor?
The 80mH inductor can be modeled, at low frequencies, as a 0.08H ideal inductor in series with a 1802 resistor. Draw the equivalent ideal circuit in the frequency domain, for the real RL circuit depicted below. The alligator clips are connected to the function generator, which is generating a 5V peak-to-peak sine wave at 2KHZ. Don't forget to draw the 502 internal resistance of the function generator. The colour bands on the resistor are brown, black, red, gold. BNAR M X****
IN Consider the discrete-time sinusoid x[n] = cos 8 a. Plot x[n] for n = 0,..., 48. b. Is this discrete-time sinusoid periodic? If so, what is the period? c. Find and plot another discrete-time sinusoid y[n] = cos(w₁n) with a different frequency (w₁ ) that yields exactly the same values as x[n].
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f electrical engin X Principles & Applications of Elec X+ O File | C:/Users/DELL/Downloads/Fundamentals%20of%20electrical%20engineering%20by%2 56 Q D Page view A Read aloud - EXAMPLE 4.8 Average Value of Sinusoidal Waveform Problem Compute the average value of the signal x(t) = 10 cos(100t). %3D Solution Known Quantities: Functional form of the periodic signal x(t). Find: Average value of x(t). Analysis: The signal is periodie with periodT = ?n/w= 2r /100, thus we need to in over only one period to compute the average value: 1 (x(t)) T. 2л 100 100 x(t') dt' = 10 cos(100t) dt 10 (sin(27) sin(0)) = 0 Type here to search 11

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