3 Determine the :-transforms and sketch thc ROC of the following signals ()". n20 (G)-", n< 0 (a) x(n) = – 2". u20 (b) xşta) = {E" (b) x2(n) %3D 0, n < 0 (c) 13(n) = x1(n+ 4) %3D
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- A discrete time signal x[n]= {4,4,0,2} is applied to a 4-bit microprocessor to compute the frequency domain sequence which is periodic and discrete in nature. Assume the microprocessor computes the frequency coefficients in a fast and efficient manner than the conventional method.A continuous time signal, x(t) = sin(20πt) + cos(40πt), is sampled uniformly at intervals of T to obtaina discrete time signal,x(n) = sin(πn/5) + cos(2πn/5).a) What is the value of T assuming no aliasing has occurred?b) Assume both frequency components have been aliased. In this case, is your choice of T unique? If not,specify some choices of T consistent with the information givenMessage mark; m (t) = cos (100πt), carrier sign; c (t) = 100cos (500πt), frequency modulation It is modulated with. Modulation index (B) = 3. Express the modular signal in the time domain (the Bessel function expression is sufficient). Also Bessel If you open this expression up to the 6th harmonic of the function, the power of the modulated signal you count the amount of slice.
- The message signal to be transmitted is f(t) = 10cos(2π1000t) + 5cos(2π2500t) + 8cos(2π5000t), carrier signal fc(t)= cos(2π10000t) with fTYB(t) = f(t) f(c) + f''(t) f''c(t) It is transmitted by modulating. f''(t) denotes the hilbert function. a) Find the time domain and frequency domain representation fTYB (t) and FTYB (t) of the modular signal. b) Draw the Frequency Spectrum.a. Show that 2-D discrete Fourier Transform of a M × N digital image is periodic.That is, you must prove that F(u + M, v + N) = F(u, v). b. Suggest two methods to bring the frequency origin of a discrete Fourier Transform of an image to the center ofthe 2-D array of frequency plane.A single-sideband (SSB) amplitude modulated signal is generated by modulating a carrier signal with frequency 10 kHz and amplitude 4 V. If the message signal is,m(t )= 2cos (4000πt+π/3)+ sin (2000πt+π/3). a) Find the Hilbert transform of message signal represented by mˆ(t).b) Determine the (time-domain) expression for the lower sideband of the SSB-AM signal.c) Determine and plot the magnitude spectrum (frequency) of the lower sideband SSB-AM signal.
- expressed by P(??Ω), G(??Ω), K(??Ω)Find the Fourier transform (DTFT) of the signals p [n], g [n] and k [n].The conventional amplitude modulated signal is in the time domain; m(t) message sign, Ac carrier the amplitude of the signal and fc the frequency of the carrier signal in the form below. What we did in our laboratory with a sinusoidal message signal with a single tone (that is, a single frequency component) The modulated signal time we obtained as a result of the traditional amplitude modulation experiment in the domain Qm (t)= 0.5cos (1800πt)+ 2cos (2000πt)+ 0.5 cos(2200πt) a) Draw the spectrum of the modulated signal in the frequency domain. In the modulated signal Show the lower sideband and the upper sideband. Sideband frequencies with carrier signal specify. b) Determine the message sign in the time domain m(t) and the carrier sign in the time domain c(t). These signs Write the Fourier transform and plot it in the frequency domain. c) Draw the modulated sign in the time domain. find the Modulation index (μ) . d) Interpret by determining the ratio of the power in the sidebands to…a. Which of the following is true? The Fourier transform of a unit rectangular pulse is A. real. B. not oscillating. C. complex. D. neither real nor complex. b. Which of the following is true? For system and signal operations, the symbol “*” is typically shared between A. convolution and complex conjugate. B. linear combination and complex conjugate. C. orthogonality and complex conjugate. D. multiplication and complex conjugate. c. Which of the following is true? The Fourier transform is based on A. The Fourier series by substituting the signal x(t) into Fourier coefficient’s expression. B. The Fourier series by substituting the Fourier coefficient’s expression into a random signal which is periodic over a defined period. C. The Fourier series by substituting the Fourier coefficient’s expression into x(t). D. The Fourier series because this is a logical process.
- Explain the duality between the discrete and continuous domains in signal processing. How does the Fourier transform illustrate this duality?Suppose that we have the LTI system defined by the differential/integralequations given below, where x(t) and y(t) denote the system input andoutput, respectively. Find the frequency response ?(jw) and the impulseresponse (h(t)) of the system. ******Only use Fourier Transform properties for the solution, the othersolutions will not be considered.Q2. What is the physical significance of Fourier transform of δ(t) becoming 1 and why does it results in a real number?