Problem 6. (15 points.) Determine the Fourier series coefficients of the following signal c(t) = y...
Problem 6: I7 Points For the following periodic signal, x(t) 4OSesi a) Express the signal exponent +cos(9t) +2cos(15t) al in complex exponential Fourier series form. 13 r series coefficients and sketch the spectral line. [2 Find the fundamental frequency and identilY the harmonics in the signal. 12) Solution Problem 6: I7 Points For the following periodic signal, x(t) 4OSesi a) Express the signal exponent +cos(9t) +2cos(15t) al in complex exponential Fourier series form. 13 r series coefficients and sketch the...
Problem 2: For the signal g(t) t, a) (25 points) Find the exponential Fourier series to represent g(t) over the interval (-π, π). Sketch the spectra (amplitude and phase of Fourier series coefficients). b) (25 points) Find the average power of g(t) within interval (- ,r). Using this result and given that Σ00.-6, verify the Parseval's theorem
Problem 3. Determine the trigonometric Fourier series coefficients an and bn for signal a(t) sin(3t 1)2 cos(7t 2) Determine also the signal's fundamental radian frequency w. No integration is required to solve this problem.
6) If a continuous-time periodic signal has the Fourier series coefficients ak, where k = 0, +1, +2, +3,..., derive the Fourier series coefficients bk of the following signals in terms of aki a) <(-t) b) x*(t) c) x(t – t.) where t, is a constant e) (t) dt In part e), assume that the average value of x(t) is zero.
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)
Determine the trigonometric Fourier series coefficients an and bn for signal x(t) sin(3m + 1) + 2 cos(7m-2) . Determine also the signal's fundamental radian frequency wo. No integration is required to solve this cos( ( ? problem
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series coefficients Dn. Show that the power P of f(t) is This is Parseval's theorem for the exponential Fourier series. 2. (12 points) If f(t) is real-valued, Parseval's theorem can be as a) (3 points) Find the power of the PWM signal shown in figure 1. Hint: for this part don't use Parseval's theorem b) (9 points) Use Parseval's theorem for a real-valued signal to...
1. [10 Marks] Determine the Fourier series coefficients of the following signal, which is periodic in T 10. 10 -3-1 1 3 10 2. 10 Marks] Determine the Fourier transform of the following signal, which is zero outside the indicated range. -3-1 1 3
2. A continuous-time periodic signal with Fourier series coefficients c^ = and period T, 0.1sec pass through an ideal lowpass filter with cut off frequency =102.5Hz. The resulting signal y, (t) is sampled periodically with T 0.005 sec determine the spectrum of the sequence y(n) = ya(nT)
signal and system Find the trigonometric Fourier series coefficients for the following signal: f(t) 00 = 1 T/2 T 37/2 271