4- Plot the following signals
a. x (t) = cos 2 (3 π t)
b. x (t) = cos 2 (3 π t + π/ 2)
c. x [ n] = (− 1) n
d. x [ n] = j n (N o t e j = √ − 1)
e. x [ n] = e − a | n | (a > 0)
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Question 3 (30 points) Consider the signals defined below: *:(t) = cos(2) xz(t) = cos(4+) a) Determine the fundamental period for each signal. b) Determine the fundamental period and fundamental frequency of the signal: y(t) = x;(C)x(0) (t) and x2(c) when the fundamental frequency is c) Determine the Fourier Series coefficients of defined as determined in part (b). d) Using Parseval's relation, determine the power of xy(t) and xy(t) e) Determine and plot the Fourier Series Coefficients of y(t). Show...
Determine the Fourier transform of the following signals and plot the spectrum a. x(t) 4 sin 2T1000t b, x(t)= 4sin 2πί000t cos 2π4000t c. x(t)= (4 + cos 272000) cos 2π5000t
Supposez1 =4 cos 3 +isin 3 andz2 =2 cos 6 +isin 6 . Computez1z2. (a) 8(cos?π?+isin?π?) 22 (b) 4(cos?4π?+isin?4π?) 66 (c) 2(cos?π?+isin?π?) 66 (d) cos(π)+isin(π) (e) 8(cos?π?+isin?π?) 66 17. Suppose z1 = 4 (cos (1) + i sin (5)) and z2 = 2 (cos () + i sin (7)). Compute z122. (a) 8(cos (7) + i sin (7)) (b) 4(cos (4) + i sin (*)) (c) 2(cos (7) + i sin ()) (d) cos(T) + i sin(TT) (e) 8(cos (7)...
2. Determine the CTFT of the following signals, then plot the magnitude spectrum (a) X(t) e2lt| (b) X(t) ea u(t), a > 0 (c) X(t) e4 (d) X(t) 6(t-3) 2. Determine the CTFT of the following signals, then plot the magnitude spectrum (a) X(t) e2lt| (b) X(t) ea u(t), a > 0 (c) X(t) e4 (d) X(t) 6(t-3)
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are passed through a filter with unit impulse response h(t) so that the output is z(t)-h(t)*y(t) . Ifthe frequency response of the filter is sketch by hand the Fourier transforms Z(j for 4a-4e Fromjust observing your sketches of Z (jo), which z(1) if any in a-e equal to the original
O 3 Gitt parametriseringa ppgave 7(t) = (cos(t),sin(t), t"), te[0, π], t) - (cos(t), sin(t), t-), og funksjonen f(x, y, z) = (x2 + y2 + 4 . rekn ut kurveintegralet J, / ds O 3 Gitt parametriseringa ppgave 7(t) = (cos(t),sin(t), t"), te[0, π], t) - (cos(t), sin(t), t-), og funksjonen f(x, y, z) = (x2 + y2 + 4 . rekn ut kurveintegralet J, / ds
2. Find the CTFT for the following PERIODIC signals: a. xdt) = sin(2t + π/4)) b. Xb(t) = 2 + cos(2π/3 t) + 4sin(5π/3 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...
Define f: R2R3 b f(s,t) (sin(s) cos(t), sin(s) sin(t), cos(s)). (a) Describe and draw the image of f. (b) Proeve i.baat uts dilikur#xot.ial le. (c) Find the Jacobian matrix of f at (π/3, π/4) (d) Describe and draw the im age of Df(m/3, π/4). (e) Draw the image of Df(n/3, π/4) translated by f(n/3, π/4). (f) Describe the relationship between the image of f and the translated image of Df(T/3,/4) in nart (e Define f: R2R3 b f(s,t) (sin(s) cos(t),...
(a) The signal x(t) 3 cos (2n404 t + π/4) + cos(2n660t-n/5) is sampled at 20kHz. How many samples would be stored after 60 ms? (b) If x(t) = 4 cos(2π250t + 2n/7), what is the period of this signal? (c) For CDs, the sampling rate is 44,100 samples per second. How often (in seconds) must the ADC sample the signal? (a) The signal x(t) 3 cos (2n404 t + π/4) + cos(2n660t-n/5) is sampled at 20kHz. How many samples...