Question 3 a) A linear-phase, Finite Impulse Response (FIR) digital filter with the transfer func...
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...
(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 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...
1. It is desired to design a linear phase, length N FIR filter via the window method. The desired amplitude response is given by the function A(u), i.e Show how to calculate the filter coefficients h(n), n 0,1,..., N-1 from A(u) if the window function is wn
1. It is desired to design a linear phase, length N FIR filter via the window method. The desired amplitude response is given by the function A(u), i.e Show how to calculate the...
The transfer function of a digital filter is, H(z) - ao t a1z-1+ .avz-M (a) [5 points] For a Finite Impulse Response (FIR) filter, where ao is non-zero, which of the following must be true? (circle all that apply) i. There will be at least one non-zero value within b bM ii. There will be at least one non-zero value within a1 aN a0 fori 1,2,..N iv. bi = 0 for i = 1,2, M v.bo=1
b) When designing a FIR filters, the impulse response of the ideal low-pass filter is usually modified by multiplying it by a windowing function such as the Hamming window which is defined, for an odd number N of samples, by: (2n)-(N-I)-ns(N-1) N-12 wlnl 0.54 + 0.46 cos i What are the advantages of windowing with this function compared 2 with a standard rectangular window? ii) Design a 10th Order Hamming windowed FIR low-pass filter with cut- off frequency at 1000...
Determine the coefficients b0,
b1, b2, of a generalized linear-phase FIR filter
1. (GLP FIR Filters] Determine the coefficients bo, bi, b2, of a generalized linear-phase FIR filter | d[n] = box[n] + b n - 1]+b22[n – 2] such that (i) it rejects any frequency component at wo = /3; and (ii) its frequency response is normalized so that Ha(0) = 1. Compute and sketch the magnitude and phase response of the filter to check that it satisfies the...
4. Consider a certain system defined by impulse response h(n) such that calculate the following: i. transfer function ii. magnitude response of the filter i phase response of the filter iv. sketch magnitude and phase response of the filter at intervals (π/10) radians (13 Marks) (3 Marks) (3 Marks) (6 Marks)
Design a linear-phase, bandpass FIR filter using the window-based approach to meet the following specifications: ws,L = 0.3T,ap.L = 0.45T,Wp u = 0.65T, "Au-0.8T, mini- mum stopband at (i) Is there a unique window to meet the desired specifications? If not, choose the window with minimum transition width (ii) Plot the magnitude and phase response of the designed filter using MATLAB. (iii Using the MATLAB command firpm, design the same linear-phase bandpass FIR filter via the Parks-McClellan algorithm. Plot the...
Give the transfer function of the digital filter with impulse response; h(n) = 0.7n u(n) + 0.7(n-1) u(n-1)