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(0) 3x10 2104 (b) The Figures (a) and (b) above show the Fourier spectra of signals...
(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...
CHAPTER 2-FOURIER TRANSFORMS (30) The table shows a sequence of signals or operations (rows A to...
CHAPTER 2-FOURIER TRANSFORMS (30) The table shows a sequence of signals or operations (rows A to E) in the time 1. domain. Note the symbols for multiplication X and convolution a. Draw the signals and the results in the time and frequency domains b. Draw to scale. Label and tick-mark all the graphs. c. Justify. Use the last column to back up your answer SIGNALS AND OPS FREQUENCY EXPLANATION (AMPLITUDE) TIME MATH Sine wave A Period T Pulse width 4×T...
Using the electrical engineering Fourier notation convention for time and angular frequency, show that sinwT 2...
Using the electrical engineering Fourier notation convention for time and angular frequency, show that sinwT 2 t rect 2T FT(w) ω and that sinQt ω rect 202 fra() Fra(w) πί Sketch the time domain situation for the case when the spectral entry is for a single frequency (here denoted with f), ö(f - fu0er) upper and the sampling is at the Nyquist frequency, fsample 2f upper Do you see a problem? Check out "bandpass sampling" and explain what it is....
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each sign...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)]
2) (Fourier Transforms Using Properties)...
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum...
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the sampled signal if the sampling rate is 25% higher than the Nyquist rate. a.) ft)sinc E 2T 10 b.) h)=sinc 2T For all the following, use ft) given in part a.) c.) glt)= f(l-7) d.) c(t)- f)cos() 1 e.) x(t)= fit)+ _ sinc (t
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the...
e) Given that Fourier series can be written in the form of x)A4,Cosn+B, sn), determine i)...
e) Given that Fourier series can be written in the form of x)A4,Cosn+B, sn), determine i) An (ii) Fourier series representation of x 4 marks] 3 marks Question 6 (20 marks) continuous time signal is represented by: x)-2cos 200a +sin 300 a) Explain the flow of converting a continuous time signal into a discrete time signal. (b) Determine the Nyquist frequency of the signal xtt). 3 marks] 3 marks] Explain why the minimum sampling frequency must be at least twice...
Find and plot the Fourier transforms of the following signals. (if the Fourier transform is a...
Find and plot the Fourier transforms of the following signals. (if the Fourier transform is a complex function, plot the magnitude absolute value) and phase (argument) parts separately) [70 points]. [Hint: You can use the time shifting property if applicable] 5, 0 <ts3 Xs(t)-〈0, otherwise
4. (a) Use the convolution theorem to show that otherwise (b) Let a > 0. Use the Fourier transfor...
4. (a) Use the convolution theorem to show that otherwise (b) Let a > 0. Use the Fourier transforms of sincx and sin(), together with the basic tools of Fourier transform theory to show the following sin as /sin as
4. (a) Use the convolution theorem to show that otherwise (b) Let a > 0. Use the Fourier transforms of sincx and sin(), together with the basic tools of Fourier transform theory to show the following sin as /sin as
3.11-For each of the following signals compute the complex exponential Fourier series by using tr...
3.11-For each of the following signals compute the complex exponential Fourier series by using trigonometric identities,and then sketch the amplitude and phase spectra for all values of k (a) x(t)-cos(5t-π/4) (b) x(t) sint+ cos t 756 Chapter & The Series and fourier Translorm 023 4 5 ibi FIGURE Pa P33 3.13 Problems 157 in 0 14 12 3 I) ain FIGURE ,3.3 (antísndj (c) sti)-cos(1-1) + sin(,-%) 3.12. Determine the exponential Fourier series tor the Following periodic signals
3.11-For each...
Question 3 (25pts]: Determine the Fourier transforms of the following signals and plot their coresponding magnitude...
Question 3 (25pts]: Determine the Fourier transforms of the following signals and plot their coresponding magnitude spectra. a) Spts] x(t) = cos(3t) u(t). b) [8pts] x(t) = u(t + 2) – u(t – 2). c) 19pts] x(f) = e(1+ j20#)u(t).
(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...
CHAPTER 2-FOURIER TRANSFORMS (30) The table shows a sequence of signals or operations (rows A to E) in the time 1. domain. Note the symbols for multiplication X and convolution a. Draw the signals and the results in the time and frequency domains b. Draw to scale. Label and tick-mark all the graphs. c. Justify. Use the last column to back up your answer SIGNALS AND OPS FREQUENCY EXPLANATION (AMPLITUDE) TIME MATH Sine wave A Period T Pulse width 4×T...
Using the electrical engineering Fourier notation convention for time and angular frequency, show that sinwT 2 t rect 2T FT(w) ω and that sinQt ω rect 202 fra() Fra(w) πί Sketch the time domain situation for the case when the spectral entry is for a single frequency (here denoted with f), ö(f - fu0er) upper and the sampling is at the Nyquist frequency, fsample 2f upper Do you see a problem? Check out "bandpass sampling" and explain what it is....
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)]
2) (Fourier Transforms Using Properties)...
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the sampled signal if the sampling rate is 25% higher than the Nyquist rate. a.) ft)sinc E 2T 10 b.) h)=sinc 2T For all the following, use ft) given in part a.) c.) glt)= f(l-7) d.) c(t)- f)cos() 1 e.) x(t)= fit)+ _ sinc (t
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the...
e) Given that Fourier series can be written in the form of x)A4,Cosn+B, sn), determine i) An (ii) Fourier series representation of x 4 marks] 3 marks Question 6 (20 marks) continuous time signal is represented by: x)-2cos 200a +sin 300 a) Explain the flow of converting a continuous time signal into a discrete time signal. (b) Determine the Nyquist frequency of the signal xtt). 3 marks] 3 marks] Explain why the minimum sampling frequency must be at least twice...
Find and plot the Fourier transforms of the following signals. (if the Fourier transform is a complex function, plot the magnitude absolute value) and phase (argument) parts separately) [70 points]. [Hint: You can use the time shifting property if applicable] 5, 0 <ts3 Xs(t)-〈0, otherwise
4. (a) Use the convolution theorem to show that otherwise (b) Let a > 0. Use the Fourier transforms of sincx and sin(), together with the basic tools of Fourier transform theory to show the following sin as /sin as
4. (a) Use the convolution theorem to show that otherwise (b) Let a > 0. Use the Fourier transforms of sincx and sin(), together with the basic tools of Fourier transform theory to show the following sin as /sin as
3.11-For each of the following signals compute the complex exponential Fourier series by using trigonometric identities,and then sketch the amplitude and phase spectra for all values of k (a) x(t)-cos(5t-π/4) (b) x(t) sint+ cos t 756 Chapter & The Series and fourier Translorm 023 4 5 ibi FIGURE Pa P33 3.13 Problems 157 in 0 14 12 3 I) ain FIGURE ,3.3 (antísndj (c) sti)-cos(1-1) + sin(,-%) 3.12. Determine the exponential Fourier series tor the Following periodic signals
3.11-For each...
Question 3 (25pts]: Determine the Fourier transforms of the following signals and plot their coresponding magnitude spectra. a) Spts] x(t) = cos(3t) u(t). b) [8pts] x(t) = u(t + 2) – u(t – 2). c) 19pts] x(f) = e(1+ j20#)u(t).
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