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Consider the following signal with period T = 4: It ä(t) = { 14- t 0<t<2...
" 2.9.2 USC volalled in Example 2.5.1. Represent the signal f(t)*= 1 -1<t< 0 0<i<1 elsewhere...
" 2.9.2 USC volalled in Example 2.5.1. Represent the signal f(t)*= 1 -1<t< 0 0<i<1 elsewhere over the interval (-2,2). a) Use the exponential Fourier series. b) Use the trigonometric Fourier series. c) Compare your results using Eqs. (2.49)-(2.51).
4. Consider the signal co(t) = et, 0<t<1 , elsewhere Determine the Fourier transform of each...
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
A signal x(t) is defined as; 3 0 -0.2 <t < 0.2 - 1.8<t< -0.2 To...
A signal x(t) is defined as; 3 0 -0.2 <t < 0.2 - 1.8<t< -0.2 To implement Fourier Series (t)---> (ults) -1 1 0 t---> (sec) (ii) To= Wo=- Do- Dn= Sketch D vs nw.. (vi) Sketch <D, (e.) vs nw.. (vii) Power of r(t) = (viii) Express x(t) as sum of Sine Waves, Cosine waves and DC (ix) Show that the expression found in part(viii) is real
2. Find the Fourier Series of f(T). TER,(-2,2) (1) So, -2 <r<0, 2-I, 0<I<2.
2. Find the Fourier Series of f(T). TER,(-2,2) (1) So, -2 <r<0, 2-I, 0<I<2.
Consider a signal x(t) which is given as 1 x(t) - 2 <t<2 2 0, otherwise...
Consider a signal x(t) which is given as 1 x(t) - 2 <t<2 2 0, otherwise a) Sketch x(t) b) Sketch 3x(t – 1) c) Sketch – 2x(-t - 1) Identify all labels and amplitudes to get the whole score.
Problem 1 (20 pts) Suppose that x(t) = e 2 for 0 st <3 and is...
Problem 1 (20 pts) Suppose that x(t) = e 2 for 0 st <3 and is periodic with period 3. a) Determine the fundamental frequency of this signal. (2 pts) b) Determine the Fourier series representation for this signal. (7 pts) c) Suppose that this signal is the input to an LTI system with impulse response h(t) = 5sinc(0.5t). Determine the Fourier series representation for the output signal y(t). Be sure to specify the fundamental period and all Fourier series...
3. One period of a signal is given by the following equation: +1 1 0<t <3...
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...
Consider the following signal t/2+1 -2 <t<0 2(t) = {-t/2+1 0<t<2 elsewhere a) Draw x() b)...
Consider the following signal t/2+1 -2 <t<0 2(t) = {-t/2+1 0<t<2 elsewhere a) Draw x() b) Draw y(t) = +(2(1 – t)) and show all the intermediate steps in your transformation.
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
3. Consider a periodic signal c(t) with period T, = 2s (i.e. c(t) = c(t +nT)...
3. Consider a periodic signal c(t) with period T, = 2s (i.e. c(t) = c(t +nT) for any integer n), given by S-t for-1<t<0s it for 0 <t<1s This signal is input to a 256-level uniform quantizer with a dynamic range of 1.5 volts. Find the SQNR (in dB) at the quantizer output when the input is c(t). (t) =
" 2.9.2 USC volalled in Example 2.5.1. Represent the signal f(t)*= 1 -1<t< 0 0<i<1 elsewhere over the interval (-2,2). a) Use the exponential Fourier series. b) Use the trigonometric Fourier series. c) Compare your results using Eqs. (2.49)-(2.51).
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
A signal x(t) is defined as; 3 0 -0.2 <t < 0.2 - 1.8<t< -0.2 To implement Fourier Series (t)---> (ults) -1 1 0 t---> (sec) (ii) To= Wo=- Do- Dn= Sketch D vs nw.. (vi) Sketch <D, (e.) vs nw.. (vii) Power of r(t) = (viii) Express x(t) as sum of Sine Waves, Cosine waves and DC (ix) Show that the expression found in part(viii) is real
2. Find the Fourier Series of f(T). TER,(-2,2) (1) So, -2 <r<0, 2-I, 0<I<2.
Consider a signal x(t) which is given as 1 x(t) - 2 <t<2 2 0, otherwise a) Sketch x(t) b) Sketch 3x(t – 1) c) Sketch – 2x(-t - 1) Identify all labels and amplitudes to get the whole score.
Problem 1 (20 pts) Suppose that x(t) = e 2 for 0 st <3 and is periodic with period 3. a) Determine the fundamental frequency of this signal. (2 pts) b) Determine the Fourier series representation for this signal. (7 pts) c) Suppose that this signal is the input to an LTI system with impulse response h(t) = 5sinc(0.5t). Determine the Fourier series representation for the output signal y(t). Be sure to specify the fundamental period and all Fourier series...
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...
Consider the following signal t/2+1 -2 <t<0 2(t) = {-t/2+1 0<t<2 elsewhere a) Draw x() b) Draw y(t) = +(2(1 – t)) and show all the intermediate steps in your transformation.
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
3. Consider a periodic signal c(t) with period T, = 2s (i.e. c(t) = c(t +nT) for any integer n), given by S-t for-1<t<0s it for 0 <t<1s This signal is input to a 256-level uniform quantizer with a dynamic range of 1.5 volts. Find the SQNR (in dB) at the quantizer output when the input is c(t). (t) =
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