Team MSD 1. Technical Filter Primer

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Oliver Atkinson
6 years ago
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1 Team MSD 1 Technical Filter Primer Filters are used in a variety of configurations to perform a multitude of tasks within the engineering world. Whether used to clean up the biomedical signals from an EKG monitor or to select specific frequencies bands on a military grade radio, they provide an invaluable tool to today s design engineer in implementing frequency-based solutions. Manipulation of different frequency bands, including the electromagnetic spectrum for radio signals as well as the human range of audible sound frequencies, allows the designer to narrow their range of inputs or selectively determine the desired output. In general, electrical filters can be defined by in terms of their response to alternating current electrical signals in terms of a band of frequencies denoted by either radians per second (r/s) or cycles per second (Hertz, or Hz). The major types of filters used include low-pass, highpass, band-pass, and band-reject filters. Low-pass filters will pass lower frequencies (defined by a cutoff frequency) and attenuate higher frequencies. High-pass filters do the opposite, passing the highs and attenuating the lows. Band-pass filters select a band of frequencies to pass through, and attenuate all others. Band-reject filters will severely attenuate a specific band of certain frequencies and pass all others.

2 The primary components used to specify any filter type include a pass band, a stop band, and a cutoff frequency. The pass band defines the range of frequencies that are ideally not attenuated at all, as these frequencies pass through. The stop band includes those frequencies that are heavily attenuated and are not desired in the output. The cutoff frequency is the frequency where the magnitude response drops by 3 decibels from its pass band value. A typical low-pass filter magnitude response is shown below: Source- Of the types of realized filters available, a common example is the lowly RC analog filter. These simple filters use the variable frequency response of passive linear circuit elements to shape and alter the AC signals that pass through them. Different configurations can yield lowpass, high-pass, band-pass, and band-reject filters depending on the position of the filter elements within the circuit. These filters can be cascaded to chain multiple desired frequency responses together. A typical first order low-pass RC circuit is shown below: Source-

For more advanced designer capabilities, the operational amplifier can be used to produced more complex and intricate circuits with more desirable response characteristics.

3 For more advanced designer capabilities, the operational amplifier can be used to produced more complex and intricate circuits with more desirable response characteristics. The fascinating behavior that op-amps provide allows for incredibly interesting combinations of otherwise very abstract components. Analysis is done through nodal equations written at the input nodes which describe the currents flowing, and determinants and Cramer s Rule can be used to solve for the resulting equations. A more advanced band pass circuit utilizing the powerful op-amp is shown below: Source- Depending on the number and configuration of the components used, the designed filters have a specified order. This order defines the response of the circuit and the transfer function used to describe it. In general, the more capacitors or inductors that are used in a filter, the higher the order of the filter. In addition, higher order filters can be made by stringing multiple 1 st or 2 nd order filters together as such: Source-

4 The magnitude response of the filter with respect to the frequency axis is the main area of focus for most filter designs. However, often times the phase response of the filter will have a significant effect on the operation of the circuit. Some circuits are designed purely to affect the phase response of a circuit and leave its magnitude component unchanged. An all-pass circuit produces constant gain at all frequencies, but due to the nature of the op-amp circuitry, will introduce phase into the circuit where desired. An example is provided here: Source-

5 Equation 1: 2D convolution I = imread('cameraman.tif'); subplot(2,2,1); imshow(i); title('original Image'); H = fspecial('motion',20,45); H = [ ; ; ]/16; HighPass = imfilter(i,h,'replicate'); subplot(2,2,2); imshow(highpass);title('high Pass'); H = fspecial('disk',10); blurred = imfilter(i,h,'replicate'); subplot(2,2,3); imshow(blurred); title('blurred Image'); H = fspecial('unsharp'); sharpened = imfilter(i,h,'replicate'); subplot(2,2,4); imshow(sharpened); title('sharpened Image'); close all F = fft2(highpass); figure(2); pcolor(log(1+abs(f))); axis ij; Example Code 1: Basic image processing using predefined functions.

6 Figure 1: Output from example code 1. Figure 2: Spectrum of output filters

7 Figure 3: Example of High pass filter before layered back into image [1] Wikipedia Figure 4: Example of a PhotoShop Highpass filter This image shows the effects of a high pass filter when super imposed on the original layer. Phase portion

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