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a The impulse response of a filter is given by h(t) = where a, b, and...
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...
Problem 2.13 A wireless channel has impulse response given by h(t) 2t 0.1) +j8(t 0.64)-0.86(t-2.2...
Problem 2.13 A wireless channel has impulse response given by h(t) 2t 0.1) +j8(t 0.64)-0.86(t-2.2), where the unit of time is in microseconds (a) What is the delay spread and coherence bandwidth? (b) Plot the magnitude and phase of the channel transfer function H(f) over the interval -2Be,2Be], where Be denotes the coherence bandwidth computed in (a). Comment on how the phase behaves when H(f) is small. (c) Express | H(f)l in dB, taking 0 dB as the gain of...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000 e 3000 e20 where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. (0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). (i) Using part (0, write out the Frequency Response, H(jo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response...
A fourth order, Type I, linear phase, FIR filter, h[n], is to be designed using the window method. The ideal impulse response of the filter is defined as: hd[n] = sin([pi/4]*[n - N/2]) / ([n - N/2]*pi) , where N is the filter order and 'pi' denotes the ma
A fourth order, Type I, linear phase, FIR filter, h[n], is to be designed using the window method. The ideal impulse response of the filter is defined as:hd[n] = sin([pi/4]*[n - N/2]) / ([n - N/2]*pi) ,where N is the filter order and 'pi' denotes the mathematical (irrational) constant number 3.14159.... Given that a stopband attenuation of 50 dB is required,a) Find and sketch h[n]b) Determine the transfer function of the resulting digital filterc) Draw the filter block diagramd) Determine...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h(t) 4000e...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h(t) 4000e 3000 c0, where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. 0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). () Using part (0). write out the Frequency Response, HGo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response system. and...
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...
aliasing? A continuous-time system is given by the input/output differential equation 4. H(s) v(t) dy(t) dt dx(t) + 2 (+ x(t 2) dt (a) Determine its transfer function H(s)? (b) Determine its impulse...
aliasing? A continuous-time system is given by the input/output differential equation 4. H(s) v(t) dy(t) dt dx(t) + 2 (+ x(t 2) dt (a) Determine its transfer function H(s)? (b) Determine its impulse response. (c) Determine its step response. (d) Is the stable? (a) Give two reasons why digital filters are favored over analog filters 5. (b) What is the main difference between IIR and FIR digital filters? (c) Give an example of a second order IIR filter and FIR...
Question 3 a) A linear-phase, Finite Impulse Response (FIR) digital filter with the transfer func...
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Question 3 a) A linear-phase, Finite Impulse Response (FIR) digital filter with the transfer function H() shown as follow is desired: (4 marks) (3 marks) iii) Based on (a)(ii), determine the truncated impulse response ha(n) for a 5-tap FIR filter by i) Sketch the spectrum of the transfer function H (w). ii) Determine the impulse response h(n) from H() using rectangular window method. (6 marks) iv) Calculate all the filter coefficient of ha (n). (5 marks)
Question 3 a)...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] –...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
The transfer function of an ideal low-pass filter is given by: 4. a) i Prove that its impulse response is given by: a s...
The transfer function of an ideal low-pass filter is given by: 4. a) i Prove that its impulse response is given by: a sin(na) π (na) where (Q is the cut-off frequency [-consoo] ii Is hIn] a FIR or an IIR filter? Is it causal or anti-causal filter? Explain 3 your answer. iii) If g. 0.1 π, plot the magnitude responses for the following impulse responses:
The transfer function of an ideal low-pass filter is given by: 4. a) i...
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...
Problem 2.13 A wireless channel has impulse response given by h(t) 2t 0.1) +j8(t 0.64)-0.86(t-2.2), where the unit of time is in microseconds (a) What is the delay spread and coherence bandwidth? (b) Plot the magnitude and phase of the channel transfer function H(f) over the interval -2Be,2Be], where Be denotes the coherence bandwidth computed in (a). Comment on how the phase behaves when H(f) is small. (c) Express | H(f)l in dB, taking 0 dB as the gain of...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000 e 3000 e20 where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. (0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). (i) Using part (0, write out the Frequency Response, H(jo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h(t) 4000e 3000 c0, where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. 0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). () Using part (0). write out the Frequency Response, HGo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response system. and...
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...
aliasing? A continuous-time system is given by the input/output differential equation 4. H(s) v(t) dy(t) dt dx(t) + 2 (+ x(t 2) dt (a) Determine its transfer function H(s)? (b) Determine its impulse response. (c) Determine its step response. (d) Is the stable? (a) Give two reasons why digital filters are favored over analog filters 5. (b) What is the main difference between IIR and FIR digital filters? (c) Give an example of a second order IIR filter and FIR...
Thanks
Question 3 a) A linear-phase, Finite Impulse Response (FIR) digital filter with the transfer function H() shown as follow is desired: (4 marks) (3 marks) iii) Based on (a)(ii), determine the truncated impulse response ha(n) for a 5-tap FIR filter by i) Sketch the spectrum of the transfer function H (w). ii) Determine the impulse response h(n) from H() using rectangular window method. (6 marks) iv) Calculate all the filter coefficient of ha (n). (5 marks)
Question 3 a)...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
The transfer function of an ideal low-pass filter is given by: 4. a) i Prove that its impulse response is given by: a sin(na) π (na) where (Q is the cut-off frequency [-consoo] ii Is hIn] a FIR or an IIR filter? Is it causal or anti-causal filter? Explain 3 your answer. iii) If g. 0.1 π, plot the magnitude responses for the following impulse responses:
The transfer function of an ideal low-pass filter is given by: 4. a) i...
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