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A digital filter is a system that performs mathematical operations on a discrete and sampled time signal, so as to enhance or reduce certain aspects of that particular signal as may be necessary. It is largely used in signal processing and differs from an analog filter, which is an electronic circuit working with continuous signals. Digital filters are expensive compared to analog ones, but they can turn many impractical or impossible designs into possibilities. In everyday life, they can be found in devices like cell phones, radios and audio/video receivers.
A digital filter contains an analog-to-digital converter (ADC), which samples the signal coming in as input, a microprocessor and some other components for storing filter coefficients and data. There is also a digital-to-analog converter that is present just before the output stage. The software that runs on the microprocessor implements a digital filter by acting on a number from the ADC and performing mathematical operations. It can perform several effects such as amplification and delay on the sample signal.
The behavior of a digital filter is also important. Different mathematical approaches are used for understanding the reactions. The simplest way is to analyze the response when a simple input is passed to the filter, for example an impulse. Then based on the result, complex inputs can also be analyzed.