Q.6 (a) (4 pts) A Butterworth filter has been designed with 22. = 0.578 and N=3....
A digital low pass IIR filter is to be designed with Butterworth approximation using the Bilinear transformation technique having the following specifications:(i) Passband magnitude is constant within 1 dB for frequencies below 0.2 π.(ii) Stopband attenuation is greater than 15 dB for frequencies between 0.3 π to π. Determine the order of the filter, cutoff frequency, poles location and transfer function of digital filter in order to meet the above specifications.
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...
Part II: Design of Butterworth Filters Butterworth filters, described in a paper by Stephen Butterworth in 1930, are widely used for CT frequency-selective filtering. Butterworth filters have a simple analytic form and are designed to have a magnitude response that is maximally flat in the passband. In this section, you will use the Laplace transform to design and analyze Butterworth filters in the frequency domain. The textbook has some useful information about Butterworth filters, so check it out to help...
Problem 3 (LSM3) (20 pts) Consider a Butterworth filter of order one with a cutoff frequency of we [rad/sec]. (a) Determine the transfer function H(s) of the Butterworth filter so that it is causal and stable (b) Determine the output of the filter in response to the input 1 + cos Problem 3 (LSM3) (20 pts) Consider a Butterworth filter of order one with a cutoff frequency of we [rad/sec]. (a) Determine the transfer function H(s) of the Butterworth filter...
QUESTION 6 Зро Design a second-order IIR digital low-pass filter using Butterworth approximation. Use the bilinear transformation to convert the analogue fiter to a digital one (choose the sampling period T- 2 s and the cut-off frequency as 1 rad/'s). Express the digital transfer function of the filter H(z) as: In the box below, provide the numerical answer for b1. [Note: Don't normalise the transfer func on, i.e. b0 # 1). r98111acontentid1837836_1&step QUESTION 7 Windowing based FIR filter design techniques...
just do 4 , 3 is solved 3. Use a Bilinear Transform to design a Butterworth low-pass filter which satisfies the filter specifications: Pass band: -1Ss0 for 0sf s0.2 Stop band: (e/40 for 0.35sf s0.s Transition Band: 0.2<f<0.35 Sampling Frequency: 10 kHz a. (3) Determine the stop-band and pass-band frequencies, Fstop and Fpas, in kHz. b. (3) Calculate the fater order, n, which is necessary to obtain the desired filter specifications. (3) Calculate the corner frequency, Fe, if you want...
Using matlab to design H(z) as a 6th order Butterworth filter with bandedges of 0.3 and 0.5. Plot the frequency response of the above filter. Use the quantization function below to quantize the coefficients of the filter to 8 bits, and plot the frequency response. Implement H(z) in cascade form and quantize the coefficients to 8 bits, then plot the frequency response of the resulting filter. Compare the two approaches of implementing a filter and the effects of quantization on...
2. Second-order Butterworth CT and DT filters. (a) [5 pts] Given that He (s)- (s+e4(steJr/4 and that the corresponding fiter is causal, verify that He(0) 1. that Hc (jw) decreases monotonically with increasing positive values of u. that I He (j) | 2-1/2 (i.e., that wc-1 is the half-power frequency), and that (b) [3 pts] Give an expression for Hd(z), the bilinear transform applied to Hc(s) in part a. Choose T - 2 in the bilinear-transform formula, ie., (1- z1/(1z1)-(z...
show all calculations 0.5 a) Hz(2) is a type-3 GLP filter and it has a zero at Z - j. Find Hz(Z) b) Convert Hz(2) to Hz(es) then calculate Hz (e)and H, (e- c) What is the relationship between the results of part (a) and part(b)? 0.6 Hap(Z) is a real all-pass filter and it has a pole at Z = + and another pole at Za bmZ- MM M Construct Hap(Z) as one block and without fractions, i.e. H(Z)...
QUESTION 28 3 points Save The Siter coefficients of a second-order digital IR filter are: ao-1,a1-2, a2-2, bo-1. b1-1/2, b2 1/8. (a's are numerator coetficients and b's are the denominator coefficients). Determine the value of the impulse response N4? QUESTION 29 6 points Save Answer An image is to be sampled with a signal-to-quantisation ratio of at least 55 dB. The image samples are non-negative. The image sample values fall within the range from 0 to 1. How many bits...