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" 2.9.2 USC volalled in Example 2.5.1. Represent the signal f(t)*= 1 -1<t< 0 0<i<1 elsewhere...
2.9.1 a) Determine the trigonometric Fourier series representation for the signal f(t) = 0 elsewhere over the interval (-1,1) b) Compare your results with those obtained in Example 2.5.1 2.0' D^-
2. Find the Fourier Series of f(T). TER,(-2,2) (1) So, -2 <r<0, 2-I, 0<I<2.
The trigonometric Fourier series of the signal f(t) derived in the lecture notes as e-a, 0 < t T, with T π was n=1 where, 16n 1-e 2 a0 = π (1-e-2), a,- 41-e 2 2 and bn - Show that, f(t) = (1-e-2) +- COSL2n n=1
4. Consider the signal co(t) = et, 0<t<1 , elsewhere Determine the Fourier transform of each of the signals shown in Figure 2. You should be able to do this by explicitly evaluating only the transform of co(t) and then using properties of the Fourier transform. X(t) X2(t) Xolt) Xp(t) -Xol-t) X3(t) Xolt +1) X4(t) Xolt) txo(t) My Lane 1 0
3. One period of a signal is given by the following equation: +1 1 0<t <3 x(t) = 3 NI+ 3 st 35 5 st 57 N Hint: Use the heaviside function in MATLAB to define x(t) for each time interval. Compute and plot for two periods the approximations of x(t) using 1. Complex Exponential Fourier Series computing 7 and 15 terms 2. Trigonometric Fourier Series computing 11 and 17 terms Note: You should get two figures at the end...
problem E
1. 20 points Consider the signal g(t) = t2 over the interval (-1,1) and it's periodic extension. (a) Find the exponential Fourier series (F.S.) for this signal. (b) Find the compact trigonometric Fourier series. (c) From the exponential F.S., plot the amplitude and phase spectrum. (d) Plot the approximated signal you obtain via the Fourier Series with (i) the DC component only; (ii) up to the first harmonic, and (iii) up to the second harmonic e) Using Parseval's...
solve it using matlab
2.7-1 (a) Sketch the signal g(t) = 12 and find the exponential Fourier series to represent 8(1) over the interval (-1, 1). Sketch the Fourier series p(i) for all values of 1.
Is (20 points) The complex exponential Fourier series of a signal xt) over 0<t<T is given as shown below. icos nas x(t)= (a) Calculate the period T (b) Determine the average value of x(1) (C) Find the amplitude of the fifth harmonic,
Problem 1 The complex exponential Fourier Series of a signal over an interval 0 < t S T,-2π/wo is known to be (d) Suppose x(t) is the input to a stable, continuous-time, single-input/single-output LTI system whose impulse response is given by 9sine (wot/4 2 cos (u) Determine the output y(t) for -oo<t<oo. Answer: y(t)-4m 2r(1 +9π (2r(1+9r2) tan 1(3m) cos 9T
Problem 1 The complex exponential Fourier Series of a signal over an interval 0
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t) +j2 exp(-j10t) +3 -j2 exp^10t)+ (2-j2) expG300t) a. Find the compact trigonometric Fourier series of f(t). b. Find the bandwidth of the signal c. Find the Fourier Transform of f(t) d. Design a simple low pass filter (RC circuit) that reduces the amplitude of the highest frequency part oft(t) by at least 50%. Write down its H(0) and plot its spectrum. e. Plot the spectrum...