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Question 7 The diagram depicts a digital filter that samples the continuous time input signal x(t)...
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).
Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[...
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...
The continuous signal x(t) = 3 cos(2pi 70 t) is converted to a discretized signal. What...
The continuous signal x(t) = 3 cos(2pi 70 t) is converted to a discretized signal. What is the expression for the discrete signal if the sampling frequency is 200 Hz? What is the frequency of the discrete signal if it is sampled at 3Hz?
Q7) A frequency of 46 kHz is higher than the normal audible range of 20 Hz to 20 kHz for a human ...
Q7) A frequency of 46 kHz is higher than the normal audible range of 20 Hz to 20 kHz for a human being. Consider a continuous-time signal x(t) - cos(2mfot) where fo 46 kHz. Sample the signal using a sampling rate of fs 48 kHz. A) Derive a formula for the discrete-time signal x[n] that results from sampling x (t) B) Using only analysis of x[n] in the discrete-time domain, determine the discrete-time frequency to which the continuous-time frequency of...
Question 5 (a) The impulse response of a discrete-time filter is given as, hin) 0.56n-1] +n-2)0.5...
Question 5 (a) The impulse response of a discrete-time filter is given as, hin) 0.56n-1] +n-2)0.56 n -3]. i. Derive the filter's frequency response; 11. Roughly sketch the filter's magnitude response for 0 ii. Is it a low-pass or high-pass filter? Ω 2m; (b) A continuous-time signal se(t) is converted into a discrete-time signal as shown below. s(t) is a unit impulse train. s(t) x,) Conversion into x(1) __→ⓧ一ㄅㄧ-discrete-time sequence ー→ xu [n] The frequency spectrum of ap (t) is...
10. Find the Fourier transform of a continuous-time signal x(t) = 10e Su(t). Plot the magnitude...
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...
please, provide answer along with its matlab code. 10. Consider the continuous- time signal kite a1ua(-t) + kze-a2t...
please, provide answer along with its matlab code.
10. Consider the continuous- time signal kite a1ua(-t) + kze-a2t cos (2mfi t) ua (t), Ta(t) where ki =-400, k2 2, a1 = -57.5364, a2 21.0721, and fi=300 Hz. (a) Plot ra(t). Identify the non-causal part of Ta (t) as Tal(t) and the causal part as Ta2(t). (b) Assuming that aa(t) is sampled using the sampling frequency fsamp 200 Hz, determine the discrete-time counter-parts corresponding to aal (t) and ra2(t), named a1(n)...
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
Problem 1 A sinusodial signal x(t)- sin2t (t in seconds) is input to a system with frequency resp...
Problem 1 A sinusodial signal x(t)- sin2t (t in seconds) is input to a system with frequency response: H(G What signal y(t) is observed at the output? Problem 2 The inverse Fourier transform of a system frequency response is given by h(t)t. The signal x(t) 3 cos(4t 0.5) is input to the system (t in seconds). (a) What is the expression of the signal y(t) at the system output? (b) What is the power attenuation in dB caused by the...
21. The signal x(t) = cos(1,8001t – 1/6) is sampled uniformly at the rate of 1...
21. The signal x(t) = cos(1,8001t – 1/6) is sampled uniformly at the rate of 1 kHz and passed through an ideal low-pass filter with a DC gain of 0.001 and a cutoff frequency of 500 Hz. Find the filter's output.
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).
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...
Q7) A frequency of 46 kHz is higher than the normal audible range of 20 Hz to 20 kHz for a human being. Consider a continuous-time signal x(t) - cos(2mfot) where fo 46 kHz. Sample the signal using a sampling rate of fs 48 kHz. A) Derive a formula for the discrete-time signal x[n] that results from sampling x (t) B) Using only analysis of x[n] in the discrete-time domain, determine the discrete-time frequency to which the continuous-time frequency of...
Question 5 (a) The impulse response of a discrete-time filter is given as, hin) 0.56n-1] +n-2)0.56 n -3]. i. Derive the filter's frequency response; 11. Roughly sketch the filter's magnitude response for 0 ii. Is it a low-pass or high-pass filter? Ω 2m; (b) A continuous-time signal se(t) is converted into a discrete-time signal as shown below. s(t) is a unit impulse train. s(t) x,) Conversion into x(1) __→ⓧ一ㄅㄧ-discrete-time sequence ー→ xu [n] The frequency spectrum of ap (t) is...
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...
please, provide answer along with its matlab code.
10. Consider the continuous- time signal kite a1ua(-t) + kze-a2t cos (2mfi t) ua (t), Ta(t) where ki =-400, k2 2, a1 = -57.5364, a2 21.0721, and fi=300 Hz. (a) Plot ra(t). Identify the non-causal part of Ta (t) as Tal(t) and the causal part as Ta2(t). (b) Assuming that aa(t) is sampled using the sampling frequency fsamp 200 Hz, determine the discrete-time counter-parts corresponding to aal (t) and ra2(t), named a1(n)...
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
Problem 1 A sinusodial signal x(t)- sin2t (t in seconds) is input to a system with frequency response: H(G What signal y(t) is observed at the output? Problem 2 The inverse Fourier transform of a system frequency response is given by h(t)t. The signal x(t) 3 cos(4t 0.5) is input to the system (t in seconds). (a) What is the expression of the signal y(t) at the system output? (b) What is the power attenuation in dB caused by the...
21. The signal x(t) = cos(1,8001t – 1/6) is sampled uniformly at the rate of 1 kHz and passed through an ideal low-pass filter with a DC gain of 0.001 and a cutoff frequency of 500 Hz. Find the filter's output.
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