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Please help. an ideal boedpass filter with inguney A rendom preass xt) response H(4) = 0, otherwise Let Y() be the output ot the Ailler, Show that an ideal boedpass filter with inguney A rend...
5.17 The frequency response of an ideal low-pass filter is -1/2 S2 > 0 |H(S2) =...
5.17 The frequency response of an ideal low-pass filter is -1/2 S2 > 0 |H(S2) = - -2 <92 < 2 otherwise ZH (12) = 0 1/2 12 < 0 (a) Calculate the impulse response h(t) of the ideal low-pass filter. (b) If the input of the filter is a periodic signal x(t) having a Fourier series 2 X(t) = cos(3kt/2) k=1 determine the steady-state response yss(t) of the system. Answers: h(t) = (1 - cos(2t))/(nt); Yss(t) = 2 sin(1.5t).
(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...
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H()...
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H() | 2,7 - periodic elsewhere (a) (10 pts) Find the output for an input signal x[n]=2 cosnr/2 (b) (10 pts) Find the output for an input signal xnsinc (n /2) (c) (10 pts) Find the output for an input signal x[n]sinc(n/8) cos (n)
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H() | 2,7 - periodic elsewhere...
(a) The impulse response hfn of an FIR filter satisfies the following property: h[n]- otherwise where...
(a) The impulse response hfn of an FIR filter satisfies the following property: h[n]- otherwise where M is an even integer. Derive the filter's frequency response and show that it has a linear phase. Why is linear phase a desired property ? (b) You are asked to design a linear-phase FIR filter. The required pass-band is from 1,000 Hz to 3,000 Hz. The input signal's sampling frequency is 16, 000Hz e the pass-band in the w domain 1. GlV n...
a) The transfer function of an ideal low-pass filter is and its impulse response is where...
a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given...
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...
The impulse response of an ideal band pass filter is given by the equation: n 0 h(n)=-sin(nw.) wl...
The impulse response of an ideal band pass filter is given by the equation: n 0 h(n)=-sin(nw.) wl sin(nw!) nヂ0 Using the above equation, write a Matlab program that implements an approximation for the band pass filter with cut-off frequencies ω1-0.2π rad/sample and c02-0.3t rad/sample. Set the order of the filter to 100 or 101. Use a Bartlett window here. Plot the frequency and phase responses of this digital filter.
The impulse response of an ideal band pass filter is...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts)...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n]...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n] is the weighted average of the present (current) and the two previous values of the input signal x[n] such that y[n]=> b x[n- k) where the filter coefficients (bk's) are selected k-0 based on the following constraints: • 0<b«<l, • Zb= 1, k = 0, 1, 2 2b, – 56, +10b, = 3, 36, +4b, +2b, = k=0 a. Determine the filter coefficients bo,...
1. The impulse response of an ideal band pass filter is given by the equation: n=0 h(n)w2 sin(n w...
Do it using Matlab.
1. The impulse response of an ideal band pass filter is given by the equation: n=0 h(n)w2 sin(n w2) w1 sin (n w1) T nwW2 Using the above equation, write a Matlab program that implements an approximation for the band pass filter with cut-off frequencies (1-0.2π rad/sample and ω2-0.3π rad/sample. Set the order of the filter to 100 or 101. Use a Bartlett window here. Plot the frequency and phase responses of this digital filter. Hint...
5.17 The frequency response of an ideal low-pass filter is -1/2 S2 > 0 |H(S2) = - -2 <92 < 2 otherwise ZH (12) = 0 1/2 12 < 0 (a) Calculate the impulse response h(t) of the ideal low-pass filter. (b) If the input of the filter is a periodic signal x(t) having a Fourier series 2 X(t) = cos(3kt/2) k=1 determine the steady-state response yss(t) of the system. Answers: h(t) = (1 - cos(2t))/(nt); Yss(t) = 2 sin(1.5t).
(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...
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H() | 2,7 - periodic elsewhere (a) (10 pts) Find the output for an input signal x[n]=2 cosnr/2 (b) (10 pts) Find the output for an input signal xnsinc (n /2) (c) (10 pts) Find the output for an input signal x[n]sinc(n/8) cos (n)
#2: Consider the ideal lowpass filter DT filter described by -j60 e 4 0, 4 H() | 2,7 - periodic elsewhere...
(a) The impulse response hfn of an FIR filter satisfies the following property: h[n]- otherwise where M is an even integer. Derive the filter's frequency response and show that it has a linear phase. Why is linear phase a desired property ? (b) You are asked to design a linear-phase FIR filter. The required pass-band is from 1,000 Hz to 3,000 Hz. The input signal's sampling frequency is 16, 000Hz e the pass-band in the w domain 1. GlV n...
a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given...
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...
The impulse response of an ideal band pass filter is given by the equation: n 0 h(n)=-sin(nw.) wl sin(nw!) nヂ0 Using the above equation, write a Matlab program that implements an approximation for the band pass filter with cut-off frequencies ω1-0.2π rad/sample and c02-0.3t rad/sample. Set the order of the filter to 100 or 101. Use a Bartlett window here. Plot the frequency and phase responses of this digital filter.
The impulse response of an ideal band pass filter is...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n] is the weighted average of the present (current) and the two previous values of the input signal x[n] such that y[n]=> b x[n- k) where the filter coefficients (bk's) are selected k-0 based on the following constraints: • 0<b«<l, • Zb= 1, k = 0, 1, 2 2b, – 56, +10b, = 3, 36, +4b, +2b, = k=0 a. Determine the filter coefficients bo,...
Do it using Matlab.
1. The impulse response of an ideal band pass filter is given by the equation: n=0 h(n)w2 sin(n w2) w1 sin (n w1) T nwW2 Using the above equation, write a Matlab program that implements an approximation for the band pass filter with cut-off frequencies (1-0.2π rad/sample and ω2-0.3π rad/sample. Set the order of the filter to 100 or 101. Use a Bartlett window here. Plot the frequency and phase responses of this digital filter. Hint...
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