Given the signal x(t) = 3 + 2 cos(15πt) + 3cos(20πt)
Find the fundamental period
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Given the signal x(t) = 3 + 2 cos(15πt) + 3cos(20πt) Find the fundamental period
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)
The Signal x(t)= e^(j*(3pi/2)*t)*cos((5pi/2)*t)+j*sin(pi*t) i) show that x(t) is periodic and what is the fundamental period? ii) What is the average value and power of x(t)?
2: (a) Consider a discrete-time sequence x[n] = cos(n+3). Find the fundamental period(N). (b) Consider the sinusodal signal x(t) = 10 sin(21 Fot) with analog frequency F. Write an equa- tion for the discrete time signal n. (c) In part(b) if Fe = 400Hz and the sampling frequency F. = 4kHz, determine the fundamen- tal period of x[n].
Problem 1. x(t) = 2 cos(210.8t) + 3cos(270.2t) 1) Sketch x(t) for 0<t<2 2) Find the Fourier Series coefficients for x(t)
) + 4 sin(300m), w a) (2 points) Given the signal x(t) = 5 cos(200 period, T, is needed to avoid aliasing? 3. b) (8 points) If you sample x() with sampling period T/2 where T is your answer to part a), what is the resulting discrete signal, x[n]?
Find all solutions of the following: cos(2x)+3cos(x)=-2
cos(2x) + 3 cos(x) = -2 9. Find all solutions of the following:
GIven the signal s(t)- 3cos(2T30t1.5708) +4cos(2T210t 0.523599) find the Fourier series coefficients of the exponential representation Find the fundamental frequency radians Wo Give the indices and the values (polar representation) of the nonzero coefficients, starting with the most negative index and proceeding to the most positive index. For example if indices n = ±3 and n-±7 are the only nonzero terms, the order is-Z-3, 3, 7 S(n)l- S(n)l S(n) S(n)l ZS(n) - LS (n)- ZS(n) - LS (n)- radians radians...
A signal is of the form f(t) = 2 cos(2πt) + 3cos(10πt). It is desired to filter out the higher frequency in the signal using a low-pass filter constructed using a resistance R and a capacitor C =10 μF. What is the value of the resistance R that will attenuate the higher frequency signal to 10% of its original value? What is the corresponding alteration to the low frequency signal?
5. Find the fundamental period and fundamental frequency of the following function: 8(t) = cos(2.74) + sin(3/t) + cos(571 – 31/A)
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist frequency (sampling frequency) which guarantees That x() can be recovered from it's sampled version xIn] with no aliasing. B.(10 pts) If the sampling period of Ts 0.4 see is used identify all discrete frequencies Of the signal x(t), also indicate if this sampling period is adequate to recover x(t) from xn] C.(10 pts) Suppose signal x(t) is modulated by signal e(t) = cos(2000mt) what...