ECE_161B_HW4_IFIR

Solve using the concpts of Digital Signal ProcessingShow each formula wherever necessary and please show all the steps of the design process

a) What kind of filter is this? Be as detailed as you can be. b) What is the equation for the transfer function Vo/v; of this filter? c) What is the equation for the break frequency? Vi R₁ www www R₂ VOUT

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4. A simple band-pass filter can be designed by cascading one-pole high-pass and one-pole low-pass filters. Using op- amp circuits similar to the one shown below, design band-pass filter with cutoff frequencies of 200Hz and 50 kHz and with a midband gain of 10dB. Resistor values must be no larger than 200k, but the input resistance must be as large as possible. Vic C oV₂ V₁ www OV

A) Write the equation for the small-signal gain function Vout/Vinfor the followingop-amp circuit B) What kind of filter is this circuit? C)Write the equation for the cutoff frequency of the filter D) Sketch the Frequency Response of the system

Design an ACTIVE band-pass filter for the midrange part of a loudspeaker so that the bandpass region is 400 Hz-2000 Hz (as defined by the -3dB points). Design the circuit so that the absolute gain is 2. a. Draw the circuit diagram and specify the resistor and capacitor values. Assume you can use either 100, 330, 500, or 1000 Ohm resistors and can select any value of capacitor. b. Sketch the frequency response (Gain [dB] vs. frequency (Hz)). Note that you will need to convert your gain to dB before plotting. Magnitude (dB) 15 10 5 midrange 12 1 -5 -10 -15 -20 -25 10 100 1,000 Frequency (Hz) 10,000 100,000

2. a) Consider the circuit shown in figure 3. i) Determine what type of filter is shown in Figure 3 i) Calculate the corner or cutoff frequency. Take R = 4 k &, L= 2 H, and C= 1 uF. R Figure 3 b) Describe the possibility of building a second order filter with only resistors and capacitors? and design the cutoff frequency of second order filter for low pass filter (Expected: Describe the possibility , design the second order filter for low pass filter circuit and design the cutoff frequency as equation only).

What is the function of a low pass filter? Draw a diagram of a simple low-pass filter using a capacitor and a resistor.

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How can I design an active filter circuit (just the low pass) using resistors, capacitors, and op-amps that will implement the transfer function. You will need to factor the function into cascade functions in order to make this easier. I jus want the drwan design with a litte explanation if possible.

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Draw a low pass filter and a high pass filter

Please show work

Design a filter using the window method and provides the specifications for the filter design. Here is a summary of the specifications given: Stopband: [0 kHz, 4 kHz] Passband: [5.5 kHz, 16 kHz] Maximum ripple in the passband: 0.1 dB Minimum attenuation in the stopband: 51 dB Sampling frequency: 32 kHz The task is to design a filter (by hand, with the impulse response formula) that meets these specifications.

Q4 Design an active highpass filter with a gain of 10, a corner frequency of 2 kHz, and a gain roll-off rate of 40 dB/decade.

Answer the following wuth illustration and solutions. 1.) A second-order band pass filter is to be constructed using RC components that will only allow a range of frequencies to pass above 500Hz and below 1.5kHz. Assuming that both the resistor have values of 1kohms, calculate the values of the two capacitors required. Find also the center frequency of the two frequencies. This is the example/guide that might help.