Consider the following signal. x(t) =( rect t/ T) − rect (t − T) /T − rect( t + T) T )
Draw x(t)
Calculate and plot the autocorelation of x(t).
Consider the following signal. x(t) =( rect t/ T) − rect (t − T) /T −...
Question #1 [15 points) Consider the following signal, x(t)=rect(t/50) (i) Find X(w) by definition (ii) Sketch the magnitude and phase response of X(w) (iii) Energy of x(t)= Page 1 of 2
. Problem 2: The signal (t) rect ) is first bandlimited with a low pass filter. The bandlimited 4 . If the bandlimited signal is sampled with f signal has a maximum frequency component of plot the spectrum of the sampled signal. ,
Q2 Consider a communication signal x(t) described by the following mathematical expression: x(t)=2 cos(2000) + 4 sin? (2000) – 2+4rec(t)cos(6000mt) Analyse the communication signal x(t) then consider the following: (i) Determine the Fourier transform of the signal x(t). (ii) Plot the double-sided amplitude spectrum of the signal x(t).
how to derive the underlying signal x(t) using the
definition of the Inverse Fourier transform
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Q. Find and plot the CTFT of the following signal (without using any computer simulation) x(t)cos(2t) rect (t) Explain and provide details of the steps.
7 (10pt) Signal s(t) is created by multiplying a rectangular pulse with a sinusoidal signal: s(t) A cos(2mfet) rect where rect(t) is a rectangular pulse with width 1 and amplitude 1 which occupies -0.5 to 0.5 in time domain. Please find out s(t)'s null-to-null bandwidth.
7 (10pt) Signal s(t) is created by multiplying a rectangular pulse with a sinusoidal signal: s(t) A cos(2mfet) rect where rect(t) is a rectangular pulse with width 1 and amplitude 1 which occupies -0.5 to...
3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t).
3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t).
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...
1. Consider the signal represented in Figure 1. a) Write an analytical formula to represent the signal x(t). b) Consider the signal x(t). For each of the following combinations, draw the signal and indicate its duration, extension and area: Xa(t) = x(t – 3); xo(t) = x(2t); Ic(t) = x(-3(t + 1)); Id(t) = 2x(2t) – x(t) – 2x(-(t + 4)); Le(t) = xd(t) + rect(476). c) Compute the Fourier transform of r(t). AX(t) 2 1 2 5 7 t...
1. Signal f(t) : (5 + rect( )) cos(60πt) is mixed with signal cos(60πt) to produce the signal y(t). Subsequently, COS y(t) is low-pass filtered with a system having frequency response H(w) = 4recG ) to produce q(t). Sketch F(w),Y(w), Q(u), and determine q(t) 2. If signal f(t) is not band-limited, would it be possible to reconstruct f(t) exactly from its samples f(nT) taken with some finite sampling interval T> 0? Explain your reasoning
1. Signal f(t) : (5 +...