Consider the function r (t)7sin (11π) A discrete-time signal is produced by sampling x (t) at...
The question was let x(t)=7sin(11*pi*t). in each of the following parts, the discrete time signal x[n] is obtained by sampling x(t) at a rate fs, and the resultant x[n] can be written as x[n]=Acos(wo*n+phi). (d) What is the continuous-time period of x(t)? What is the discrete-time period after x(t) has been sampled at fs = 15 samples/s?
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...
Please explain why. Thank you. (5%) The following signals r t) is sanpled periodically to obtained the discrete-time signal [n. For each of the given sampling rates in F, Hz or in T period, (i) determine the spectrum x(eM) of x[n]; (ii) plot its magnitude and phase as a function of w in and as a function of sampling frequency Fs in HZ; and (iii explain whether e(t) can be recovered from rn] (a) re(t) 8 +12e-3207e-j0(+), with sampling rate...
Consider the continous time signal x(t) - u(t) where u(t) is the unit step, sampled at a sampling period Ts- 1/4 to produce a discrete time signal rn] (a) Plot the signal r[n] over an appropriate interval (b) Compute and plot the short term energy for 10 successive blocks using a rectangular window of width 4 (c) Compute and plot the Zero Crossing Rate for 10 successive blocks using a rectangular window of width 4 Consider the continous time signal...
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]...
Signal xo(t) 5 cos (200π1+ 품 ) + 4 sin (300π) is sampled at a rate of Fs = 1 kHz to obtain the discrete-time signal x[n]. (a) Determine the spectrum X(ej ) of x[n] and plot its magnitude as a function of ω rad sam in tad and as a function of F in Hz. Explain whether the original signal xe(t) can be recovered from xln]. (b) Repeat part (a) for 500 Hz. (c) Repeat part (a) for 100...
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) 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...
(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...