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Fundamental Frequency of Continuous Signals To identify the period T, the frequencyf= 1/T, or the angular...
Fundamental Frequency of Continuous Signals To identify the period T, the frequencyf= 1/T, or the angular...
Fundamental Frequency of Continuous Signals To identify the period T, the frequencyf= 1/T, or the angular frequency ω = 2nf= 2m/T of a given sinusoidal or complex exponential signal, it is always helpful to write it in any of the following forms: sin (gd-sin(2nf)-sin(2t/T) The fundamental frequency of a signal is the greatest common divisor (GCD) of all the frequency components contained in a signal, and, equivalently, the fundamental period is the least common multiple (LCM) of all individual periods...
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%]...
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%] What is the fundamental period (i.e., T) and fundamental frequency (ie, wo) of (+)? (b) [8%] Calculate the time average, average power and total energy of x(t). Is x(t) an energy signal? Explain. (c) [8%] Calculate the Fourier series coefficients of (t), i.e., {x}. [Hint: You can make use of the result in Q1(a).] (d) [8%] What is the percentage of power loss if...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given bel...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this ...
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this signal both in the time-domain and frequency domain. (b) For the following square wave v(t), determine if it is a periodic signal, and if yes, what 10 V sin 4. [61 are its amplitude, period T and fundamental frequency f? Why do we need to convert this signal into sine/cosine wave for transmission? 2 o-oims (c) () According to Fourier Theorem, the above signal...
In MATLAB plot the following: The function is periodic, with time period 2T=2, after t=2 the...
In MATLAB plot the following: The function is periodic, with time period 2T=2, after t=2 the same sinusoidal components repeat in the same way as when 0 st < 2. The function its expanded from one time period 27, in terms of the sinusoidal components. All sinusoidal components have frequencies which are integral multiples of the fundamental frequency. 1 1 = = = 0.5Hz to = fo = cot I am cos(womt) + b, sin(wont) m=1 rad wo = 2nfo...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fund...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
1. Periodic signals with period To can be presented by Fourier Series in Complex Exponential or...
1. Periodic signals with period To can be presented by Fourier Series in Complex Exponential or Trigonometric form. i.e. X(t) = a ewa, H or where Mx = 2|az|; 0x = Zat Find the Fourier series coefficients at, as well as My and et, for the following signals. . (a). Sinusoidal: X(t) = sin 277. A (b). Square: -A TO Procedures: Use the Signal Generator to generate the above signals according to the setting listed in Table I and measure...
This is taken from Section 4.6, "Amplitude Modulation and the Continuous-Time Fourier Transform," in the course...
This is taken from Section 4.6, "Amplitude Modulation and the
Continuous-Time Fourier Transform," in the course text Computer
Explorations in signals and systems by Buck, Daniel, Singer, 2nd
Edition. I need the answers for the basic and intermediate
questions.
4.6 Amplitude Modulation and the Continuous-Time Fouriei Transform This exercise will explore amplitude modulation of Morse code messages. A simple ampli tude modulation system can be described by x(t) = m(t) cos(Crfot), (4.13) where m(t) is called the message waveform and...
Program from problem 1: (Using MATLAB) % Sampling frequency and sampling period fs = 10000; ts...
Program from problem 1: (Using MATLAB)
% Sampling frequency and sampling period
fs = 10000;
ts = 1/fs;
% Number of samples, assume 1000 samples
l = 1000;
t = 0:1:l-1;
t = t.*ts; % Convert the sample index into time for generation and
plotting of signal
% Frequency and amplitude of the sensor
f1 = 110;
a1 = 1.0;
% Frequency and amplitude of the power grid noise
f2 = 60;
a2 = 0.7;
% Generating the sinusoidal waves...
B oth 100 Day PH262 Page 1 of 5 Lab #13 AC Circuits, Part 1 RC...
B oth 100 Day PH262 Page 1 of 5 Lab #13 AC Circuits, Part 1 RC & RL, Phase Measurements THEORY The rotating phase representation for series AC circuits should be familiar from textbook and lecture notes A brief outline of the essential points is provided here. If a series RLC circuit is connected across a source of om which is a sinusoidal function of time, then und all its derivatives will also be inside. Sonce all demits in a...
Fundamental Frequency of Continuous Signals To identify the period T, the frequencyf= 1/T, or the angular frequency ω = 2nf= 2m/T of a given sinusoidal or complex exponential signal, it is always helpful to write it in any of the following forms: sin (gd-sin(2nf)-sin(2t/T) The fundamental frequency of a signal is the greatest common divisor (GCD) of all the frequency components contained in a signal, and, equivalently, the fundamental period is the least common multiple (LCM) of all individual periods...
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%] What is the fundamental period (i.e., T) and fundamental frequency (ie, wo) of (+)? (b) [8%] Calculate the time average, average power and total energy of x(t). Is x(t) an energy signal? Explain. (c) [8%] Calculate the Fourier series coefficients of (t), i.e., {x}. [Hint: You can make use of the result in Q1(a).] (d) [8%] What is the percentage of power loss if...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this signal both in the time-domain and frequency domain. (b) For the following square wave v(t), determine if it is a periodic signal, and if yes, what 10 V sin 4. [61 are its amplitude, period T and fundamental frequency f? Why do we need to convert this signal into sine/cosine wave for transmission? 2 o-oims (c) () According to Fourier Theorem, the above signal...
In MATLAB plot the following: The function is periodic, with time period 2T=2, after t=2 the same sinusoidal components repeat in the same way as when 0 st < 2. The function its expanded from one time period 27, in terms of the sinusoidal components. All sinusoidal components have frequencies which are integral multiples of the fundamental frequency. 1 1 = = = 0.5Hz to = fo = cot I am cos(womt) + b, sin(wont) m=1 rad wo = 2nfo...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
1. Periodic signals with period To can be presented by Fourier Series in Complex Exponential or Trigonometric form. i.e. X(t) = a ewa, H or where Mx = 2|az|; 0x = Zat Find the Fourier series coefficients at, as well as My and et, for the following signals. . (a). Sinusoidal: X(t) = sin 277. A (b). Square: -A TO Procedures: Use the Signal Generator to generate the above signals according to the setting listed in Table I and measure...
This is taken from Section 4.6, "Amplitude Modulation and the
Continuous-Time Fourier Transform," in the course text Computer
Explorations in signals and systems by Buck, Daniel, Singer, 2nd
Edition. I need the answers for the basic and intermediate
questions.
4.6 Amplitude Modulation and the Continuous-Time Fouriei Transform This exercise will explore amplitude modulation of Morse code messages. A simple ampli tude modulation system can be described by x(t) = m(t) cos(Crfot), (4.13) where m(t) is called the message waveform and...
Program from problem 1: (Using MATLAB)
% Sampling frequency and sampling period
fs = 10000;
ts = 1/fs;
% Number of samples, assume 1000 samples
l = 1000;
t = 0:1:l-1;
t = t.*ts; % Convert the sample index into time for generation and
plotting of signal
% Frequency and amplitude of the sensor
f1 = 110;
a1 = 1.0;
% Frequency and amplitude of the power grid noise
f2 = 60;
a2 = 0.7;
% Generating the sinusoidal waves...
B oth 100 Day PH262 Page 1 of 5 Lab #13 AC Circuits, Part 1 RC & RL, Phase Measurements THEORY The rotating phase representation for series AC circuits should be familiar from textbook and lecture notes A brief outline of the essential points is provided here. If a series RLC circuit is connected across a source of om which is a sinusoidal function of time, then und all its derivatives will also be inside. Sonce all demits in a...
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