Homework Answers
MATLAB code is given below in bold letters to plot the frequency response of the filter.
figure;freqz([1 2 2 1],1);
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T/2, , and 370|2. 4.22 A four-point Hanning window (filter) has the z transform 1 -z...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. T...
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...
Given the following FIR digital filter, H(z) = (1 – 2-1) (1+z-1) 3 1) Sketch the...
Given the following FIR digital filter, H(z) = (1 – 2-1) (1+z-1) 3 1) Sketch the pole zero diagram of this filter. 2) Sketch magnitude and phase spectrum (not decibels) 3) Could you comment on the type of filter (LP, HP, BP or BS) and justify your answer?
Topics: Filter Design by Pole Zero Placement PROBLEM Problem #2 . a) Design a simple FIR...
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...
Problem 4 Questions about the frequency response of an FIR filter: (a) Determine a formula for th...
Please show all work
Problem 4 Questions about the frequency response of an FIR filter: (a) Determine a formula for the frequency response of an FIR filter defined by the pole-zero plot below: Pole-Zero Plot #1 0.5 -0.5 -1 1 -0.5 0 051 Real part (b) For the FIR filter in part (a), write a simplified version of the frequency response H(e'ω) and use it to prove that the maximum value of the frequency response magnitude will be at ω-tr/2....
3) Given a filter with the following structure X(n); Hi(Z) y(n) H2(z) H(z) where Hi(2) 11+1+0.09z...
3) Given a filter with the following structure X(n); Hi(Z) y(n) H2(z) H(z) where Hi(2) 11+1+0.09z and H(z)--4z1+z1+0.09z2] Hi(Z)- 1/[1+z1+ Find the z-transform H(z) and the frequency response H(e2*) . Say if the filter is FIR or IIR, and if it is stable or not » Find the I/O equatio n and draw the block diagram
A filter has two poles at -0.6±0.8j and a zero at -1 on the z-plane. The...
A filter has two poles at -0.6±0.8j and a zero at -1 on the z-plane. The DC gain is 1. What is the transfer function H(z)? Draw the pole-zero plot.
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (...
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (1.5 point) Sketch the magnitude spectrum, H(e i), of the filter. Find the exact values of lH(eml. IH(efr/2)I, and IH(e") , (sol) 1-3. (1 point) Relocate only one pole so that 9 s Hle)s 10 (sol) 1-4 (1 point) Take the inverse Z-transform on H(z) to find the impulse...
DSP Lab Exercise 9 Given below are the Impulse Response h(n), of the four main types of FIR Digit...
DSP Lab Exercise 9 Given below are the Impulse Response h(n), of the four main types of FIR Digital filters. Use appropriate MATLAB expressions to find: a) System Response (H(z) b) Pole-zero diagram c) Amplitude Response d) Phase Response 1. FIR Low-Pass Digital Filter ,n= 0.1 |[d(n) + δ(n-I))-1 h(n) 0, otherwise 2. FIR High-Pass Digital Filter 0, otherwise 3. FIR Band-Pass Digital Filter 0, otherwise 4. FIR Band-Stop Digital Filter , n = 0,2 0, otherwise Note: Your final...
Fill all Answer Blanks and show all calculations in a separate sheet of paper. Problem: Given...
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:...
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...
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...
Given the following FIR digital filter, H(z) = (1 – 2-1) (1+z-1) 3 1) Sketch the pole zero diagram of this filter. 2) Sketch magnitude and phase spectrum (not decibels) 3) Could you comment on the type of filter (LP, HP, BP or BS) and justify your answer?
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...
Please show all work
Problem 4 Questions about the frequency response of an FIR filter: (a) Determine a formula for the frequency response of an FIR filter defined by the pole-zero plot below: Pole-Zero Plot #1 0.5 -0.5 -1 1 -0.5 0 051 Real part (b) For the FIR filter in part (a), write a simplified version of the frequency response H(e'ω) and use it to prove that the maximum value of the frequency response magnitude will be at ω-tr/2....
3) Given a filter with the following structure X(n); Hi(Z) y(n) H2(z) H(z) where Hi(2) 11+1+0.09z and H(z)--4z1+z1+0.09z2] Hi(Z)- 1/[1+z1+ Find the z-transform H(z) and the frequency response H(e2*) . Say if the filter is FIR or IIR, and if it is stable or not » Find the I/O equatio n and draw the block diagram
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (1.5 point) Sketch the magnitude spectrum, H(e i), of the filter. Find the exact values of lH(eml. IH(efr/2)I, and IH(e") , (sol) 1-3. (1 point) Relocate only one pole so that 9 s Hle)s 10 (sol) 1-4 (1 point) Take the inverse Z-transform on H(z) to find the impulse...
DSP Lab Exercise 9 Given below are the Impulse Response h(n), of the four main types of FIR Digital filters. Use appropriate MATLAB expressions to find: a) System Response (H(z) b) Pole-zero diagram c) Amplitude Response d) Phase Response 1. FIR Low-Pass Digital Filter ,n= 0.1 |[d(n) + δ(n-I))-1 h(n) 0, otherwise 2. FIR High-Pass Digital Filter 0, otherwise 3. FIR Band-Pass Digital Filter 0, otherwise 4. FIR Band-Stop Digital Filter , n = 0,2 0, otherwise Note: Your final...
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:...
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