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In all what follows, the sampling frequency is fixed to fs = 40KHz. Part 2 -...
A Digital Signal Processing system is taking at its input the following analogue signal s(t); s(t)...
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...
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).
3 Sampling and aliasing The aim of this part is to demonstrate the effects of aliasing...
3 Sampling and aliasing The aim of this part is to demonstrate the effects of aliasing arising from improper sampling. A given analog signal z(t) is sampled at a rate fs = 1/T, the resulting samples (nT) are then reconstructed by an ideal reconstructor into the analog signal rat). Improper choice of f, will result in different signals ra(t) + (t), even though they agree at their sample values, that is, tanT) = x(nT). The procedure is illustrated by the...
number 2 ECE 300 Continuous-Time Signals and Systems H(jø π/2 Plot the spectrum Z (jø) of the filtered input signal z()...
number 2
ECE 300 Continuous-Time Signals and Systems H(jø π/2 Plot the spectrum Z (jø) of the filtered input signal z(), the spectrum Z, (jo) of the sampled signal z.(t), and the spectrum Y(ja) of the reconstructed signal y(t). Show clearly how the output spectrum Y (ja) differs from the original spectrum G(jo) C. Which system, A or B, produces less distortion between the input g(t) and the output y(4) or ()? Explain. You can measure distortion by finding the...
3. You have bought a data acquisition device from Ebay. The sampling interval of the device is 1 msec. a. What is the sampling frequency of the device? What is the folding frequency of the device? No...
3. You have bought a data acquisition device from Ebay. The sampling interval of the device is 1 msec. a. What is the sampling frequency of the device? What is the folding frequency of the device? Now, you are measuring following sinusoidal signals with the data acquisition device. For each signal, draw 1) Fourier transform magnitude of the original continuous-time signal, 2) Fourier transform magnitude of the sampled signal (draw at least first positive replica and first negative replica), 3)...
passband ripple and the stopband attenuation in db formula
Block diagram of a real time signal processing system is shown in Figure 1. Assuming that the system operates in audio frequency band (0 to 20 KHz) and uses bipolar, analog to digital converter (ADC) with peak to peak input voltage range= 10 Volt is used, estimate: i. The quantization step size; (2 Marks) ii. The minimum stop band attenuation in dB, Amin, for the anti-aliasing filter; (4 Marks) iii. Sketch the frequency response of the antialiasing filter; iv. The...
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...
3.(30 points) Pulse Code Modulation A-to-D Ideal Lowf Pass Filter xit)- #x) cos(2rfet) (10 points...
3.(30 points) Pulse Code Modulation A-to-D Ideal Lowf Pass Filter xit)- #x) cos(2rfet) (10 points) Consider the system in the above figure. The ideal low pass filter is one which has a brick-wall frequency response (or an ideal sinc function for its impulse response). If the bandwidth of the ideal low pass filter is IkHz and B 2kHz is the bandwidth of a bandpass signal x(t) that is centered at fo 19700Hz, determine the minimum sampling rate fs to avoid...
Below is the MATLAB code of low-cut shelving filter which can cut the low frequency of given music signal and low-boost...
Below is the MATLAB code of low-cut shelving filter which can cut the low frequency of given music signal and low-boost shelving filter which can boost the low frequency of given music signal. Design your low-boost shelving filter and low-cut shelving filter to have noticeablly different sound. Compare the sounds of two music signals after filtering, and explain the difference in sounds briefly. If there are any mistakes in code, correct them. Low-cut shelving filter code: close all, clear all,...
Program from problem 1: (Using MATLAB) % Sampling frequency and sampling period fs = 10000; ts...
Program from problem 1: (Using MATLAB)
% Sampling frequency and sampling period
fs = 10000;
ts = 1/fs;
% Number of samples, assume 1000 samples
l = 1000;
t = 0:1:l-1;
t = t.*ts; % Convert the sample index into time for generation and
plotting of signal
% Frequency and amplitude of the sensor
f1 = 110;
a1 = 1.0;
% Frequency and amplitude of the power grid noise
f2 = 60;
a2 = 0.7;
% Generating the sinusoidal waves...
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...
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).
3 Sampling and aliasing The aim of this part is to demonstrate the effects of aliasing arising from improper sampling. A given analog signal z(t) is sampled at a rate fs = 1/T, the resulting samples (nT) are then reconstructed by an ideal reconstructor into the analog signal rat). Improper choice of f, will result in different signals ra(t) + (t), even though they agree at their sample values, that is, tanT) = x(nT). The procedure is illustrated by the...
number 2
ECE 300 Continuous-Time Signals and Systems H(jø π/2 Plot the spectrum Z (jø) of the filtered input signal z(), the spectrum Z, (jo) of the sampled signal z.(t), and the spectrum Y(ja) of the reconstructed signal y(t). Show clearly how the output spectrum Y (ja) differs from the original spectrum G(jo) C. Which system, A or B, produces less distortion between the input g(t) and the output y(4) or ()? Explain. You can measure distortion by finding the...
3. You have bought a data acquisition device from Ebay. The sampling interval of the device is 1 msec. a. What is the sampling frequency of the device? What is the folding frequency of the device? Now, you are measuring following sinusoidal signals with the data acquisition device. For each signal, draw 1) Fourier transform magnitude of the original continuous-time signal, 2) Fourier transform magnitude of the sampled signal (draw at least first positive replica and first negative replica), 3)...
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...
3.(30 points) Pulse Code Modulation A-to-D Ideal Lowf Pass Filter xit)- #x) cos(2rfet) (10 points) Consider the system in the above figure. The ideal low pass filter is one which has a brick-wall frequency response (or an ideal sinc function for its impulse response). If the bandwidth of the ideal low pass filter is IkHz and B 2kHz is the bandwidth of a bandpass signal x(t) that is centered at fo 19700Hz, determine the minimum sampling rate fs to avoid...
Program from problem 1: (Using MATLAB)
% Sampling frequency and sampling period
fs = 10000;
ts = 1/fs;
% Number of samples, assume 1000 samples
l = 1000;
t = 0:1:l-1;
t = t.*ts; % Convert the sample index into time for generation and
plotting of signal
% Frequency and amplitude of the sensor
f1 = 110;
a1 = 1.0;
% Frequency and amplitude of the power grid noise
f2 = 60;
a2 = 0.7;
% Generating the sinusoidal waves...
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