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## Collection Book Analog and Digital Filters: Design and Realization

Embeds 0 No embeds. No notes for slide. The range of frequencies of signal that are passed through the filter is called passband and those frequencies that are blocked is called stopband. Analog filters are designed using discrete components such as R resistor , L inductor and C capacitor.

Digitalfilter Digital filter is used to filter out signals after conversion of the analog signal to the digital form , meaning they are used after ADC in the circuit mainly in the digital processing part of the system. Lin, P. Bobis, J. IEEE 51, p. Orchard, H. I , 44, pp.

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Huelsman, L. McGraw-Hill, Holt, A. Circuit Theory 15, pp. In progress. Lam, H. Prentice-Hall, Lindquist 2 1. Motorola, Inc. Boynton Beach 2.

MicroUnity Systems Engineering, Inc. Figure 6: Frequency left and time right domain representations of filter shape. The input to the filter is time series x n , and the output of the filter is a time series y n. Each equation has three series of numbers: an input time history, a filter, and an output time history Figure 7. An IIR filter has an advantage that for a similar filter roll off as a FIR, a lower order or number of terms can be used. This means that less computations are needed to achieve the same result, making the IIR faster computationally.

However, an IIR has nonlinear phase and stability issues. It is a bit like the fable of the tortoise and the hare. The FIR filter is like the tortoise in the race — slow and steady, and always finishes. The hare is like the IIR filter — very fast, but sometimes crashes and does not complete the race.

## Digital filter - Wikipedia

For example, if there were 5 terms in the filter versus 10, the filter computations would take twice as long. However, the filter roll off would be sharper, as shown in Figure 9. Figure 9: Top — The roll off sharpness of the filter top with fewer terms is less sharp than filter with more terms bottom. A filter with more terms i. An example comparison of the same filter type, calculated with different orders, is shown below in Figure Figure Increasing the order of filter, but keeping all else the same, increases the sharpness of the filter roll off.

Making a filter sharper is done by increasing the order. This requires more calculations, and also has an impact on the time delay introduced by the filter.

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Because of the recursive nature of an IIR filter see Equation 1 , where part of the filter output is used as input, it achieves a sharper roll off with the same order filter. If a filter has to be implemented in real-time application for example interactive filtering while listening , it is typically done with an IIR filter. After applying a filter to time data, and comparing to the original time history, a slight shift, or time delay, can be seen in the data.

In Figure 13, simultaneously acquired sound red curve, top and vibration data blue curve, bottom are shown. Filtering the sound data green curve, top causes events between the sound and vibration to not be aligned. Figure Top - Original time signal red is time delayed green by filter. Bottom — Vibration signal blue no longer aligned with filtered sound signal green.

Take the equation for a FIR filter from Figure Working through the equation, the cause for the time delay can be observed. Figure To be fully realized i. A number of time data samples from the input signal x must pass thru the filter that is proportional to the number of terms N , before the filter will work. The filtered output data does not start until the number n data points passed through the filter is greater than N.

Because some data must pass through the filter to even create an output, a delay in the output time history y is created when compared to the input time history x as shown in Figure By making the filter sharper, this delay is increases. Usually the biggest time delay in the IIR filter is at the cut off frequency of the filter. All filters create a delay of some sort — analog and digital. Depending on the filter characteristics, the delay can be shorter or longer.

They can also be variable as a function of frequency. After the time history x n is filtered, and the new output time history y n is created, it can be fed backward into the filter. The data points in y n are reversed in order in time to do this, and fed into the filter again. The result is shown in Figure Figure Original signal red filtered directly green and with zero phase blue. Zero phase removes the delay, but data is lost at the end of zero phase filtered time history.

Notice that the time delay is at the end of the zero-phase filtered trace blue. There are trade-offs when using zero phase filters:. The coefficients, a n , of a filter can be selected to control specific filter attributes.