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(a) Sketch the spectrum of the signal r(t). Show the spectrum as a function of f...
3. (50 points] Consider the signal (t= cos(27 (100)+]: 1) Let's take samples of x(t) at...
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...
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π...
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)...
A signal f(t) sinc (200 t) is sampled by periodic pulse train pr(t) resented in Fig. P5.1-6. Find and sketch the spectrum of the sampled signal. Explain if you 0.8 ms 4 ms 8 ms Fig. P5.1-6 will be ab...
A signal f(t) sinc (200 t) is sampled by periodic pulse train pr(t) resented in Fig. P5.1-6. Find and sketch the spectrum of the sampled signal. Explain if you 0.8 ms 4 ms 8 ms Fig. P5.1-6 will be able to reconstruct f(t) from these samples. If the sampled signal is passed through an ideal lowpass filter of bandwidth 100 Hz and unit gain, find the filter output. What is the filter output if its bandwidth is B Hz, where...
Problem 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t)...
Problem 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t) = Ek=-08(t - kt), where the sampling period Tg = 1ms. a) Sketch the signal w(t) and its corresponding impulse-sampled function ws(t) = w(t)s(t) b) What is the sampling frequency fs of this signal? c) Write an expression for the spectrum W (f) and the spectrum of the sampled signal Ws(f). Sketch W, (f) and specify the coordinates of its frequency components.
The signal ?(?) = cos200?? + 0.25cos700?? is sampled at the rate of 400 samples per...
The signal ?(?) = cos200?? + 0.25cos700?? is sampled at the rate of 400 samples per second. Sampled waveform is then passes through an ideal low pass filter with 200 Hz bandwidth. Write an expression for filter output. Sketch the frequency spectrum of sampled signal.
The signal x(t)=cos(2πt) is ideally sampled with a train of impulses
The signal x(t)=cos(2πt) is ideally sampled with a train of impulses. Sketch the spectrum Xδ(f) of the sampled signal, and find the reconstructed signal x(t), for the following values of sampling period Ts and ideal lowpass reconstruction filter bandwidth W': (a) Ts = 1/4, W' = 2 (b) Ts= 1, W' = 5/2(c) Ts = 2/3, W' = 2
2.5. Given an analog signal x(t)5cos(2T 2, 5001) + 2cos(2T 4, 5001), for t2 0 sampled...
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.
onsider the sampling and reconstruction system shown in the figure. x(t) IdealIdeal) D-to-C Converter Converter Assume...
onsider the sampling and reconstruction system shown in the figure. x(t) IdealIdeal) D-to-C Converter Converter Assume that the sampling rates of the C-to-D and D-to-C converters are equal, and the input to the Ideal C-to-D converter is x(t) = 2 cos (2m(50)t +π) + cos(2π(150e) a. (5) If the output of the Ideal D-to-C converter is equal to the input x(t) i.e. ()2 cos (2m(50)t +7)+cos(2(150)) b. (5) If the sampling rate is fs = 250 samples/sec, determine the discrete-time...
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate...
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate of F, and sent through a unity-gain ideal low-pass filter with the cutoff frequency at F,/2. Find and plot the Fourier transform of the reconstructed signal z(t) at filter's output if a. F=20 kHz b. Fs =800 Hz
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 sampl...
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...
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 signal f(t) sinc (200 t) is sampled by periodic pulse train pr(t) resented in Fig. P5.1-6. Find and sketch the spectrum of the sampled signal. Explain if you 0.8 ms 4 ms 8 ms Fig. P5.1-6 will be able to reconstruct f(t) from these samples. If the sampled signal is passed through an ideal lowpass filter of bandwidth 100 Hz and unit gain, find the filter output. What is the filter output if its bandwidth is B Hz, where...
Problem 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t) = Ek=-08(t - kt), where the sampling period Tg = 1ms. a) Sketch the signal w(t) and its corresponding impulse-sampled function ws(t) = w(t)s(t) b) What is the sampling frequency fs of this signal? c) Write an expression for the spectrum W (f) and the spectrum of the sampled signal Ws(f). Sketch W, (f) and specify the coordinates of its frequency components.
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.
onsider the sampling and reconstruction system shown in the figure. x(t) IdealIdeal) D-to-C Converter Converter Assume that the sampling rates of the C-to-D and D-to-C converters are equal, and the input to the Ideal C-to-D converter is x(t) = 2 cos (2m(50)t +π) + cos(2π(150e) a. (5) If the output of the Ideal D-to-C converter is equal to the input x(t) i.e. ()2 cos (2m(50)t +7)+cos(2(150)) b. (5) If the sampling rate is fs = 250 samples/sec, determine the discrete-time...
36. Sampling a low-pass signal. A signal x(t) = sin( 1,000.71) is sampled at the rate of F, and sent through a unity-gain ideal low-pass filter with the cutoff frequency at F,/2. Find and plot the Fourier transform of the reconstructed signal z(t) at filter's output if a. F=20 kHz b. Fs =800 Hz
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...
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