Suppose that a period signal x(t) is defined by the plot below
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Suppose that a period signal x(t) is defined by the plot
below
No idea how they're...
Let a periodic signal x(t) with a fundamental frequency ??e2? have a period 4.6 (a) Plot...
Let a periodic signal x(t) with a fundamental frequency ??e2? have a period 4.6 (a) Plot x(t), and indicate its fundamental period To (b) Compute the Fourier series coefficients of x(t) using their integral (c) (d) Answers: x(t) is periodic of fundamental period definition. Use the Laplace transform to compute the Fourier series coefficients Xk. Indicate how to compute the dc term. Suppose that y(t) = dx(t)/dt, find the Fourier transform of x(t) by means of the Fourier series coefficients...
A periodic signal, x(t) is shown below. A = 10, T-4 sec. -T Write a MATLAB script to plot the sig...
A periodic signal, x(t) is shown below. A = 10, T-4 sec. -T Write a MATLAB script to plot the signal, using enough points to get a smooth curve. Compute the Fourier series coefficients for the signal (if you can find them in the text, that is ok). Plot the single-sided or double-sided spectra for each signal. Include enough frequencies in the plots to adequately represent the frequency content of the signals. Plot partial sums of the Fourier series for...
A square wave of amplitude A and period T can be defined as -A, 5<t<0, with...
A square wave of amplitude A and period T can be defined as -A, 5<t<0, with f(t) = f(t + T), since the function is periodic. Compute the Fourier series for the function in the form f(t) = aneinwot, n=- where wo = 21/T and the coefficients an are the complex Fourier coefficients. Show all your work. Make a simple sketch of the signal and its series. The FIR filter is defined by the filter coefficients bk = [3,-1,2,1] Write...
1. We have a signal, x (t), with period of T - 2 second with the signal in one period given below: x(t)- ^x,(t+nT) wher...
1. We have a signal, x (t), with period of T - 2 second with the signal in one period given below: x(t)- ^x,(t+nT) wherex,) 1-2 (t - ) Kt<1 n=-oo 0 1/2 (a) Find the Fourier series coefficients for this signal. That is, find the values of ak so that x (t) Hint: te-jwt teJwt dt (b) Write some MATLAB code which will plot the signal resulting from a truncated Fourier Series using the coefficients you calculated in part...
3.59. (a) Suppose x[n] is a periodic signal with period N. Show that the Fourier series coefficie...
please
3.59. (a) Suppose x[n] is a periodic signal with period N. Show that the Fourier series coefficients of the periodic signal are periodic with period N. (b) Suppose that x() is a periodic signal with period T and Fourier series coeffi cients a with period N. Show that there must exist a periodic sequence g[n] such that (c) Can a continuous periodic signal have periodic Fourier coefficients?
3.59. (a) Suppose x[n] is a periodic signal with period N. Show...
Section 2.1 I. Suppose 2(t) if 4<t 5 otherwise Determine the absolute time duration of this signal and plot it. 2. Suppose rn]-1 if n 23 otherwise Classify this signal as left-sided, right-sided,...
Section 2.1 I. Suppose 2(t) if 4<t 5 otherwise Determine the absolute time duration of this signal and plot it. 2. Suppose rn]-1 if n 23 otherwise Classify this signal as left-sided, right-sided, two-sided, or time-limited and plot it. Section 2.2 3. Suppose r(t) is as given in Problem 1. Plot and give an expression for y(t) - (^ + ^t). Also determine the turn-on and turn-off times for y(t) 4. Suppose a[n] is as given in Problem 2. Plot...
3. Let the following periodic signal : x(t) = m+0 8(t -- 3m) + 8(t-1-3m) +...
3. Let the following periodic signal : x(t) = m+0 8(t -- 3m) + 8(t-1-3m) + 8(t – 2 – 3m) be the input to a LTI system with a system function: H(s) = es/4 – e-s/4, Let by represent the Fourier series coefficients of the resulting output signal y(t). Determine bk. (5 points)
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...
2. If x(t) is a real periodic signal with fundamental period T and Fourier series coefficients...
2. If x(t) is a real periodic signal with fundamental period T and Fourier series coefficients ak, show that if r(t) is even, then its Fourier series coefficients must be real and even. [10 points]
d) [10] The figure below shows the Fourier series coefficients ak of the DT periodic signal...
d) [10] The figure below shows the Fourier series coefficients ak of the DT periodic signal x[n]. i. ii. [5] Use Parseval's relation to determine the average power of x[n]. [5] Let bx be the Fourier series coefficients of a DT signal y[n). Without computing x[n], determine bk in terms of ak if y[n] is related to x[n] by y[n] = ejinx[n] Plot bk for k=0,1,2, ... 7. ak 16
A periodic signal, x(t) is shown below. A = 10, T-4 sec. -T Write a MATLAB script to plot the signal, using enough points to get a smooth curve. Compute the Fourier series coefficients for the signal (if you can find them in the text, that is ok). Plot the single-sided or double-sided spectra for each signal. Include enough frequencies in the plots to adequately represent the frequency content of the signals. Plot partial sums of the Fourier series for...
A square wave of amplitude A and period T can be defined as -A, 5<t<0, with f(t) = f(t + T), since the function is periodic. Compute the Fourier series for the function in the form f(t) = aneinwot, n=- where wo = 21/T and the coefficients an are the complex Fourier coefficients. Show all your work. Make a simple sketch of the signal and its series. The FIR filter is defined by the filter coefficients bk = [3,-1,2,1] Write...
1. We have a signal, x (t), with period of T - 2 second with the signal in one period given below: x(t)- ^x,(t+nT) wherex,) 1-2 (t - ) Kt<1 n=-oo 0 1/2 (a) Find the Fourier series coefficients for this signal. That is, find the values of ak so that x (t) Hint: te-jwt teJwt dt (b) Write some MATLAB code which will plot the signal resulting from a truncated Fourier Series using the coefficients you calculated in part...
please
3.59. (a) Suppose x[n] is a periodic signal with period N. Show that the Fourier series coefficients of the periodic signal are periodic with period N. (b) Suppose that x() is a periodic signal with period T and Fourier series coeffi cients a with period N. Show that there must exist a periodic sequence g[n] such that (c) Can a continuous periodic signal have periodic Fourier coefficients?
3.59. (a) Suppose x[n] is a periodic signal with period N. Show...
Section 2.1 I. Suppose 2(t) if 4<t 5 otherwise Determine the absolute time duration of this signal and plot it. 2. Suppose rn]-1 if n 23 otherwise Classify this signal as left-sided, right-sided, two-sided, or time-limited and plot it. Section 2.2 3. Suppose r(t) is as given in Problem 1. Plot and give an expression for y(t) - (^ + ^t). Also determine the turn-on and turn-off times for y(t) 4. Suppose a[n] is as given in Problem 2. Plot...
3. Let the following periodic signal : x(t) = m+0 8(t -- 3m) + 8(t-1-3m) + 8(t – 2 – 3m) be the input to a LTI system with a system function: H(s) = es/4 – e-s/4, Let by represent the Fourier series coefficients of the resulting output signal y(t). Determine bk. (5 points)
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...
2. If x(t) is a real periodic signal with fundamental period T and Fourier series coefficients ak, show that if r(t) is even, then its Fourier series coefficients must be real and even. [10 points]
d) [10] The figure below shows the Fourier series coefficients ak of the DT periodic signal x[n]. i. ii. [5] Use Parseval's relation to determine the average power of x[n]. [5] Let bx be the Fourier series coefficients of a DT signal y[n). Without computing x[n], determine bk in terms of ak if y[n] is related to x[n] by y[n] = ejinx[n] Plot bk for k=0,1,2, ... 7. ak 16
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