5. If we a signal fAt): f(o A 0 A=1, T=2 Find the Fourier series of...
0.2 Find the Fourier seris for (periodic extension of) 1, t e [0,2): f(t) = (-1, t E [2,4). Determine the sum of this series. 2. Find the Fourier series for (periodic extension of) t 1, te[0, 2): 3-t, te[2, 4) Determine the sum of this series. 3. Find the sine Fourier series for (periodic extension of) t -1, t[o,2) , (t)- Determine the sum of this series. 4 Pind the Fosine Fourier series for (periodic extension of) 1, tE...
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...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
(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...
l, f) is a periodic signal with period f(t)-n(t)-u(t-t/2 ) for 0 2π a.) Find the exponential Fourier series of f() and sketchf). What is the fundamental radian frequency. b.) Evaluate and sketch |Dml, the magnitude of the Fourier series coefficients vs.o in the range of -4s n S4 c.) Evaluate and sketch the phase angle of D, vs. co in the same range (-4S n S4) d.) Find the signal average power e) Find the approximate average power of...
Please solve parts d and e The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t)+j2 exp(-j10t) +3 -j2 exp(j10t) + (2-j2) exp(300t) 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 of f(t) by at least 50%. Write down its H(o) and...
signal and system Find the trigonometric Fourier series coefficients for the following signal: f(t) 00 = 1 T/2 T 37/2 271
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
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...
Find the Fourier series representation of the following periodic signal. The expressions for the coefficients, Dn, and for the Fourier series representation of x(t) must not contain complex expressions (combine complex exponentials into sinusoids). 3 2.5 exp(t/2 1.5 0.5 -4