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a) 12 >(FT)> 24 pi s(w)
b) x(w)= 5[pi...
Question 4 For the given x(t) signal determine X(w) (Fourier Transform) X(t)= 5(2t - 1) -...
Question 4 For the given x(t) signal determine X(w) (Fourier Transform) X(t)= 5(2t - 1) - 5(2t + 1) Your answer: X(w)= j sin(w/2) X(w)= j cos(w/2) X(w)=sin(w/2) X(w)= sin(2) X(w)= cos(2w) Clear answer Back Next 19 w MacBook esc Q Search or enter website nam
Find the Fourier transform f(t) a. X(w-3) 8(+3) 3. 2cos3tx(t) with x(t)'s FT is X(a) 2X(w-3)...
Find the Fourier transform f(t) a. X(w-3) 8(+3) 3. 2cos3tx(t) with x(t)'s FT is X(a) 2X(w-3) + 2x(w + 3) ?(0-3) + ?(w + 3) c. d.
(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 bel...
(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...
Can you please help me answer Task 2.b? Please show all work. fs=44100; no_pts=8192; t=([0:no_pts-1]')/fs; y1=sin(2...
Can you please help me answer Task 2.b?
Please show all work.
fs=44100; no_pts=8192;
t=([0:no_pts-1]')/fs;
y1=sin(2*pi*1000*t);
figure;
plot(t,y1);
xlabel('t (second)')
ylabel('y(t)')
axis([0,.004,-1.2,1.2]) % constrain axis so you can actually see
the wave
sound(y1,fs); % play sound using windows driver.
%%
% Check the frequency domain signal. fr is the frequency vector and
f1 is the magnitude of F{y1}.
fr=([0:no_pts-1]')/no_pts*fs; %in Hz
fr=fr(1:no_pts/2); % single-sided spectrum
f1=abs(fft(y1)); % compute fft
f1=f1(1:no_pts/2)/fs;
%%
% F is the continuous time Fourier. (See derivation...
3. A system is excited by a signal x(t) = rect (2t) and its response is...
3. A system is excited by a signal x(t) = rect (2t) and its response is y(t) = (2 – 2e-(t+1/4))u(t +1/4) -(2 – 2e-(t-1/4))u(t – 1/4) Hint1: try to factor inside Y@) and produce (279-e3€)/2j which will be sind. Hint2: don't simplify 1ljo and 1/(jo+a) and keep them “as is” until the last step when you want to do inverse Fourier Transform to find h(t) impulse responseis h(t) h(t) FT (0) Y(0) y(t)=h(t)*x(1) FT →Y(©)=H(@)X(@)= H(o)= X() rect(t) FT...
Fourier transforms using Properties and Table 1·2(t) = tri(t), find X(w) w rect(w/uo), find x(t) 2....
Fourier transforms using Properties and Table 1·2(t) = tri(t), find X(w) w rect(w/uo), find x(t) 2. X(w) 3, x(w) = cos(w) rect(w/π), find 2(t) X(w)=2n rect(w), find 2(t) 4. 5, x(w)=u(w), find x(t) Reference Tables Constraints rect(t) δ(t) sinc(u/(2m)) elunt cos(wot) sin(wot) u(t) e-ofu(t) e-afu(t) e-at sin(wot)u(t) e-at cos(wot)u(t) Re(a) >0 Re(a) >0 and n EN n+1 n!/(a + ju) sinc(t/(2m) IIITo (t) -t2/2 2π rect(w) with 40 2r/T) 2Te x(u) = F {r) (u) aXi(u) +X2() with a E...
3.5 Determine the Laplace transform of each of the following functions by applying the properties given...
3.5 Determine the Laplace transform of each of the following functions by applying the properties given in Tables 3-1 and 3-2. (a) xi(t) = 16e-2t cos 4t u(t) (b) x2(t) = 20te-21 sin 4t u(t) (c) x3(t) = 10e-34 u(t – 4) Table 3-1: Properties of the Laplace transform for causal functions; i.e., x(t) = 0 for t < 0. Property x(t) 1. Multiplication by constant K x(t) 2. Linearity K1 xi(t) + K2 x2(t) X($) = L[x(t)] K X(s)...
(a) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the s...
(a) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the sampling frequency w used by this system? What is the equation for the output Fourier Transform X,(jw) in terms of X(jw)? ii. (5 pts) Using your equation from (i), sketch the output spectrum X, (jw) vs. w. Make sure to label all critical points iii. (5 pts) Using your sketch from (ii), determine if there is aliasing or not....
f(t) -S -8 -7 -3 --1 3 5 1 2 13 4 7 8 9 12...
f(t) -S -8 -7 -3 --1 3 5 1 2 13 4 7 8 9 12 t(ms 15 16 4. For the above periodic signal f(t), specify the symmetry (if any) and determine all coefficients as well as the value for w, so as to find the Fourier series representation of f(t) in the following forms. (24 pts) GO A. f(t) = a + ancos(not) + b sin(nw.t): B. f(t) = R-Cneinwor. n=1 Type A
4. X(c)-1 for lol < 5 and is zero elsewhere. Use the theorems to find and sketch the amplitude ve...
4. X(c)-1 for lol < 5 and is zero elsewhere. Use the theorems to find and sketch the amplitude versus ω and the phase angle versus ω of the transforms of the following signals. (a) t0, (b, (e) x(2), and (e) x() expG10) dx(t) dt' TABLEme Selected Properties of the Fourier Transform X (o) 2. 3. x(-t) X (-o) 5. x(-o) x (at) la l 8. lx ()12 dr x(t)h(C) x (t) 9. 10. 2π X (ω-@g) d"X (0) 12....
Question 4 For the given x(t) signal determine X(w) (Fourier Transform) X(t)= 5(2t - 1) - 5(2t + 1) Your answer: X(w)= j sin(w/2) X(w)= j cos(w/2) X(w)=sin(w/2) X(w)= sin(2) X(w)= cos(2w) Clear answer Back Next 19 w MacBook esc Q Search or enter website nam
Find the Fourier transform f(t) a. X(w-3) 8(+3) 3. 2cos3tx(t) with x(t)'s FT is X(a) 2X(w-3) + 2x(w + 3) ?(0-3) + ?(w + 3) c. d.
(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...
Can you please help me answer Task 2.b?
Please show all work.
fs=44100; no_pts=8192;
t=([0:no_pts-1]')/fs;
y1=sin(2*pi*1000*t);
figure;
plot(t,y1);
xlabel('t (second)')
ylabel('y(t)')
axis([0,.004,-1.2,1.2]) % constrain axis so you can actually see
the wave
sound(y1,fs); % play sound using windows driver.
%%
% Check the frequency domain signal. fr is the frequency vector and
f1 is the magnitude of F{y1}.
fr=([0:no_pts-1]')/no_pts*fs; %in Hz
fr=fr(1:no_pts/2); % single-sided spectrum
f1=abs(fft(y1)); % compute fft
f1=f1(1:no_pts/2)/fs;
%%
% F is the continuous time Fourier. (See derivation...
3. A system is excited by a signal x(t) = rect (2t) and its response is y(t) = (2 – 2e-(t+1/4))u(t +1/4) -(2 – 2e-(t-1/4))u(t – 1/4) Hint1: try to factor inside Y@) and produce (279-e3€)/2j which will be sind. Hint2: don't simplify 1ljo and 1/(jo+a) and keep them “as is” until the last step when you want to do inverse Fourier Transform to find h(t) impulse responseis h(t) h(t) FT (0) Y(0) y(t)=h(t)*x(1) FT →Y(©)=H(@)X(@)= H(o)= X() rect(t) FT...
Fourier transforms using Properties and Table 1·2(t) = tri(t), find X(w) w rect(w/uo), find x(t) 2. X(w) 3, x(w) = cos(w) rect(w/π), find 2(t) X(w)=2n rect(w), find 2(t) 4. 5, x(w)=u(w), find x(t) Reference Tables Constraints rect(t) δ(t) sinc(u/(2m)) elunt cos(wot) sin(wot) u(t) e-ofu(t) e-afu(t) e-at sin(wot)u(t) e-at cos(wot)u(t) Re(a) >0 Re(a) >0 and n EN n+1 n!/(a + ju) sinc(t/(2m) IIITo (t) -t2/2 2π rect(w) with 40 2r/T) 2Te x(u) = F {r) (u) aXi(u) +X2() with a E...
3.5 Determine the Laplace transform of each of the following functions by applying the properties given in Tables 3-1 and 3-2. (a) xi(t) = 16e-2t cos 4t u(t) (b) x2(t) = 20te-21 sin 4t u(t) (c) x3(t) = 10e-34 u(t – 4) Table 3-1: Properties of the Laplace transform for causal functions; i.e., x(t) = 0 for t < 0. Property x(t) 1. Multiplication by constant K x(t) 2. Linearity K1 xi(t) + K2 x2(t) X($) = L[x(t)] K X(s)...
(a) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the sampling frequency w used by this system? What is the equation for the output Fourier Transform X,(jw) in terms of X(jw)? ii. (5 pts) Using your equation from (i), sketch the output spectrum X, (jw) vs. w. Make sure to label all critical points iii. (5 pts) Using your sketch from (ii), determine if there is aliasing or not....
f(t) -S -8 -7 -3 --1 3 5 1 2 13 4 7 8 9 12 t(ms 15 16 4. For the above periodic signal f(t), specify the symmetry (if any) and determine all coefficients as well as the value for w, so as to find the Fourier series representation of f(t) in the following forms. (24 pts) GO A. f(t) = a + ancos(not) + b sin(nw.t): B. f(t) = R-Cneinwor. n=1 Type A
4. X(c)-1 for lol < 5 and is zero elsewhere. Use the theorems to find and sketch the amplitude versus ω and the phase angle versus ω of the transforms of the following signals. (a) t0, (b, (e) x(2), and (e) x() expG10) dx(t) dt' TABLEme Selected Properties of the Fourier Transform X (o) 2. 3. x(-t) X (-o) 5. x(-o) x (at) la l 8. lx ()12 dr x(t)h(C) x (t) 9. 10. 2π X (ω-@g) d"X (0) 12....
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