Consider the signal y(t)=5+10cos(32πt)+15cos(180πt). Determine
1.The frequencies contained in the signal
2.The minimum sampling rate to avoid aliasing
Consider the signal y(t)=5+10cos(32πt)+15cos(180πt). Determine 1.The frequencies contained in the signal 2.The minimum sampling rate to...
Consider the signal y(t) = 10cos(30ft) +15cos(80nt). c) If a sampling frequency of 30 Hz is used to sample y(t), the resulting discrete signal y(n) will also have two components, one from sampling 10 cos(30nt), the other from sampling 15cos(80ft). Calculate the frequencies of the two components in y(n) (10pts)
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...
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...
Problem A: Suppose you want to sample the signal f(t) = 100sinc(100nt). Determine the sampling rate needed to avoid aliasing. Hint: The Fourier transform of c(t) = sinca (W) is X(w) = A (W) for constant W. (This is problem 5.1-2b from the book by Lathi cited in the syllabus.)
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...
Plot the signal s(t) = cos(2πt), and then illustrate the resulting samples with the following sampling intervals: [30 points] • Ts= 0.5 sec. • Ts= 0.75 sec • Ts =1 sec. (a) For each case, also sketch the reconstructed continuous time signal from the samples using linear interpolation (i.e. connecting samples by straight lines). (b) In which case the sampled signal has aliasing distortion? What is the minimal sampling frequency and the corresponding sampling interval needed to avoid aliasing? 3....
In an effort to digitize an analog signal Y(t), we would like to select the right sampling rate for the following signal: Y (t)= 4sin(251)t + 4sin (751) a) Select the right sampling rate for this signal. b) What will happen if the sampling rate from the above answer (a), is used to sample the following signal Y= 3sin(2507). c) Discuss if Aliasing is happening for answer (b) and if yes why? What will be the observing Aliasing Frequency?
please answer all parts with explaining to study it with clear hand writing Two sinusoid signals are defined as x2 (1)-4cos (2π10t) 4(1)-2sin (16m) a) Find all the frequencies of y(r) (List only frequencies in y(i)) b) What is the minimum sampling rate to avoid aliasing in the y(t)? c) If fs 40, find a the frequencies and the corresponding magnitude values (don't worry about the phase values) (make sure it is now in the discrete time domain) d) If...
17. The following system is used to sample and reconstruct the signal x(t)-1-cos(15π) with a sampling interval T-0.1 sec. p(t) xIn] y(t) x(t) -0.5 0.5 1B 1B X.(o) X (o) [2 Marks each] Given that the input signal, x(t) -1+cos(15rt) Sketch |X(a) The sampling interval is set to T= 0, 1 ec. SketchXs(o) where x(t) = p(t)x(t). Determine the expression for y(t). Is y(t) a reconstruction of x()? Does aliasing occur? explain 17. The following system is used to sample...
3- a) Determine the minimum sampling rate for perfect reconstruction of the signal given by Sin(6280) 628 b) The Fourier transfer of signal, x(t) is given by XU)sine) find the autocorrelation function R,(e)