A signal, given by x(t) = 2 cos(8x3.14t), is sampled at a frequency of 20 Hz,
starting at time t=0.
(a) Is the signal sampled frequently enough? Explain your answer
(b) Find the first six samples of the sequence.
(c) Given that the sampled signal is represented by x[n], how could the above
signal, delayed by three sample periods, be represented?
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
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...
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...
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).
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π . 5500t) sampled at a rate of 10,000 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 frequency/frequencies of aliasing noise . Q2)...
Non-linear system If x1(n)=1*sin(2*pi*n*ts), x2(n)=0.5*sin(2*pi*2*n*ts) & y(n)=x(n)*x(n) What is the spectral representation of Ysum(m)? Sampling of a signal x(t)=sin(1000 t)+ sin (6280 t) What is the minimum sampling frequency? If fs=10 kHz, draw the spectrum (frequency domain) of the sampled signal
(0point A sipnal st0)-S cos ( 210 m) is sampled at fi e of he signal. a Determine the numbers of samples taken in three normalized redienety sine signal stn) in term of cosine (notes: digital angular frequency c) Can signal x(t) be reconstructed ? Explain. c. (10 points) Find the inverse z transform of the following function in closed form. X(z) z +0.1z+0.16 (0point A sipnal st0)-S cos ( 210 m) is sampled at fi e of he signal....
Digital Signal Processing QUESTION SIX A digital filter system has a transfer function given by 1-0.4z-1 T(z) = 1 + 0.2z-2 a) Draw the z-domain version of the block diagram for the filter 110) Derive an expression for the output sequence yin], in terms of the input b) sequence, xla], and delayed input and output sequences 10 151 e) Find the unit sample response for the filter (first three terms only) QUESTION SIX A digital filter system has a transfer...
3. (50 points] Consider the signal (t= cos(27 (100)+]: 1) Let's take samples of x(t) at a sampling rate fs = 180 Hz. Sketch the spectrum X (f) of the sampled signal x (t). Properly label x-axis and y-axis. 2) Now suppose we will use an ideal lowpass filter of gain 1/fs with a cutoff frequency 90 Hz for the sampled signal xs(t). What is the output of the filter x,(t)? 3) Now let's take samples of x(t) at sampling...
A Digital Signal Processing system is taking at its input the following analogue signal s(t); s(t) - 20+ 20 cos(24xt)cos(xt), Where time t is expressed in ms. Part 1 - Setting the sampling frequency: (11 Marks) As a start, the system comprises only a sampler and an ideal analogue reconstructor as follows: w(t) s(t) Sampler Analogue Reconstructor s,(t) Figure a) Find the frequency spectrum S(t) of s(t) and deduce its bandwidth. You may directly use the table provided at the...
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]