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How does a digital filter work?
Digital filters capitalize on the fact that digital electronics looks at waveforms as a timed sequence of values, rather than instantaneous voltages. Digital filters start with an analog waveform, convert it to a digital waveform, perform operations on the digital values, then convert the waveform back to an analog waveform.
The figure below shows the steps in this process. The analog waveform is a time-varying voltage called the baseband signal. Passing this baseband signal through an analog-to-digital convertor (ADC) changes it to a series of voltage measurements, which are stored as an ordered set of numbers with a time interval associated with each. A digital signal processor (DSP), which may be an ASIC, FPGA, or even a fast microprocessor, performs a Fourier transform on the data streaming in. This changes it from a series of numbers associated with time intervals to another series of numbers associated with frequency intervals — a digital spectrum.
The digital filter is actually an ordered set of numbers representing the filter function. That is, they can take on any values from zero to one (inclusive) and each number is associated with a frequency interval. It is important that the frequency intervals match the frequency intervals associated with the digital spectrum.
Next, the DSP convolves the spectrum with the filter. Convolution is simply the process of taking the spectral value associated with each frequency interval and multiplying it by the associated filter value. The result is another set of numbers representing the filtered spectrum.
In the fourth step, the DSP performs an inverse Fourier transform, which recovers a digital representation of the filtered baseband signal. Finally, a digital-to-analog converter produces a time-varying voltage that closely matches the analog signal that would result from passing the analog baseband signal through an analog filter having the same filter function as the digital filter.
Digital filters have three major advantages over analog filters. First and foremost, digital filters can use any filter function. Unlike analog filters, digital filters are not limited to those functions attainable with resistor-capacitor-inductor networks. The filter function need not be continuous. It need not have definable derivatives. It’s just a bunch of numbers assigned to frequency intervals. This characteristic provides essentially limitless flexibility.
The second advantage is size. Analog filters are as big as the components needed to make them, which can be quite large for complex filters operating at low frequencies. Digital filters can be and have been completely integrated on a single IC.
Finally, reprogramming a digital filter is simply a matter of loading in a new set of numbers for the filter function. Reprogramming an analog filter generally means designing and building an entirely new filter.
Digital filtering’s main disadvantage is speed. The calculations, especially the Fourier transforms, are computationally intensive. The filter bandwidth can be only as wide as the speed of the processor(s) allow. This is why digital filters are often implemented with FPGAs or ASICs, which do the math in fast hardware rather than much slower software.
Also read: What’s an FPGA, and what’s it good for? and ASICs Versus FPGAs
How does a digital filter work?
June 30, 2008
Digital filters capitalize on the fact that digital electronics looks at waveforms as a timed sequence of values, rather than instantaneous voltages. Digital filters start with an analog waveform, convert it to a digital waveform, perform operations on the digital values, then convert the waveform back to an analog waveform. The figure below shows the steps in this process. The analog waveform is a time-varying voltage called the baseband signal. Passing this baseband signal through an analog-to-digital convertor (ADC) changes it to a series of voltage measurements, which are stored as an ordered set of numbers with a time interval associated with each. A digital signal processor (DSP), which may be an ASIC, FPGA, or even a fast microprocessor, performs a Fourier transform on the data streaming in. This changes it from a series of numbers associated with time intervals to another series of numbers associated with frequency intervals — a digital spectrum.
The digital filter is actually an ordered set of numbers representing the filter function. That is, they can take on any values from zero to one (inclusive) and each number is associated with a frequency interval. It is important that the frequency intervals match the frequency intervals associated with the digital spectrum.
Next, the DSP convolves the spectrum with the filter. Convolution is simply the process of taking the spectral value associated with each frequency interval and multiplying it by the associated filter value. The result is another set of numbers representing the filtered spectrum.
In the fourth step, the DSP performs an inverse Fourier transform, which recovers a digital representation of the filtered baseband signal. Finally, a digital-to-analog converter produces a time-varying voltage that closely matches the analog signal that would result from passing the analog baseband signal through an analog filter having the same filter function as the digital filter.
Digital filters have three major advantages over analog filters. First and foremost, digital filters can use any filter function. Unlike analog filters, digital filters are not limited to those functions attainable with resistor-capacitor-inductor networks. The filter function need not be continuous. It need not have definable derivatives. It’s just a bunch of numbers assigned to frequency intervals. This characteristic provides essentially limitless flexibility.
The second advantage is size. Analog filters are as big as the components needed to make them, which can be quite large for complex filters operating at low frequencies. Digital filters can be and have been completely integrated on a single IC.
Finally, reprogramming a digital filter is simply a matter of loading in a new set of numbers for the filter function. Reprogramming an analog filter generally means designing and building an entirely new filter.
Digital filtering’s main disadvantage is speed. The calculations, especially the Fourier transforms, are computationally intensive. The filter bandwidth can be only as wide as the speed of the processor(s) allow. This is why digital filters are often implemented with FPGAs or ASICs, which do the math in fast hardware rather than much slower software.
Also read: What’s an FPGA, and what’s it good for? and ASICs Versus FPGAs
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| Digital filters use a five-step process that starts and ends with an analog signal, but performs all the mathematical operations digitally. |
Posted by Charlie Masi on June 30, 2008 | Comments (0)
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