Homework Answers
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t –...
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...
Problem 2: For each of the following functions find f'(x) Problem 2 (20 points): For each...
Problem 2: For each of the following functions find
f'(x)
Problem 2 (20 points): For each of the following functions, find f'(x) and simplify if possible. (Show necessary details.) (a) s tant dt (b) Socos * V1 – tdt (0) Bent Int dt
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of si...
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions. (c) Evaluate the gain and phase (in degrees) of H(f) at 0.2 Hz from each expression.
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions.
(c) Evaluate the gain and phase (in degrees)...
need help with these questions as soon as possible PROBLEM 3: Simplify the following expressions (to...
need help with these questions as soon as possible
PROBLEM 3: Simplify the following expressions (to review the properties of the unit impulse): a. f(t 5)6(t -5) etn dt PROBLEM 4: Mathematical Review Problem 1.54(a, b, d) PROBLEM 5: a) Consider the signal t) defined below 0, t<0 n(t) = t<2 t, 0, 1 t2 2 Write a single equation for xi(t) using the unit step function (i.e. do not use bracket notation). b) Sketch the signal z2(t) = u(t...
ECE3204 F19 HW-3 Due: Wed. 10/2/2019 3 Problem 1: Find and sketch c(t) = f(t)* 12(t)...
ECE3204 F19 HW-3 Due: Wed. 10/2/2019 3 Problem 1: Find and sketch c(t) = f(t)* 12(t) for the pairs of functions illustrated below 2₂ (1) ECE3204 F19 HW-3 Due: Wed. 10/2/ Problem 3: By direct integration find the Laplace transform of the signal x(t) given by: cos(1) 0<t< x(1) = 10 elsewhere Note that cos(t) = (alt+e)
1. Use combinations of STEP FUNCTIONS to describe each continuous-time signal shown below. f(t) 0 2...
1. Use combinations of STEP FUNCTIONS to describe each continuous-time signal shown below. f(t) 0 2 4 6 0 1 2 3 0 1 2 3 4 2. Sketch the following signals: (a) x (t)=1 [u(t+2)-u(t-1)] (c) X(t)=\fety (b) X(t)=t.e (d) x (t) = u(t) u(t-1).ult-2).u(t-3) 3. Determine whether the systems below are linear and time invariant. Justify your answer! (a) y(t) = x(31) (b) y(t)= 2x(1-t) y(t)=cos(x(t)] 4. Simplify the expressions: (a) y(t)=1.8(t+2)+(t +1) 8(1-1)+(t+3). 8(t) (b) y(t) =...
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series ...
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series coefficients Dn. Show that the power P of f(t) is This is Parseval's theorem for the exponential Fourier series. 2. (12 points) If f(t) is real-valued, Parseval's theorem can be as a) (3 points) Find the power of the PWM signal shown in figure 1. Hint: for this part don't use Parseval's theorem b) (9 points) Use Parseval's theorem for a real-valued signal to...
Problem 2: For the signal g(t) t, a) (25 points) Find the exponential Fourier series to...
Problem 2: For the signal g(t) t, a) (25 points) Find the exponential Fourier series to represent g(t) over the interval (-π, π). Sketch the spectra (amplitude and phase of Fourier series coefficients). b) (25 points) Find the average power of g(t) within interval (- ,r). Using this result and given that Σ00.-6, verify the Parseval's theorem
Laplace Transform Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace...
Laplace Transform
Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace Transform table 9.2 find the bilinear Laplace transform, F($) and sketch the region of convergence (ROC) in the s-plane showing all poles. State the ROC as an inequality. b) Another function is added so that fa(t) = 4e-2tu(t) + 7u(-t) – 10e-10t u(-t). Find the Bilinear Laplace Transform of fa(t) and sketch the region of convergence in s-plane also showing all the poles. State...
No mathematical expression for x(t). Problem 2: A message signal x(t), is illustrated in the graphs...
No mathematical expression for x(t).
Problem 2: A message signal x(t), is illustrated in the graphs below x(t) 1.5 1 0.5 -1 3 -0.5 1 -1.5 Time (s) 2 1 -45 -30 -15 0 15 Frequency (kHz) This signal is applied to a Narrow Band FM generator as shown below; x(t) Ф. (t) NBFM 5.60 MHz. anda frequency deviation The NBFM Signal p(t) has a center frequency f Afi 2.4 kHz - A. Sketch the time-domain signal p1(t) using the...
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...
Problem 2: For each of the following functions find
f'(x)
Problem 2 (20 points): For each of the following functions, find f'(x) and simplify if possible. (Show necessary details.) (a) s tant dt (b) Socos * V1 – tdt (0) Bent Int dt
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions. (c) Evaluate the gain and phase (in degrees) of H(f) at 0.2 Hz from each expression.
3. Consider the signal h(t) -2u(t) +4u(t-2) 6u(t-6) (a) Sketch h(t). (b) Find H(f) in terms of sinc functions in three different ways to get three different expressions.
(c) Evaluate the gain and phase (in degrees)...
need help with these questions as soon as possible
PROBLEM 3: Simplify the following expressions (to review the properties of the unit impulse): a. f(t 5)6(t -5) etn dt PROBLEM 4: Mathematical Review Problem 1.54(a, b, d) PROBLEM 5: a) Consider the signal t) defined below 0, t<0 n(t) = t<2 t, 0, 1 t2 2 Write a single equation for xi(t) using the unit step function (i.e. do not use bracket notation). b) Sketch the signal z2(t) = u(t...
ECE3204 F19 HW-3 Due: Wed. 10/2/2019 3 Problem 1: Find and sketch c(t) = f(t)* 12(t) for the pairs of functions illustrated below 2₂ (1) ECE3204 F19 HW-3 Due: Wed. 10/2/ Problem 3: By direct integration find the Laplace transform of the signal x(t) given by: cos(1) 0<t< x(1) = 10 elsewhere Note that cos(t) = (alt+e)
1. Use combinations of STEP FUNCTIONS to describe each continuous-time signal shown below. f(t) 0 2 4 6 0 1 2 3 0 1 2 3 4 2. Sketch the following signals: (a) x (t)=1 [u(t+2)-u(t-1)] (c) X(t)=\fety (b) X(t)=t.e (d) x (t) = u(t) u(t-1).ult-2).u(t-3) 3. Determine whether the systems below are linear and time invariant. Justify your answer! (a) y(t) = x(31) (b) y(t)= 2x(1-t) y(t)=cos(x(t)] 4. Simplify the expressions: (a) y(t)=1.8(t+2)+(t +1) 8(1-1)+(t+3). 8(t) (b) y(t) =...
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series coefficients Dn. Show that the power P of f(t) is This is Parseval's theorem for the exponential Fourier series. 2. (12 points) If f(t) is real-valued, Parseval's theorem can be as a) (3 points) Find the power of the PWM signal shown in figure 1. Hint: for this part don't use Parseval's theorem b) (9 points) Use Parseval's theorem for a real-valued signal to...
Problem 2: For the signal g(t) t, a) (25 points) Find the exponential Fourier series to represent g(t) over the interval (-π, π). Sketch the spectra (amplitude and phase of Fourier series coefficients). b) (25 points) Find the average power of g(t) within interval (- ,r). Using this result and given that Σ00.-6, verify the Parseval's theorem
Laplace Transform
Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace Transform table 9.2 find the bilinear Laplace transform, F($) and sketch the region of convergence (ROC) in the s-plane showing all poles. State the ROC as an inequality. b) Another function is added so that fa(t) = 4e-2tu(t) + 7u(-t) – 10e-10t u(-t). Find the Bilinear Laplace Transform of fa(t) and sketch the region of convergence in s-plane also showing all the poles. State...
No mathematical expression for x(t).
Problem 2: A message signal x(t), is illustrated in the graphs below x(t) 1.5 1 0.5 -1 3 -0.5 1 -1.5 Time (s) 2 1 -45 -30 -15 0 15 Frequency (kHz) This signal is applied to a Narrow Band FM generator as shown below; x(t) Ф. (t) NBFM 5.60 MHz. anda frequency deviation The NBFM Signal p(t) has a center frequency f Afi 2.4 kHz - A. Sketch the time-domain signal p1(t) using the...
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