Hint: In part (b), convert the sinusoids into the form with the smallest common period (it is the fundamental period of x(n)), and then represent each sinusoid in terms of complex exponentials (harmonics) with this period
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Hint: In part (b), convert the sinusoids into the form with the
smallest common period (it...
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. (45 pts) DT FS. Find the fundamental period and the Fourier Series (FS) spectral coefficients...
1. (45 pts) DT FS. Find the fundamental period and the Fourier Series (FS) spectral coefficients for these periodic signals. Sketch the spectrum in magnitude and phase. Express each x[n] as the sum of the spectral coefficients for k = [0, N-1]. a. ?1[?] = ???( ? 3 ?) b. ?2 [?] = cos ( ? 3 ?) + sin( ? 4 ?) c. ?3[?]
l, f) is a periodic signal with period f(t)-n(t)-u(t-t/2 ) for 0 2π a.) Find the exponential Fourier series of f() and sketchf). What is the fundamental radian frequency. b.) Evaluate and sketch...
l, f) is a periodic signal with period f(t)-n(t)-u(t-t/2 ) for 0 2π a.) Find the exponential Fourier series of f() and sketchf). What is the fundamental radian frequency. b.) Evaluate and sketch |Dml, the magnitude of the Fourier series coefficients vs.o in the range of -4s n S4 c.) Evaluate and sketch the phase angle of D, vs. co in the same range (-4S n S4) d.) Find the signal average power e) Find the approximate average power of...
Part 1: Exponential Fourier series The following MATLAB code calculates the exponential Fourier series coefficient for...
Part 1: Exponential Fourier series The following MATLAB code calculates the exponential Fourier series coefficient for the signal x(t) shown in the figure below, plots it's double sided amplitude spectrum IDn l, double sided phase spectrem LDn, and the resulting signal xn(t). 4r 4a Periodic signal x(t) 1.1 Show that the complex Fourier Series Coefficients written as: D 1.2 Use the following Matlab to general the two sided spectral line. 1.3 Execute the Matlab code with To = 2π and...
Can you do part A through B please? 2 Euler's formula relates the complex exponential to...
Can you do part A through B please?
2 Euler's formula relates the complex exponential to trigonometric functions as e" = cos(9) + j sin(9) This problem considers two alternate forms of Euler's formula. (a) Show that we can represent cos(0) in terms of complex exponentials as eje +e-je cos(e) (b) Derive a similar expression to part (a) for sin(e) (c) Use the results of part (a) to hand com pute cos(2). Verify your result with MATLAB. This result conflicts...
2. (12 points) Apply the result from part 1 to determine the response of a lowpass...
2. (12 points) Apply the result from part 1 to determine the response of a lowpass filter. a) (4 points) Determine the fundamental frequency and non-zero complex exponential Fourier series coeffi- cients of the periodic signal 2π f(t) =-2-5 sin(2nt) + 10 cos(Grt + "") and sketch the Fourier magnitude spectum D versus w and the Fourier phase spectrum LD versus w (b) (2 points) Use Parseval's theorem for the exponential Fourier series to find the power of the signal...
1. Let [n] = 6 cos(0.8nn). Note that [n] is periodic. (a) Find the period N...
1. Let [n] = 6 cos(0.8nn). Note that [n] is periodic. (a) Find the period N of 1 [n). (b) Let y[n] = [n(u[n] – z[n-N]). Find Y [k] = DFT(y[n]), k=0,1,..., N-1. Hint: x[n] = 3e08an + 3e-j0.8an (e) Find X(W) = DTFT (2[12]). How does it compare with part (b)? (a) Sketch 1 [n],y[n], X(w), Y [k]. 2. (a) Sketches in the 2D complex plane for n = 0,1,...,8. (b) Let i[n] = +2e ", n=0,1,...,8. Find X[k]...
HW : Ch 17 Part 2 (Butters, Titrations, Solubility &Complex lons) -3.4hrs)(52 credits Common-lon Effect on...
HW : Ch 17 Part 2 (Butters, Titrations, Solubility &Complex lons) -3.4hrs)(52 credits Common-lon Effect on Solubility for Lead Thiocyanate 7 of 27 Review Constants Periodic Table Lead thiocyarate, Pb(SCN), has a 2.00 x 10-5 value of Part A Calculate the molar solubility of lead thiocyanate in pure water. The molar solby is the maximum amount of lead thiocyanate the solution can hold Express your answer with the appropriate units. View Available Hints) Value Units Submit Common on Effect Consider...
4. (4.5 pts) Consider a 3D electromagnetic plane wave in vacuum, described in usual complex form...
4. (4.5 pts) Consider a 3D electromagnetic plane wave in vacuum, described in usual complex form by, (r, t) = Ēelkr-wt) in which ło = Epein/2y. Where k = -kx is the wave vector (assume k > 0) and w > 0 is the angular frequency. As usual, the real field is Er, t) = ReLEr, t)] (a) In which direction is the wave propagating? In terms of the given values k and w, what is the speed, wavelength, and...
Answer the following questions Q1. The image digitisation process consists of, in general, three components to convert...
Answer the following questions Q1. The image digitisation process consists of, in general, three components to convert the continuous signal into digital form, including sampling (or discretisation in time/space), quantization (discretisation of amplitude) and coding (generation of binary code for each quantised level) a. Name the major distortions associated with the above image digitisation process [2 marks] Name the areas of principal applications (or the basic classes of problems) which are covered by image processing. b. Discuss the main issues...
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...
l, f) is a periodic signal with period f(t)-n(t)-u(t-t/2 ) for 0 2π a.) Find the exponential Fourier series of f() and sketchf). What is the fundamental radian frequency. b.) Evaluate and sketch |Dml, the magnitude of the Fourier series coefficients vs.o in the range of -4s n S4 c.) Evaluate and sketch the phase angle of D, vs. co in the same range (-4S n S4) d.) Find the signal average power e) Find the approximate average power of...
Part 1: Exponential Fourier series The following MATLAB code calculates the exponential Fourier series coefficient for the signal x(t) shown in the figure below, plots it's double sided amplitude spectrum IDn l, double sided phase spectrem LDn, and the resulting signal xn(t). 4r 4a Periodic signal x(t) 1.1 Show that the complex Fourier Series Coefficients written as: D 1.2 Use the following Matlab to general the two sided spectral line. 1.3 Execute the Matlab code with To = 2π and...
Can you do part A through B please?
2 Euler's formula relates the complex exponential to trigonometric functions as e" = cos(9) + j sin(9) This problem considers two alternate forms of Euler's formula. (a) Show that we can represent cos(0) in terms of complex exponentials as eje +e-je cos(e) (b) Derive a similar expression to part (a) for sin(e) (c) Use the results of part (a) to hand com pute cos(2). Verify your result with MATLAB. This result conflicts...
2. (12 points) Apply the result from part 1 to determine the response of a lowpass filter. a) (4 points) Determine the fundamental frequency and non-zero complex exponential Fourier series coeffi- cients of the periodic signal 2π f(t) =-2-5 sin(2nt) + 10 cos(Grt + "") and sketch the Fourier magnitude spectum D versus w and the Fourier phase spectrum LD versus w (b) (2 points) Use Parseval's theorem for the exponential Fourier series to find the power of the signal...
1. Let [n] = 6 cos(0.8nn). Note that [n] is periodic. (a) Find the period N of 1 [n). (b) Let y[n] = [n(u[n] – z[n-N]). Find Y [k] = DFT(y[n]), k=0,1,..., N-1. Hint: x[n] = 3e08an + 3e-j0.8an (e) Find X(W) = DTFT (2[12]). How does it compare with part (b)? (a) Sketch 1 [n],y[n], X(w), Y [k]. 2. (a) Sketches in the 2D complex plane for n = 0,1,...,8. (b) Let i[n] = +2e ", n=0,1,...,8. Find X[k]...
HW : Ch 17 Part 2 (Butters, Titrations, Solubility &Complex lons) -3.4hrs)(52 credits Common-lon Effect on Solubility for Lead Thiocyanate 7 of 27 Review Constants Periodic Table Lead thiocyarate, Pb(SCN), has a 2.00 x 10-5 value of Part A Calculate the molar solubility of lead thiocyanate in pure water. The molar solby is the maximum amount of lead thiocyanate the solution can hold Express your answer with the appropriate units. View Available Hints) Value Units Submit Common on Effect Consider...
4. (4.5 pts) Consider a 3D electromagnetic plane wave in vacuum, described in usual complex form by, (r, t) = Ēelkr-wt) in which ło = Epein/2y. Where k = -kx is the wave vector (assume k > 0) and w > 0 is the angular frequency. As usual, the real field is Er, t) = ReLEr, t)] (a) In which direction is the wave propagating? In terms of the given values k and w, what is the speed, wavelength, and...
Answer the following questions Q1. The image digitisation process consists of, in general, three components to convert the continuous signal into digital form, including sampling (or discretisation in time/space), quantization (discretisation of amplitude) and coding (generation of binary code for each quantised level) a. Name the major distortions associated with the above image digitisation process [2 marks] Name the areas of principal applications (or the basic classes of problems) which are covered by image processing. b. Discuss the main issues...
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