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...
Suppose that r(l) is a band-limited signal with the bandwidth W. Suppose that we sampled this signal with the sainpling interval T, to generate the sample sequence 1 TLI suppose that 2n/T is larger than the Nyquist rate 2W Given rn, we reconstructed a conius time signal ( using the zero-order-hold method. In other words, rr(l) n for L E [nT, (n +1)T;). In the last lecture, we derived that where s(), as usual, denotes the continuous time representation of...
A signal x(t) given by: x(t) = 5cos(200mt-t/3) It is sampled at a frequency of 1000 samples/s. a. Write the discrete-time signal x[n] b. Is this signal over or under sampled? Can this signal be reconstructed? c. Write expressions for all possible aliases d. Find the first 5 aliases (all types) and write the corresponding discrete- time signals x[n]
Using QAM we wish to transmit the following baseband message signals Bcos (w t a) Show the time and frequency domain expression for the transmitted signal. Also, plot the magnitude of the frequency domain representation of the signal. b) On the receiver end, we demodulate the received signal by multiplying with 2cos(Wet +Au). Derive the expression of the demodulated signal in the time domain, before low-pass filtering. c) Derive the Fourier Transform of the demodulated signal. Using QAM we wish...
A student (A) who hasn't studied the sampling theorem properly, sampled the following signal at 200 rad/sec. The student then provided the discrete time signal to another student (B - who knows the sampling theorem and signal reconstruction very well) telling them that the signal was sampled at 200 rad/sec. (t) 3cos(500Tt) +2cos(100mt) a) Derive the discrete time signal that student A created in its most simplified form. b) Explain how student B can try to recover a continuous signal...
please can discuss how you solve it For a continuous-time band-limited signal, x(t) = cos (4000nt) compute Nyquist sampling rate, 125. Also compute first 10 samples of the sampled signal, x (nts), for n > 0, that is, n 0 1 2 3 4 5 6 7 8 9 x(nts) Re-compute first 10 samples of the sampled signal, x(nts), for n > 0, that is, 0 2 3 4 8 9 x(nts) n 1 5 6 7 if x(t) is...
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...
1. An analog signal \(\mathrm{x}(\mathrm{t})\) contains frequencies from 0 up to \(10 \mathrm{kHz}\). You can assume any arbitrary spectrum for this signal. (Note that this signals also has frequencies from 0 to \(-10 \mathrm{KHz} .)\) a) Draw the frequency spectrum of the signal after it has been sampled with a sampling frequency \(\mathrm{F}_{\mathrm{s}}=25 \mathrm{kHz}\) b) What range of sampling frequencies allows exact reconstruction of this signal from its samples? c) How is the original signal reconstructed from the sampled signal?...
Consider the function r (t)7sin (11π) A discrete-time signal is produced by sampling x (t) at a rate f, to give x [n] Acos (aon + φ) Determine values for A, a, and φ, and determine whether the signal has been over-sampled or under-sampled, when a) fs10 Hz b) f 5 Hz
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...
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1. Sketch the Fourier transform Xr(jw) of x[n] for T-to. 2. Can x(t) be recovered for T? How? What is the maximum value of T so that r(t) can be recovered? 10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1....