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11. Giving the following periodic signal of period T-4, (answer by inspection) x(t) 2 6 -1...
Let x(t) a periodic signal with period To such that x(t)-sin(coot) for。st for To/2 s t...
Let x(t) a periodic signal with period To such that x(t)-sin(coot) for。st for To/2 s t s To. To2 and x(t)-0 a) Plot x(t) b) Expand x(t) in trigonometric Fourier series (sine/cosine). c) Calculate the average power of x().
2) The exponential Fourier series of a periodic signal x(t) is given as x(t) = (4...
2) The exponential Fourier series of a periodic signal x(t) is given as x(t) = (4 + j3)e-j6t + j3e-j4t + 2 - j3ej4t + (4 - j3) jót a) What is the fundamental frequency? b) By inspection write the signal x(t) in a compact trigonometric form. c) Find the power of the signal.
6.3.6 Figure P6.3-6 shows the trigonometric Fourier spectra of a periodic signal x(t) a. By inspe...
6.3.6 Figure P6.3-6 shows the trigonometric Fourier spectra of a periodic signal x(t) a. By inspection of Fig. P6.3-6, find the trigonometric Fourier series representing x(t) D. By spectien of Eig P636 ketcir tne exponential Eourier spectra of x(t). Egunar specta obtained in part b find the expone Het Ferrer sense。「 X(t) 0, 1 2 3 4 Cn Figure P6.3-8
6.3.6 Figure P6.3-6 shows the trigonometric Fourier spectra of a periodic signal x(t) a. By inspection of Fig. P6.3-6, find...
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...
Consider the following signal that is periodic with period T=2 a) Draw a picture of this signal ...
Consider the following signal that is periodic with period T=2 a) Draw a picture of this signal for . b) For which values of t will the Fourier series provide a good approximation for this signal? Justify based on part a c) Find the complex Fourier coefficients Cn from the definition. (integrate through using a table of integrals) d) Find the real Fourier coefficients an, bn. You may use your knowledge of Cn to do this, without integrating. Alternatively, you...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
QUESTION 21 A periodic signal wic with period To-2 is shown below (note: only two pulses...
QUESTION 21 A periodic signal wic with period To-2 is shown below (note: only two pulses are shown). -T0/2 -To/4 0 To/4 T0/2 The signalhas CTFS coefficients (e. w g lven as 1/2 1 0 Using the time domain, the average power of wit) over 1 period is 1 1/2 Correct answer nat given QUESTION 22 With weglven in Question 21, consider a new signal wi(t) - 10wt 5) with FS coefficients wo o . Which is true about on?...
I need help with the following problem: Consider a periodic signal !(t), with period T, such...
I need help with the following problem:
Consider a periodic signal !(t), with period T, such that !(t) 0, 圹 From Example 2.3.1 of the class notes, the nth Fourier coefficient of r(t) is given by in012... a) Use Fourier series, and the symmetry of the sinc function, to express r(t) in terms of cosine functions. Do we also need sine functions in this representation? b) Suppase that is a signal with Fourier transform S Find and plot the Fourier...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
The periodic signal x(t) has the following Fourier Series coefficients. D" =(1+jn)". The fundamen...
The periodic signal x(t) has the following Fourier Series coefficients. D" =(1+jn)". The fundamental period of x(t) is 0.1 seconds. a. Find X(f) b. Sketch the magnitude and phase of X(f) c. How does your answer to (b) differ from what we did earlier using the FS? Why does this 3. difference occur? d. Do you expect x(t) to be real-valued? Why or why not?
The periodic signal x(t) has the following Fourier Series coefficients. D" =(1+jn)". The fundamental period...
Let x(t) a periodic signal with period To such that x(t)-sin(coot) for。st for To/2 s t s To. To2 and x(t)-0 a) Plot x(t) b) Expand x(t) in trigonometric Fourier series (sine/cosine). c) Calculate the average power of x().
2) The exponential Fourier series of a periodic signal x(t) is given as x(t) = (4 + j3)e-j6t + j3e-j4t + 2 - j3ej4t + (4 - j3) jót a) What is the fundamental frequency? b) By inspection write the signal x(t) in a compact trigonometric form. c) Find the power of the signal.
6.3.6 Figure P6.3-6 shows the trigonometric Fourier spectra of a periodic signal x(t) a. By inspection of Fig. P6.3-6, find the trigonometric Fourier series representing x(t) D. By spectien of Eig P636 ketcir tne exponential Eourier spectra of x(t). Egunar specta obtained in part b find the expone Het Ferrer sense。「 X(t) 0, 1 2 3 4 Cn Figure P6.3-8
6.3.6 Figure P6.3-6 shows the trigonometric Fourier spectra of a periodic signal x(t) a. By inspection of Fig. P6.3-6, find...
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...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
QUESTION 21 A periodic signal wic with period To-2 is shown below (note: only two pulses are shown). -T0/2 -To/4 0 To/4 T0/2 The signalhas CTFS coefficients (e. w g lven as 1/2 1 0 Using the time domain, the average power of wit) over 1 period is 1 1/2 Correct answer nat given QUESTION 22 With weglven in Question 21, consider a new signal wi(t) - 10wt 5) with FS coefficients wo o . Which is true about on?...
I need help with the following problem:
Consider a periodic signal !(t), with period T, such that !(t) 0, 圹 From Example 2.3.1 of the class notes, the nth Fourier coefficient of r(t) is given by in012... a) Use Fourier series, and the symmetry of the sinc function, to express r(t) in terms of cosine functions. Do we also need sine functions in this representation? b) Suppase that is a signal with Fourier transform S Find and plot the Fourier...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
The periodic signal x(t) has the following Fourier Series coefficients. D" =(1+jn)". The fundamental period of x(t) is 0.1 seconds. a. Find X(f) b. Sketch the magnitude and phase of X(f) c. How does your answer to (b) differ from what we did earlier using the FS? Why does this 3. difference occur? d. Do you expect x(t) to be real-valued? Why or why not?
The periodic signal x(t) has the following Fourier Series coefficients. D" =(1+jn)". The fundamental period...
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