A signal x(t) given by: x(t) = 5cos(200mt-t/3) It is sampled at a frequency of 1000...
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...
10. Find the Fourier transform of a continuous-time signal x(t) = 10e Su(t). Plot the magnitude spectrum and the phase spectrum. If the signal is going to be sampled, what should be the minimum sampling frequency so that the aliasing error is less than 0.1 % of the maximum original magnitude at half the sampling frequency. 11. A signal x(t) = 5cos(2nt + 1/6) is sampled at every 0.2 seconds. Find the sequence obtained over the interval 0 st 3...
ints) A continuous time signal is given below: x(t) = 10 + 3 sin (20t + 3) + 5 cos(40π) This is sampled at t = 0.01 n to get a the discrete-time signal x[n], which is then applied to an ideal DAC to obtain a reconstructed continuous time signal y(t). a. i. Determine x[n] and graph its samples, using Matlab, along with the signal x(t) in one plot, plot a few cycles of x(t). ii. Determine the reconstructed signal,...
An analog signal is given as below x(t) = 10sin 4rtt The signal is sampled by two different frequencies f, = 1Hz, f, = 10Hz respectively, and the output are yı, Yz. (i) Sketch signal x(t) in the time domain. (3 marks) (ii) Sketch frequency spectrum of x(t). (3 marks) (iii) After sampling, the continuous signal is converted to a discrete signal. Draw the two discrete signals Yı, Y2: (4 marks) (iv) Discuss whether f1, f, can successfully sample the...
2.5. Given an analog signal x(t)5cos(2T 2, 5001) + 2cos(2T 4, 5001), for t2 0 sampled at a rate of 8,000 Hz, a. sketch the spectrum of the sampled signal up to 20 kHz; b. sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal; c. determine the frequneuencis f aliasing noise.
Consider a sampler which samples the continuous-time input signal x(t) at a sampling frequency fs = 8000 Hz and produces at its output a sampled discrete-time signal x$(t) = x(nTs), where To = 1/fs is the sampling period. If the sampled signal is passed through a unity-gain lowpass filter with cutoff frequency of fs/2, sketch the magnitude spectrum of the resulting signal for the following input signals: (a) x(t) = cos(6000nt). (b) x(t) = cos(12000nt). (c) x(t) = cos(18000nt).
(a) Sketch the spectrum of the signal r(t). Show the spectrum as a function of f in Hz For the rest of this problem, assume that the signal is sampled at a rate of fs 50 Hz. (b) Sketch the spectrum for the sampled signal rn). Your spectrum should be shown as a function of the normalized frequency over the interval-2π < -+2T. c) Write an equation for the sampled signal [n. (d) Suppose that the signal is reconstructed from...
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...
Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[n (1)-10cos(1000m + π/3) + 20cos(2000m + π/6). 110points! ], where x a) What is the maximum sampling interval (minimum sampling frequency) that could be used to ensure an aliasing free sampling of this signal? b) Plot the spectrum of the sampled signal if x() is sampled using a sampling frequency of (i) 2500 Hz (ii) 1800 Hz and state whether there will be an aliasing...
Problem 3 For the following signals, 345 points were sampled. a) 3.75 Hz signal sampled at 10 Hz b) 24.8 Hz signal sampled at 20 Hz c) 175 Hz signal sampled at 30 Hz Determine: i) The Nyquist frequency and whether the signal is aliased. ii) The values for Af and the uncertainty in the frequency ur (round to the nearest 0.001 Hz). If aliased, what is the aliased frequency (include a marked-up folding diagram, available on Canvas for Quiz...