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Given an RC lowpass filter with R=200K and C=4uF and the bilinear transform equation as shown:...
Use Bilinear Transform to design a lowpass Butterworth digital filter that passes frequencies up ...
Use Bilinear Transform to design a lowpass Butterworth digital filter that passes frequencies up to f=1500Hz with minimum gain -7dB. The filter is to block frequencies from f = 3600Hz with a maximum gain-38dB. The sampling frequency is f = 8000 a) Find the Butterworth Filter Order = (N), 3-dB Cutoff frequency, and the numerator and denominator coefficients of the H(z) b) Which of the frequencies in the followingx()will be passed by your designed filter?x(t) = cos(1600πt)+5cos(8000πt)+3cos(2300πt)+ 2cos(1400πt)
The values of Resistor and Capacitor is shown as below R(2) 100000 C(F) 1.5432 10-6 e.1 (5pts) Pl...
High pass digital filter
The values of Resistor and Capacitor is shown as below R(2) 100000 C(F) 1.5432 10-6 e.1 (5pts) Please derive the Laplace transfrom equation V, (s) Vi(s) e.2(5pts) Please use bilinear transform equation to transform Laplace transform to 一? z-transform. Bilinear transform equation is shown as below: = T (1+2-1) Your result will be (2) =? Vi(z) e.3(10pts) Please use inverse z-transform to find the difference equation. Your result will be look like as below, you will...
6. (20 points) (1) Design an analog lowpass filter with a cut-off frequency of 9 rad/sec by starting with an analogue prototype first-order lowpass filter with cut-off frequency of 1 rad/sec. Sho...
6. (20 points) (1) Design an analog lowpass filter with a cut-off frequency of 9 rad/sec by starting with an analogue prototype first-order lowpass filter with cut-off frequency of 1 rad/sec. Show the system transfer function H(s) (2) Design an IIR digital filter Hz) that corresponds to the above H(s) by using the bilinear transform method without prewarping with T 0.1 second. Show the system transfer function Hz) and find its corresponding digital cut-off frequency Be approximately (3) What is...
A discrete-time filter is to be designed using the bilinear transform method. The sampling rate of...
A discrete-time filter is to be designed using the bilinear transform method. The sampling rate of the digital system is 2 samples/second. The continuous-time filter is given as; s + 2 5 Points Each. Circle the Best Answer 37. lf the filter is changed to a prewarped bilinear design with a prewarp frequency ot 1 Hz, the dc frequency response of the discrete-time filter lH(coo Would then equal a) arctan(2)b) 1/3c) d) 76 e) none above
Using the Bilinear Transform steps in Example-2 done in class, design a lowpass Butterworth digit...
Using the Bilinear Transform steps in Example-2 done in class, design a lowpass Butterworth digital ülier thai passos frequencies up to f,, 12K1Iz with ınaximiin kxz; ofǎ_ (1,1A and stops frequences from, fs-24KHz with a minimum loss of δ2-0.3. The sanpling frequency isf 100KHz. Find the Butterworth Filter Order(N), 3-dB Cutoff frequency and the numerator and denominator coefficients of the H(z) by hand-calculation.
Using the Bilinear Transform steps in Example-2 done in class, design a lowpass Butterworth digital ülier thai...
Design lowpass IIR filter with the following specifications: Filter order = 2, Butterworth type C...
Design lowpass IIR filter with the following specifications: Filter order = 2, Butterworth type Cut-off frequency=800 Hz Sampling rate =8000 Hz Design using the bilinear z-transform design method Print the lowpass IIR filter coefficients and plot the frequency responses using MATLAB. MATLAB>>freqz(bLP,aLP,512,8000); axis([0 4000 –40 1]); Label and print your graph. What is the filter gain at the cut-off frequency 800 Hz? What are the filter gains for the stopband at 2000 Hz and the passband at 50 Hz based...
2. Perform a lowpass prototype transform, find, given the following digital filter frequency values. a. Low...
2. Perform a lowpass prototype transform, find, given the following digital filter frequency values. a. Low pass filter with a cutoff of 750 Hz b. High pass filter with a cutoff of 12.57 rad/s c. Bandpass filter with a lower cutoff of 400 Hz and a higher cutoff 725 Hz d. Bandstop filter with a center frequency of 135.3 rad/s and a bandwidth of 84.74 rad/s
4. We wish to design a digital bandpass filter from a second-order analog lowpass Butterworth filter...
4. We wish to design a digital bandpass filter from a second-order analog lowpass Butterworth filter prototype using the bilinear transformation. The cutoff frequencies (measured at the half-power points) for the digital filter should lie at ω 5t/12 and ω-7t/12. The analog prototype is given by 1 s2+/2s+1 with the half-power point at 2 Determine the system function for the digital bandpass filter. a) b) Make the transfer from LPF to BPF in the analog domain Make the transfer from...
(Bilinear transformation and all pass systems in the Laplace domain). The bilinear transformation...
(Bilinear transformation and all pass systems in the Laplace domain). The bilinear transformation F:C→C is a mapping from the z-domain to the Laplace domain, defined as s唔倫-1) without loss of generality, let us 7 17-) Without loss of generality, let us Td 1+z-1 assume that the scaling factor Ta is not important here, so we can choose 1-z-1 Ta = 2 to simplify our discussions; hence, s(z) =-. 1+z-1 (a) Show that the transformation maps the unit circle in the...
High pass digital filter
The values of Resistor and Capacitor is shown as below R(2) 100000 C(F) 1.5432 10-6 e.1 (5pts) Please derive the Laplace transfrom equation V, (s) Vi(s) e.2(5pts) Please use bilinear transform equation to transform Laplace transform to 一? z-transform. Bilinear transform equation is shown as below: = T (1+2-1) Your result will be (2) =? Vi(z) e.3(10pts) Please use inverse z-transform to find the difference equation. Your result will be look like as below, you will...
6. (20 points) (1) Design an analog lowpass filter with a cut-off frequency of 9 rad/sec by starting with an analogue prototype first-order lowpass filter with cut-off frequency of 1 rad/sec. Show the system transfer function H(s) (2) Design an IIR digital filter Hz) that corresponds to the above H(s) by using the bilinear transform method without prewarping with T 0.1 second. Show the system transfer function Hz) and find its corresponding digital cut-off frequency Be approximately (3) What is...
A discrete-time filter is to be designed using the bilinear transform method. The sampling rate of the digital system is 2 samples/second. The continuous-time filter is given as; s + 2 5 Points Each. Circle the Best Answer 37. lf the filter is changed to a prewarped bilinear design with a prewarp frequency ot 1 Hz, the dc frequency response of the discrete-time filter lH(coo Would then equal a) arctan(2)b) 1/3c) d) 76 e) none above
Using the Bilinear Transform steps in Example-2 done in class, design a lowpass Butterworth digital ülier thai passos frequencies up to f,, 12K1Iz with ınaximiin kxz; ofǎ_ (1,1A and stops frequences from, fs-24KHz with a minimum loss of δ2-0.3. The sanpling frequency isf 100KHz. Find the Butterworth Filter Order(N), 3-dB Cutoff frequency and the numerator and denominator coefficients of the H(z) by hand-calculation.
Using the Bilinear Transform steps in Example-2 done in class, design a lowpass Butterworth digital ülier thai...
2. Perform a lowpass prototype transform, find, given the following digital filter frequency values. a. Low pass filter with a cutoff of 750 Hz b. High pass filter with a cutoff of 12.57 rad/s c. Bandpass filter with a lower cutoff of 400 Hz and a higher cutoff 725 Hz d. Bandstop filter with a center frequency of 135.3 rad/s and a bandwidth of 84.74 rad/s
4. We wish to design a digital bandpass filter from a second-order analog lowpass Butterworth filter prototype using the bilinear transformation. The cutoff frequencies (measured at the half-power points) for the digital filter should lie at ω 5t/12 and ω-7t/12. The analog prototype is given by 1 s2+/2s+1 with the half-power point at 2 Determine the system function for the digital bandpass filter. a) b) Make the transfer from LPF to BPF in the analog domain Make the transfer from...
(Bilinear transformation and all pass systems in the Laplace domain). The bilinear transformation F:C→C is a mapping from the z-domain to the Laplace domain, defined as s唔倫-1) without loss of generality, let us 7 17-) Without loss of generality, let us Td 1+z-1 assume that the scaling factor Ta is not important here, so we can choose 1-z-1 Ta = 2 to simplify our discussions; hence, s(z) =-. 1+z-1 (a) Show that the transformation maps the unit circle in the...
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