Problem 4 Questions about the frequency response of an FIR filter: (a) Determine a formula for th...
Topics: Filter Design by Pole Zero Placement PROBLEM Problem #2 . a) Design a simple FIR second order filter with real coefficients, causal, stable and with unity AC gain. Its steady state response is required to be zero when the input is: xIn]cos [(T/3)n] u[n] H(z) R.O.C: answer: b) Find the frequency response for the previous filter. H(0) c) Sketch the magnitude frequency response. T/3 t/3 d) Find the filter impulse response. h[n] e) Verify that the steady state step...
2. Consider a second IIR filter a. Determine the system function H(z), pole-zero location (patterns), and plot the pole-zero pattern. b. Determine the analytical expression for frequency response, magnitude, and phase response. c. Choose b so that the maximum magnitude response is equal to 1. d. Plot the pole-zero pattern and the magnitude of the frequency response as a function of normal frequency. 2. Consider a second IIR filter a. Determine the system function H(z), pole-zero location (patterns), and plot...
a/ If the impulse response of an FIR filter is h[n] = δ[n] - 4δ[n-1] + δ[n-2], make a plot of the output when the input is the signal: x[n] = δ[n-2] - δ[n-4]. b/ Determine the frequency response, H(ω), and give the answer as a simple formula. c/ Determine the magnitude of H(ω) and present your answer as a plot of the magnitude vs frequency. Label important features.
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 #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
T/2, , and 370|2. 4.22 A four-point Hanning window (filter) has the z transform 1 -z 2>0. H(z) 1 1) (1- +2-2) a. Draw the pole/zero diagram for H(z), noting any pole/zero cancellations. b. Sketch the magnitude response H'(o). c. Show that H(z) is FIR by finding h(n) for all n. d. Find the dc gain of the filter. T/2, , and 370|2. 4.22 A four-point Hanning window (filter) has the z transform 1 -z 2>0. H(z) 1 1) (1-...
(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...
1. Use MATLAB to design your FIR filter. Display the results of: Frequency response Magnitude response Phase response Etc.
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...
Fill all Answer Blanks and show all calculations in a separate sheet of paper. Problem: Given the Pole-Zero Plot (one pole and one zero at the origin) of a causal filter with a normalized magnitude frequency response (max |H(w)l 1): 0.8 a) It is a FIR or IIR filter? b) what is the R.O.C of the filter ? c) Is the filter stable BIBO? Answer: Answer: Izl> Arıswer: d) The magnitude frequency response has a maximum peak at w0. Answer:...