3- a) Determine the minimum sampling rate for perfect reconstruction of the signal given by Sin(6280)...
3: (Practice Problem)Consider the representation of the process of sampling followed by reconstruction shown below oce=nt) C) Assume that the input signal is Ia(t) = 2 cos(100nt – /4) + cos(300nt + 7/3) -0<t< The frequency response of the reconstruction filter is H.(12) = {T 121</T 10 1921 > A/T (a) Determine the continuous-time Fourier transform X (12) and plot it as a function of N. (b) Assume the fs = 1/T = 500 samples/sec and plot the Fourier transform...
Question 1: (Sampling and Aliasing Effeet) (25 Marks) The given analog signal x(t)--sin(16xt)+ sin(11xt)+ sin (5nt), where t is in milliseconds, is sampled at a rate of 12kHz. The resulting samples are immediately reconstructed by an ideal reconstructor. a. Find and sketch the spectrum of x(t) versus Ω. b. Find and sketch the spectrum of the sampled signal versus o. c. Determine the analog signal x (t) at the output of the reconstructor. d. Prove the x(0) and x(t) having...
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate of F, and sent through a unity-gain ideal low-pass filter with the cutoff frequency at F,/2. Find and plot the Fourier transform of the reconstructed signal z(t) at filter's output if a. F=20 kHz b. Fs =800 Hz
e) Given that Fourier series can be written in the form of x)A4,Cosn+B, sn), determine i) An (ii) Fourier series representation of x 4 marks] 3 marks Question 6 (20 marks) continuous time signal is represented by: x)-2cos 200a +sin 300 a) Explain the flow of converting a continuous time signal into a discrete time signal. (b) Determine the Nyquist frequency of the signal xtt). 3 marks] 3 marks] Explain why the minimum sampling frequency must be at least twice...
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of the sampled signal, i.e. Xs (jo). b) Plot the DTFT of the sampled signal, ie, X(eja) o) Repeat (a) with 7, 2π d) Repeat (b) with , 18 Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n]...
3. (a) Consider the signal xc(t)-sin(2π(40)t). How fast must xe(t) be sanpled to avoid aliasing? Determine the Nyquist rate (the frequency which the sampling rate fs must exceed) for ae(t) (b) Consider processing the signal xe(t) (from part (a)) using the system shown below: Conversion to a sequence Conversion to an impulse train Ideal Reconstruction Filter Hr(ju) p (t) ур y(t) The sampling period for this system is T-1/50 seconds. The DT system H(ei2) is an ideal lowpass filter with...
) (MATLAB) Assume a sampling rate of 100 Hz. Filter the signal given by x(t) = 1 + sin(0.125zt) + 0.5 sin(0.25mt) + 0.25 sin(0.5zt) + 0.125 sin(nt) by filters of progressively lower cutoff frequencies of 50, 5, 0.5, and 0.05 Hz ) (MATLAB) Assume a sampling rate of 100 Hz. Filter the signal given by x(t) = 1 + sin(0.125zt) + 0.5 sin(0.25mt) + 0.25 sin(0.5zt) + 0.125 sin(nt) by filters of progressively lower cutoff frequencies of 50, 5,...
onsider the sampling and reconstruction system shown in the figure. x(t) IdealIdeal) D-to-C Converter Converter Assume that the sampling rates of the C-to-D and D-to-C converters are equal, and the input to the Ideal C-to-D converter is x(t) = 2 cos (2m(50)t +π) + cos(2π(150e) a. (5) If the output of the Ideal D-to-C converter is equal to the input x(t) i.e. ()2 cos (2m(50)t +7)+cos(2(150)) b. (5) If the sampling rate is fs = 250 samples/sec, determine the discrete-time...
Question 8 A continuous signal x(t) is given as Not yet answered X(t) 4 sin(21t13t) + 3 cos(21732t) – sin(2nT95t) What is the minimum sampling frequency (Nyquist Rate) that can be used to sample this continuous signal? Marked out of 1.50 P Flag question Select one: a. 190 Hz O b. 95 Hz c. 285 Hz d. 32 Hz e. 13 Hz
(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...