Digital filters work by taking discrete signal samples, processing them mathematically, and producing a modified output signal. Imagine a stream of numbers, each representing the signal's amplitude at a specific point in time; the filter performs calculations on these numbers based on a predefined algorithm to achieve a desired effect.
Key Concepts Explained
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Sampling: A digital filter operates on discrete samples of the input signal. The rate at which these samples are taken is called the sampling rate (e.g., samples per second). The reference mentioned "one nano-second at a time (or some other time resolution depending on the system)" highlighting the importance of the sampling rate impacting how precise the filter operates.
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Mathematical Manipulation: At the core of every digital filter are mathematical operations. These typically involve multiplication by coefficients and addition of these results. These coefficients determine the filter's characteristics, such as which frequencies it attenuates or amplifies.
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Algorithms: The set of instructions defining how the filter processes the samples constitutes its algorithm. Two main types of digital filter algorithms are Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters.
Digital Filter Types
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Finite Impulse Response (FIR) Filters: These filters use only present and past input samples to calculate the output. They are inherently stable and can be designed to have linear phase response (meaning they don't distort the signal's phase). FIR filters are implemented using a tapped delay line structure, where the input samples are delayed and multiplied by filter coefficients.
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Infinite Impulse Response (IIR) Filters: IIR filters use present and past input samples and past output samples in their calculations. This feedback makes them more computationally efficient than FIR filters for achieving the same filter characteristics. However, IIR filters can be unstable and may introduce non-linear phase distortion.
Practical Implementation
- Analog-to-Digital Conversion (ADC): If the input signal is analog (continuous), it needs to be converted into a digital signal using an ADC before it can be processed by the digital filter.
- Processing: The digitized signal is fed into the digital filter, where the filtering algorithm is applied.
- Digital-to-Analog Conversion (DAC): If an analog output signal is required, the filtered digital signal is converted back to analog using a DAC.
Simplified Analogy
Think of a digital filter like a specialized calculator that processes numbers representing sound or sensor readings. You feed it a stream of numbers, and it applies a specific formula to each number (and perhaps some of the previous numbers) to produce a new stream of numbers – the filtered output.
Example
Consider a simple moving average filter. It calculates the average of a certain number of previous input samples and uses that average as the current output. This effectively smooths out the signal by reducing high-frequency noise. The "coefficients" in this case are all equal to 1/N, where N is the number of samples being averaged.
