1. Find and graph the frequency domain representation of the periodic signal given below: X(+) =...
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.
please solve it fast
Determine the Time Domain Representation, alt)of the Frequency Domain signal, X[k], with the following Magnitude and Phase Spectra (The time domain signal is periodic with a period of 1 milli second) *IX[k]1 -8 -5 8 X[k] Tt/2 8 -8 -TV/2
6- A contiuous-time periodic signal x(t) is given graphically below. (a) Determine the exponential Fourier coefficients for k+oo a ()-ΣGeko, k-oo where c is given by T/2 1 (t)ek dt J-T/2 Ck= T (b) r(t) is applied as an input to an LTI system whose frequency response is H(ju)=2 sin(w Determine the corresponding output y(t) (e) Sketch y(t). Be sure to mark the axes properly -JT
6- A contiuous-time periodic signal x(t) is given graphically below. (a) Determine the exponential...
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this signal both in the time-domain and frequency domain. (b) For the following square wave v(t), determine if it is a periodic signal, and if yes, what 10 V sin 4. [61 are its amplitude, period T and fundamental frequency f? Why do we need to convert this signal into sine/cosine wave for transmission? 2 o-oims (c) () According to Fourier Theorem, the above signal...
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
Non-linear system If x1(n)=1*sin(2*pi*n*ts), x2(n)=0.5*sin(2*pi*2*n*ts) & y(n)=x(n)*x(n) What is the spectral representation of Ysum(m)? Sampling of a signal x(t)=sin(1000 t)+ sin (6280 t) What is the minimum sampling frequency? If fs=10 kHz, draw the spectrum (frequency domain) of the sampled signal
a) Derive the frequency domain representation X() of a band-limited signal r(t) that has been uniformly sampled in time to become r(n). b) Derive the expression of the reconstructed signal r(t) from the discrete time signal (n). Show all steps in detail: the sampling/reconstruction functions and processes both in the time and the frequency domain
a) Derive the frequency domain representation X() of a band-limited signal r(t) that has been uniformly sampled in time to become r(n). b) Derive the...
6- A continuous-time periodic signal r(t) is given graphically below (a) Determine the exponential Fourier coefficients c for k+oo r(t) Cet k=-oo where ck is given by T/2 x(t)ejkwotdt -T/2 Ск T (b) (t) is applied as an input to an LTI system whose frequency response is H(jw)2 sin(w) = Determine the corresponding output y(t) (c) Sketch y(t). Be re to mark the ces properly su x(t)t 0 -T
6- A continuous-time periodic signal r(t) is given graphically below (a)...
Problem 1 (10 pts). A time-domain signal x(t) is given in the figure below: - - - - - - - 9 X(t) 0 2 t, msec (a) Compute the simplest real-valued math function for the spectrum X($). (b) Plot X(f) over a Hz frequency range large enough to show all the important properties.
4. Consider the Fourier series for the periodic function given below: x(t) = 3 + 5Cost + 6 Sin(2t + /4) Find the Fourier coefficients of the combined trigonometric form for the signal.