What are the potential problems of sampling the input signal at a sampling rate of exactly...
What are the potential problems of sampling the input signal at a sampling rate of exactly equal to the Nyquist rate?
Homework Answers
If sampling of input signal is done at nyquist rate there will not be any separation between highest frequency of signal and lowest frequency of sampled signal ie fs- fm = fm. The main potential problem faced can be explained by one example
Suppose signal y(t)=sin(2
ft) is sampled at 2f
frequency. Since all the samples are at zero crossings, we get zero
signal after sampling instead of recovering the sinusoid.
So it is recommended to sample at higher rate than nyquist rate.
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What are the potential problems of sampling the input signal at
a sampling rate of exactly...
If the input signal is a pure sinusoidal signal at a frequency exactly equal to half...
If the input signal is a pure sinusoidal signal at a frequency exactly equal to half the sampling rate, there is still a condition under which that signal can be recovered. What is it?
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(...
just looking for #2, 3, and 4
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(t) = 2 cos(2m50t) + 4cos(2m100t) a. (10 points) Determine S(f) and plot it b. (20 points) Let the sampling rate to be: fs 300 samples/sec. Plot the spectrum of the Ideal sample, that is plot S8(f) c. Let the sampling rate to be: fs 175 samples/sec. i. (30 points) Plot S8(f) ii. (10 points) Let...
19. 1 mark) What is the Nyquist sampling rate for a band-pass signal with a bandwidth...
19. 1 mark) What is the Nyquist sampling rate for a band-pass signal with a bandwidth of 300kHz if the lowest frequency is 100kHz? 20. 1 mark) In a block code, the codeword is 8 bits long. How long is the dataword if the number of valid codewords in this block are 64? How many codewords exist in total?
1. (15) By the Sampling Theorem the Nyquist sampling rate must be twice the highest bandwidth...
1. (15) By the Sampling Theorem the Nyquist sampling rate must be twice the highest bandwidth of the message signal. For the three message signals below determine the Nyquist rate and the Nyquist interval for each. a) m(t) = 0.5 cos(150 ) + sin(300Ft) + 0.75 cos(350ft) b) m(t) = 2 cos(120rt) sin(3007) c) m(t) = sinc(4000) = sin(400m) Recall: the Fourier transform of a sinc waveform is a rectangular pulse
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...
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t) (a) (10 pts) Fi...
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t) (a) (10 pts) Find and plot the Fourier Transform of x(t) (b) (10 pts) What is the Nyquist frequency and period for sampling? (c) (10 pts) Find and plot the Fourier Transform of xp(t) using the Nyquist rate.
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t)...
The signal m)811 + cos(20rt) cos(1o0t)] (t is in seconds) is sa using an ideal sampling...
The signal m)811 + cos(20rt) cos(1o0t)] (t is in seconds) is sa using an ideal sampling function at the rate of 150 samples/sec. Ea is encoded using a 16-level quantizer. ch sample a. Calculate the bandwidth of the signal m(). (2 Points) b. Is sampling done at, below or above Nyquist rate? Show your work (2 Points) (2 Points) c. Determine the rate of transmission (in bps). (3 Points) d. Find the signal-to-quantization noise ratio (SNR).
2. Consider the signal f(t) = 20 cos(5t) + cos(9t) sin(5t) - 7 (a) What is the highest angular frequency present in thi...
2. Consider the signal f(t) = 20 cos(5t) + cos(9t) sin(5t) - 7 (a) What is the highest angular frequency present in this signal? What is the highest numerical frequency present in this signal? (b) What is the Nyquist frequency? rate for this signal? Did you use the angular or the numerical (c) If you sample this signal with sampling period T, which values of T may you choose to be in accordance with the Nyquist rate? Choose and fix...
Consider a sampler which samples the continuous-time input signal x(t) at a sampling frequency fs =...
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).
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that ...
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that x(t) is sampled with sampling rate 3f. Sketch the spectrum of x(e ) (g) Suppose that we want to generate x(t using a discrete-to continuous converter operating at two times the Nyquist rate. What function xnl do you need to input into the discrete-to-continuous converter to generate x(t)?
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt
(f...
just looking for #2, 3, and 4
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(t) = 2 cos(2m50t) + 4cos(2m100t) a. (10 points) Determine S(f) and plot it b. (20 points) Let the sampling rate to be: fs 300 samples/sec. Plot the spectrum of the Ideal sample, that is plot S8(f) c. Let the sampling rate to be: fs 175 samples/sec. i. (30 points) Plot S8(f) ii. (10 points) Let...
19. 1 mark) What is the Nyquist sampling rate for a band-pass signal with a bandwidth of 300kHz if the lowest frequency is 100kHz? 20. 1 mark) In a block code, the codeword is 8 bits long. How long is the dataword if the number of valid codewords in this block are 64? How many codewords exist in total?
1. (15) By the Sampling Theorem the Nyquist sampling rate must be twice the highest bandwidth of the message signal. For the three message signals below determine the Nyquist rate and the Nyquist interval for each. a) m(t) = 0.5 cos(150 ) + sin(300Ft) + 0.75 cos(350ft) b) m(t) = 2 cos(120rt) sin(3007) c) m(t) = sinc(4000) = sin(400m) Recall: the Fourier transform of a sinc waveform is a rectangular pulse
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...
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t) (a) (10 pts) Find and plot the Fourier Transform of x(t) (b) (10 pts) What is the Nyquist frequency and period for sampling? (c) (10 pts) Find and plot the Fourier Transform of xp(t) using the Nyquist rate.
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t)...
The signal m)811 + cos(20rt) cos(1o0t)] (t is in seconds) is sa using an ideal sampling function at the rate of 150 samples/sec. Ea is encoded using a 16-level quantizer. ch sample a. Calculate the bandwidth of the signal m(). (2 Points) b. Is sampling done at, below or above Nyquist rate? Show your work (2 Points) (2 Points) c. Determine the rate of transmission (in bps). (3 Points) d. Find the signal-to-quantization noise ratio (SNR).
2. Consider the signal f(t) = 20 cos(5t) + cos(9t) sin(5t) - 7 (a) What is the highest angular frequency present in this signal? What is the highest numerical frequency present in this signal? (b) What is the Nyquist frequency? rate for this signal? Did you use the angular or the numerical (c) If you sample this signal with sampling period T, which values of T may you choose to be in accordance with the Nyquist rate? Choose and fix...
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).
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt (f Suppose that x(t) is sampled with sampling rate 3f. Sketch the spectrum of x(e ) (g) Suppose that we want to generate x(t using a discrete-to continuous converter operating at two times the Nyquist rate. What function xnl do you need to input into the discrete-to-continuous converter to generate x(t)?
19. Suppose that we wish to create a signal x(t) = cos(2π10%) sin(100nt) 100Tt
(f...
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