Homework Answers
Here signal is pass through the filter. Since calculation are much easily performed in frequency domain so we convert the signal in frequency domain.
As convolution in time domain correspond to multiplication in frequency domain.
So here in case (a) signal is inside the filter so out result the input signal without any diatortion.
As in case (b) signal is out side the filter this results the no signal at the output.
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2.48 A filter has frequency response function H(f) Π(f/28) and input x(t) = 2Wsinc (2W1). (a) Find the output y(t) for W < B (b) Find the output y(a) for W > B. (c) In which case does the outpu...
6.(20%) Given a filter with frequency response function 5 F[h(t)=H=4+j(2f) 3 and given an input x(t)...
6.(20%) Given a filter with frequency response function 5 F[h(t)=H=4+j(2f) 3 and given an input x(t) eu(t) with its Fourier transform by 1 = *U)-3+ j(27f) F[x()] (10%) (a) Obtain the energy spectral density G,(f) for the input signal x(t) (10%) (b) Obtain the energy spectral density G.(f) for the output signal y(t)
6.(20%) Given a filter with frequency response function 5 F[h(t)=H=4+j(2f) 3 and given an input x(t) eu(t) with its Fourier transform by 1 = *U)-3+ j(27f) F[x()]...
10. An input signal x(t) is processed by a filter with an amplitude | H(f) |...
10. An input signal x(t) is processed by a filter with an amplitude | H(f) | and phase θ(f) response given below H(f) 90 70 50 30 10 10 θ(f) 25 -50 70 05 35 -3-252 -15105 0 05 115 2 25 3 35 -35-3-25-2-15-1-05 0 0.5 15 2 25 35 frequency (kHz) frequency (kHz) a) For x,(t)-2cos(22500t) find output signal ya(t) b) For x,(t) 4cos(27750t) find output signal yb(t) c) For x,(t)=2cos(2π500t) +4cos(2π750t) find output signal ye(t) d) For...
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) -...
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier transform pair Pr(t) ←→ τ sine ( (b) An ideal bandpass filter has frequency response w) 0,...
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier transform pair Pr(t) ←→ τ sine ( (b) An ideal bandpass filter has frequency response w) 0, otherwise 2(t-1 Find the output response y(t) when the input is (t)-sinc 2
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier...
If g(t) and y(t) are the input and the output, respectively, of a simple RC low-pass filter (Fig....
If g(t) and y(t) are the input and the output, respectively, of a simple RC low-pass filter (Fig. 3.27a), determine the transfer function H() and sketch H(, 0h(), and td(). For distortionless transmission through this filter, what is the requirement on the bandwidth of g(t) if amplitude response variation within 2% and time delay variation within 5% are tolerable? What is the transmission delay? Find the output y(t) g(t)
If g(t) and y(t) are the input and the output, respectively,...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
The given input signal for 2.7.2 is: x(t) = 3 cos(2 π t) + 6 sin(5 π t). Plz explain ...
The given input signal for 2.7.2 is: x(t) = 3 cos(2
π t) + 6 sin(5 π t).Plz explain steps.Given a causal LTI system described by the differential equation find \(H(s),\) the \(\mathrm{ROC}\) of \(H(s),\) and the impulse response \(h(t)\) of the system. Classify the system as stable/unstable. List the poles of \(H(s) .\) You should the Matlab residue command for this problem.(a) \(y^{\prime \prime \prime}+3 y^{\prime \prime}+2 y^{\prime}=x^{\prime \prime}+6 x^{\prime}+6 x\)2.7.2 The signal \(x(t)\) in the previous problem is...
A continuous time system H has the frequency response H(jω) = 4π / (4π + jω)...
A continuous time system H has the frequency response H(jω) = 4π / (4π + jω) . a) Find and plot the magnitude as a function of radial frequency. b) Find and plot the phase as a function of radial frequency. c) Using H(jω), find the output y(t) for the input x(t) = 4cos(4πt) + 4cos(12πt)
4. Let h(t), (t), and y(t), for -oo < oo, be the impulse response function, the input, and the output of a linear ti...
4. Let h(t), (t), and y(t), for -oo < oo, be the impulse response function, the input, and the output of a linear time-invariant system, respectively. Give the following spectra: Input magnitude spectrum: Input phase spectrum: ex(2) T/2 Output magnitude spectrum: tY() Output phase spectrum: ey (2) / 2 Find H() from the above spectra and from the fact that H() 0 for not belonging to the interval (-2,2). Find the impulse response function h(t) from H() found above. Is...
6.(20%) Given a filter with frequency response function 5 F[h(t)=H=4+j(2f) 3 and given an input x(t) eu(t) with its Fourier transform by 1 = *U)-3+ j(27f) F[x()] (10%) (a) Obtain the energy spectral density G,(f) for the input signal x(t) (10%) (b) Obtain the energy spectral density G.(f) for the output signal y(t)
6.(20%) Given a filter with frequency response function 5 F[h(t)=H=4+j(2f) 3 and given an input x(t) eu(t) with its Fourier transform by 1 = *U)-3+ j(27f) F[x()]...
10. An input signal x(t) is processed by a filter with an amplitude | H(f) | and phase θ(f) response given below H(f) 90 70 50 30 10 10 θ(f) 25 -50 70 05 35 -3-252 -15105 0 05 115 2 25 3 35 -35-3-25-2-15-1-05 0 0.5 15 2 25 35 frequency (kHz) frequency (kHz) a) For x,(t)-2cos(22500t) find output signal ya(t) b) For x,(t) 4cos(27750t) find output signal yb(t) c) For x,(t)=2cos(2π500t) +4cos(2π750t) find output signal ye(t) d) For...
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier transform pair Pr(t) ←→ τ sine ( (b) An ideal bandpass filter has frequency response w) 0, otherwise 2(t-1 Find the output response y(t) when the input is (t)-sinc 2
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier...
If g(t) and y(t) are the input and the output, respectively, of a simple RC low-pass filter (Fig. 3.27a), determine the transfer function H() and sketch H(, 0h(), and td(). For distortionless transmission through this filter, what is the requirement on the bandwidth of g(t) if amplitude response variation within 2% and time delay variation within 5% are tolerable? What is the transmission delay? Find the output y(t) g(t)
If g(t) and y(t) are the input and the output, respectively,...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
The given input signal for 2.7.2 is: x(t) = 3 cos(2
π t) + 6 sin(5 π t).Plz explain steps.Given a causal LTI system described by the differential equation find \(H(s),\) the \(\mathrm{ROC}\) of \(H(s),\) and the impulse response \(h(t)\) of the system. Classify the system as stable/unstable. List the poles of \(H(s) .\) You should the Matlab residue command for this problem.(a) \(y^{\prime \prime \prime}+3 y^{\prime \prime}+2 y^{\prime}=x^{\prime \prime}+6 x^{\prime}+6 x\)2.7.2 The signal \(x(t)\) in the previous problem is...
4. Let h(t), (t), and y(t), for -oo < oo, be the impulse response function, the input, and the output of a linear time-invariant system, respectively. Give the following spectra: Input magnitude spectrum: Input phase spectrum: ex(2) T/2 Output magnitude spectrum: tY() Output phase spectrum: ey (2) / 2 Find H() from the above spectra and from the fact that H() 0 for not belonging to the interval (-2,2). Find the impulse response function h(t) from H() found above. Is...
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