Using the bilinear transformation and a lowpass analog Butterworth prototype, design a lowpass digital filter operating at a rate of 20 kHz and having passband extending to 4 kHz with maximum passband attenuation of 0.5 dB, and stopband starting at 5 kHz with a minimum stopband attenuation of 10 dB.

Using the bilinear transformation and a lowpass analog Butterworth prototype, design a lowpass digital filter operating at a rate of 20 kHz and having passband extending to 4 kHz with maximum passband attenuation of 0.5 dB, and stopband starting at 5 kHz with a minimum stopband attenuation of 10 dB.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

Exercise. There is a system that works with a sampling rate of 48 kpsp and requires a bandpass filter that allows the spectral components between the sequences fa=12kHz and fb=16kHz to pass. If you are using a 32-tap FIR filter. 3) What is the value of the central frequency, f0, in Hz of the band that the filter allows to pass? 4) what is the sketch of the frequency response for the bandpass filter?
a) A Chebyshev Type 1 filter has the following characteristics,??1=100,??2=200,??1=50,??2=300????≤1?? and bandstop gain, ??≤20??.By evaluating the characteristics, design the filter’s transfer function.b) Given a transfer function of a filter as follows,?(?)=20(?+1)?2+210?+2000Analytically, sketch the amplitude bode plot of the filter. Then name the possible filter type.
1. Show that if the low-pass filter circuit illustrated isscaled in both magnitude and frequency, the transfer function of thescaled circuit is the same with s replaced by s/kf, wherekf is the frequency scale factor.2. In the prototype version of the low-pass filter circuit ,ωc=1 rad/s, C=1 F, R2=1 Ω, and R1=1/K ohms. What is the transferfunction of the prototype circuit?3. Using the result obtained in (a), derive the transfer function of thescaled filter.
a) You are required to implement a digital filter to suppress a high frequency noise disturbance. AN (4) I. Describe the precaution you would take in selecting the sampling interval II. How may the original signal have recovered from the sampled signal? b) Consider the 1st order analog low-pass filter:G(S) = 2/(S+2), which we want to implant as a digital filter, Determine two equivalent filters, operating at a sample period of T= 0.1 sec. using the following transformation: i.Bilinear transformation without prewarping, DB(z) ii. Impulse invariant transformation, Dii(z) b. Comment briefly on how you might choose between these two filters, Assume a prewarped DB(z) for the Bilinear transformed filter
Exercise. There is a system that works with a sampling rate of 48 kpsp and requires a bandpass filter that allows the spectral components between the sequences fa=12kHz and fb=16kHz to pass. If you are using a 32-tap FIR filter. 3) What is the value of the central frequency, f0, in Hz of the band that the filter allows to pass? 4) And what is the sketch of the frequency response for the bandpass filter? 5)Center the response of the bandpass filter at zero frequency and sketch the frequency response of the resulting lowpass filter. 6) Based on the required sampling of 32 samples, it specifies the value of the frequency closest to the cutoff frequency in Hz, available in the discrete domain for the low-pass filter of the previous problem. 7) the frequency of the above response, specify it in radials normalized to the Nyquist frequency. 8) Suppose you want to take advantage of the impulse response corresponding to the low pass filter in answer 5) to obtain a high pass filter with…
Type your question here Compute the noise equivalent bandwidth of third order Butterworth filter whose magnitude frequency transfer function is (?) = √1+?6 . Compare your answer to the −3?? bandwidth.
Derive the prototype transfer function for a sixth-order high-passButterworth filter by first writing the transfer function for a sixth-orderprototype low-pass Butterworth filter and then replacing s by 1/s in thelow-pass expression.
Signals and Systems An analog signal is given as x(t) = 5 + 2 cos(20??) + 3 cos(400??)a) What is the bandwidth of x(t)? Determine the Nyquist sampling frequency for x(t), both in radian/sec (ws), and in Hz (Fs ).b) Formulate ?? (??), the signal sampled with the Nyquist frequency.c) Plot frequency spectrum of the sampled signal, Xp(jw).d) Determine the filter to reconstruct the signal x(t).e) Is it possible to reconstruct the signal x(t) for Ts = 0.004 [s]? State that if aliasing error occurs ornot
-MCQ- When the lower sideband components of the Double Sideband (DSB) signal whose spectrum is given in the figure are suppressed with a filter, when the signal obtained by suppressing it with a filter is multiplied by cos(ωct) in the time domain, which of the following signals is the result? a) 0.5 cos(2ωc + ωm)t + cosωct b) 0.25 cos(2ωc - ωm)t – 0.5 cosωct c) 0.5 cos(2ωc - ωm)t + 0.25 cosωct d) 0.5 cos(2ωc + ωm)t + 0.5 cosωct
Without reference, sketch the s-plane poles of a 2nd order butterworth filter with cutoff frequency of 2 radian/sec
For the system defined by the first-order differential equation 100y'(t) + y(t) = x(t). a) Plot the log magnitude (dB)-log frequency graph of H(jw). b) The input is assumed to be suppressed when the magnitude of H(jw) is -40 dB. It is given that the x(t)=coswat signal is suppressed by this system. What is the smallest wa value in this case? Subject: Signals and Systems
Consider the active bandpass filter shown below, which passes frequencies between 160 rad/s and 500 rad/s with a passband gain of K=5. Assuming that the capacitors are of C=500 nF, determine the values of R1, R2 and Rf.