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Problem 6 [5ptsl Find the Fourier Transform of the pulses shown below. More specifically, find the...
a) Find the Fourier Transform of the half-cosine pulse shown in Fig. 1(a). b) Then apply the time-shifting property to the result obtained in part a) to evaluate the spectrum of the half-sine pul...
a) Find the Fourier Transform of the half-cosine pulse shown in Fig. 1(a). b) Then apply the time-shifting property to the result obtained in part a) to evaluate the spectrum of the half-sine pulse shown in Fig. 1(b). c) What is the spectrum of the negative half-sine pulse shown in Fig. 1(e)? d) Find the spectrum of the single sine pulse shown in Fig. 1(d). gft T/2 -T
a) Find the Fourier Transform of the half-cosine pulse shown in Fig....
2 ANOWI 20 .202019 pd What is the spectrum of the negative half-sine pulse shown in...
2 ANOWI 20 .202019 pd What is the spectrum of the negative half-sine pulse shown in Fig. 1 e) Find the spectrum of the single sinc pulse shown in Fig. (d). Question 5 (20 points) Fourier transform X() of'n signal is shown in Fig. 2. Determine and sketch the Fourier transform of the signal x, (t) = -x(t) + x(t) cos(2000 t) + 2x(t) cos? (3000xt) Question 6 (20 points) Determine the Fourier Series expansion of the following periodic signals....
0and / is an odd function of t, find the Fourier sine sin wt d for 0<t< 1 10, (a) If f(t) = for t a 0 transfor...
0and / is an odd function of t, find the Fourier sine sin wt d for 0<t< 1 10, (a) If f(t) = for t a 0 transform of f. Deduce thato s if0<t < a. What is the value of the integral for t2 a? for 0 < t < b (b) If g(t)-{ b-t and g is an even function of t, find the Fourier 0 cosine transform of g. Deduce that foo 1-w2bw cosa t dw =...
Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier...
Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier transform of the signal x(t) shown below which consists of three rectangular pulses. (Note: this is not a periodic function.) x(t) TI Sayfa Sonu Problem 5: Use the duality property of Fourier transform to find the Fourier transform of x(t) - sinc(Wt)
Problem 1. Find the Fourier series expansion of a half-wave rectified sine wave depicted below. AS(0)...
Problem 1. Find the Fourier series expansion of a half-wave rectified sine wave depicted below. AS(0) Answer: f(t) = 1+sin at cos2nt 1 nr 15 2 Cos 4t -cost + ... 35 Problem 2. Find the Fourier series approximation of the following periodic function f(x), where the first two leading cosine and sine functions must be included. Angle sum formulas for sine / cosine functions f(x) sin(A + B) = sin A cos B + cos A sin B sin(A...
4. The Fourier transform of a rectangular pulse 1 비 r/2 0 otherwise is given by...
4. The Fourier transform of a rectangular pulse 1 비 r/2 0 otherwise is given by (a) Use pr(t) and properties of the Fourier transform to find the Fourier transform, D(w), of d(t) shown below, in terms of P(. First state the approach that you are using to find D(), then show all of the details. d(t)
Problem 3. The Fourier transform pairs of cosine and sine functions can be written as y(t)...
Problem 3. The Fourier transform pairs of cosine and sine functions can be written as y(t) = A cos 2nfot = Y(f) = 4 [86f - fo) +8(f + fo)], and y(t) = B sin 2nfot = Y(f) =-j} [8(f - fo) – 8(f + fo]. The FFT code is revised such that the resulting amplitudes in frequency domain should coincide with those in time domain after discarding the negative frequency portion of Fourier transform or the frequency domain after...
(a) Write an expression for the time-domain signal shown; (6) Find the Fourier transform of the...
(a) Write an expression for the time-domain signal shown; (6) Find the Fourier transform of the signal; (c) If this signal is passed through an ideal lowpass filter with a cutoff frequency of 1 Hz, sketch the spectrum of the filter's output, including numerical labels on vertical and horizontal axes. g(t) 2 (s) Problem completed
3 B 1. Find the third roots of 21+ Find the inverse of the Laplace transform...
3 B 1. Find the third roots of 21+ Find the inverse of the Laplace transform 2. tan" G) 3. Check the existence of the Laplace transform for the given function and hence she that -02:49 in 133+ 4 S- where LF(t)) is represent the place transform of (1) [Hint: 2 cos Acos B = (A-2).sin(A+B) + sin(A - m = sin cos sin(A + B) - Sin(A) = 0 4. Find the Fourier Sine series of f(x) <rci 5....
For the periodic signal below, find the compact trigonometric fourier series and sketch the amplitude and...
For the periodic signal below, find the compact trigonometric
fourier series and sketch the amplitude and phase spectra. If
either the sine or cosine terms are absent in the Fourier series,
explain why. Please provide a detailed solution. Thanks!
For the periodi the amplitude and phase spectra. If either the sine or cosine terms a series, explain why 6.1-1. c signal shown below, find the compact trigonometric Fourier series and sketch re absent in the Fourier b) -20
a) Find the Fourier Transform of the half-cosine pulse shown in Fig. 1(a). b) Then apply the time-shifting property to the result obtained in part a) to evaluate the spectrum of the half-sine pulse shown in Fig. 1(b). c) What is the spectrum of the negative half-sine pulse shown in Fig. 1(e)? d) Find the spectrum of the single sine pulse shown in Fig. 1(d). gft T/2 -T
a) Find the Fourier Transform of the half-cosine pulse shown in Fig....
2 ANOWI 20 .202019 pd What is the spectrum of the negative half-sine pulse shown in Fig. 1 e) Find the spectrum of the single sinc pulse shown in Fig. (d). Question 5 (20 points) Fourier transform X() of'n signal is shown in Fig. 2. Determine and sketch the Fourier transform of the signal x, (t) = -x(t) + x(t) cos(2000 t) + 2x(t) cos? (3000xt) Question 6 (20 points) Determine the Fourier Series expansion of the following periodic signals....
0and / is an odd function of t, find the Fourier sine sin wt d for 0<t< 1 10, (a) If f(t) = for t a 0 transform of f. Deduce thato s if0<t < a. What is the value of the integral for t2 a? for 0 < t < b (b) If g(t)-{ b-t and g is an even function of t, find the Fourier 0 cosine transform of g. Deduce that foo 1-w2bw cosa t dw =...
Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier transform of the signal x(t) shown below which consists of three rectangular pulses. (Note: this is not a periodic function.) x(t) TI Sayfa Sonu Problem 5: Use the duality property of Fourier transform to find the Fourier transform of x(t) - sinc(Wt)
Problem 1. Find the Fourier series expansion of a half-wave rectified sine wave depicted below. AS(0) Answer: f(t) = 1+sin at cos2nt 1 nr 15 2 Cos 4t -cost + ... 35 Problem 2. Find the Fourier series approximation of the following periodic function f(x), where the first two leading cosine and sine functions must be included. Angle sum formulas for sine / cosine functions f(x) sin(A + B) = sin A cos B + cos A sin B sin(A...
4. The Fourier transform of a rectangular pulse 1 비 r/2 0 otherwise is given by (a) Use pr(t) and properties of the Fourier transform to find the Fourier transform, D(w), of d(t) shown below, in terms of P(. First state the approach that you are using to find D(), then show all of the details. d(t)
Problem 3. The Fourier transform pairs of cosine and sine functions can be written as y(t) = A cos 2nfot = Y(f) = 4 [86f - fo) +8(f + fo)], and y(t) = B sin 2nfot = Y(f) =-j} [8(f - fo) – 8(f + fo]. The FFT code is revised such that the resulting amplitudes in frequency domain should coincide with those in time domain after discarding the negative frequency portion of Fourier transform or the frequency domain after...
(a) Write an expression for the time-domain signal shown; (6) Find the Fourier transform of the signal; (c) If this signal is passed through an ideal lowpass filter with a cutoff frequency of 1 Hz, sketch the spectrum of the filter's output, including numerical labels on vertical and horizontal axes. g(t) 2 (s) Problem completed
3 B 1. Find the third roots of 21+ Find the inverse of the Laplace transform 2. tan" G) 3. Check the existence of the Laplace transform for the given function and hence she that -02:49 in 133+ 4 S- where LF(t)) is represent the place transform of (1) [Hint: 2 cos Acos B = (A-2).sin(A+B) + sin(A - m = sin cos sin(A + B) - Sin(A) = 0 4. Find the Fourier Sine series of f(x) <rci 5....
For the periodic signal below, find the compact trigonometric
fourier series and sketch the amplitude and phase spectra. If
either the sine or cosine terms are absent in the Fourier series,
explain why. Please provide a detailed solution. Thanks!
For the periodi the amplitude and phase spectra. If either the sine or cosine terms a series, explain why 6.1-1. c signal shown below, find the compact trigonometric Fourier series and sketch re absent in the Fourier b) -20
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