![(a) Determine the Fourier transform of the sequence 0, otherwise. (b) Consider the sequence win-ı弡ーcos(쮜. 2π n 0 otherwise. Sketch win] and express We), the Fourier transform of win], in terms of R (el, the Fourier transform of In]. (Hint First express win] in terms of In] and the complex exponentials el (2M) and el 2n/M)](http://img.homeworklib.com/questions/a18c0930-d165-11ea-898c-3522e7913d9a.png?x-oss-process=image/resize,w_560)
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(Using the modulation property)
(a) Determine the Fourier transform of the sequence 0, otherwise. (b) Consider...
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)
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by...
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
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...
Problem 5. (Properties of Fourier transform) Consider a continuous time signal x(1) with the following Fourier...
Problem 5. (Properties of Fourier transform) Consider a continuous time signal x(1) with the following Fourier transform: X(jw) = J 1 - if we l-207, 207] if|wl > 207 (3) Let y(t) = x(26) cos? (507). Sketch Y (w), i.e., the Fourier transform of y(t). (Note that 2 1 + cos(20) cos? (0) = 2
2. (14 points) This problem shows an example of using the Fourier transform to analyze communicat...
2. (14 points) This problem shows an example of using the Fourier transform to analyze communication systems. The system in Figure 4, where (t)-f(t)+sin(wt) and has been proposed for amplitude modulation. f(t) + sin(o) Figure 4: System proposed for amplitude modulation. (a) (7 points) The spectrum of the input f(t) is shown in Figure 1, where 2mB o/100. Sketch and label the spectrum Y(w) of the signal y(t). Hint: You will need to use the frequency convolution property of the...
-l 2. Consider the continuous-time signal: 0 x(t)- 1sts1 0, otherwise Find the Fourier transform X(a)...
-l 2. Consider the continuous-time signal: 0 x(t)- 1sts1 0, otherwise Find the Fourier transform X(a) of x(t). Simplify ths expression as much as po e simplest expression does not involve any complex numbers.) Draw a rough plot of o) as a function of w. Identify the peak value of X(w). Identify the location of the X( first null on either side of the vertical axis.
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts)...
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
Fourier transforms using Properties and Table 1·2(t) = tri(t), find X(w) w rect(w/uo), find x(t) 2....
Fourier transforms using Properties and Table 1·2(t) = tri(t), find X(w) w rect(w/uo), find x(t) 2. X(w) 3, x(w) = cos(w) rect(w/π), find 2(t) X(w)=2n rect(w), find 2(t) 4. 5, x(w)=u(w), find x(t) Reference Tables Constraints rect(t) δ(t) sinc(u/(2m)) elunt cos(wot) sin(wot) u(t) e-ofu(t) e-afu(t) e-at sin(wot)u(t) e-at cos(wot)u(t) Re(a) >0 Re(a) >0 and n EN n+1 n!/(a + ju) sinc(t/(2m) IIITo (t) -t2/2 2π rect(w) with 40 2r/T) 2Te x(u) = F {r) (u) aXi(u) +X2() with a E...
g(t) Given the signal g(t) = cos(t)), (1) Using the frequency-shifting property, find Fourier Transform G(f)in...
g(t) Given the signal g(t) = cos(t)), (1) Using the frequency-shifting property, find Fourier Transform G(f)in "sinc" format. (2) Find the Energy Spectrum Density (ESD): Sgf) = 1G(f)12 (3) Find and sketch the Autocorrelation R,(t) by Wiener-Khintchine Theorem. -210 210
1. Consider the complex-valued signal r(t) with Fourier transform as shown in the figure. Keep in...
1. Consider the complex-valued signal r(t) with Fourier transform as shown in the figure. Keep in mind that there are no symmetry properties this signal satisfies in the fre- quency domain. In particular, the Fourier transform is zero for negative frequencies Suppose we impulse-train sample x(t) at the rate of 500 samples/second. 200 400 600 800 1000 FREQUENCY (Hz.) (a) Sketch the Fourier transform of the impulse-train sampled signal in the range of frequencies from -1000 Hz. to 1000 Hz....
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)
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
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...
Problem 5. (Properties of Fourier transform) Consider a continuous time signal x(1) with the following Fourier transform: X(jw) = J 1 - if we l-207, 207] if|wl > 207 (3) Let y(t) = x(26) cos? (507). Sketch Y (w), i.e., the Fourier transform of y(t). (Note that 2 1 + cos(20) cos? (0) = 2
2. (14 points) This problem shows an example of using the Fourier transform to analyze communication systems. The system in Figure 4, where (t)-f(t)+sin(wt) and has been proposed for amplitude modulation. f(t) + sin(o) Figure 4: System proposed for amplitude modulation. (a) (7 points) The spectrum of the input f(t) is shown in Figure 1, where 2mB o/100. Sketch and label the spectrum Y(w) of the signal y(t). Hint: You will need to use the frequency convolution property of the...
-l 2. Consider the continuous-time signal: 0 x(t)- 1sts1 0, otherwise Find the Fourier transform X(a) of x(t). Simplify ths expression as much as po e simplest expression does not involve any complex numbers.) Draw a rough plot of o) as a function of w. Identify the peak value of X(w). Identify the location of the X( first null on either side of the vertical axis.
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
Fourier transforms using Properties and Table 1·2(t) = tri(t), find X(w) w rect(w/uo), find x(t) 2. X(w) 3, x(w) = cos(w) rect(w/π), find 2(t) X(w)=2n rect(w), find 2(t) 4. 5, x(w)=u(w), find x(t) Reference Tables Constraints rect(t) δ(t) sinc(u/(2m)) elunt cos(wot) sin(wot) u(t) e-ofu(t) e-afu(t) e-at sin(wot)u(t) e-at cos(wot)u(t) Re(a) >0 Re(a) >0 and n EN n+1 n!/(a + ju) sinc(t/(2m) IIITo (t) -t2/2 2π rect(w) with 40 2r/T) 2Te x(u) = F {r) (u) aXi(u) +X2() with a E...
g(t) Given the signal g(t) = cos(t)), (1) Using the frequency-shifting property, find Fourier Transform G(f)in "sinc" format. (2) Find the Energy Spectrum Density (ESD): Sgf) = 1G(f)12 (3) Find and sketch the Autocorrelation R,(t) by Wiener-Khintchine Theorem. -210 210
1. Consider the complex-valued signal r(t) with Fourier transform as shown in the figure. Keep in mind that there are no symmetry properties this signal satisfies in the fre- quency domain. In particular, the Fourier transform is zero for negative frequencies Suppose we impulse-train sample x(t) at the rate of 500 samples/second. 200 400 600 800 1000 FREQUENCY (Hz.) (a) Sketch the Fourier transform of the impulse-train sampled signal in the range of frequencies from -1000 Hz. to 1000 Hz....
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