Digital Filtering

NI High-Speed Digitizers Help (NI-SCOPE)

Edition Date: January 2017

Part Number: 370592AB-01

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Analog filter design is one of the most important areas of electronic design, but it is often reserved for specialists because it requires advanced mathematical knowledge and understanding of the processes involved in the system affecting the filter. With the digital filters in NI-SCOPE, however, you do not have to be a design expert. NI-SCOPE handles all the design issues, computations, memory management, and actual filtering internally.

Although digital filters have advantages over analog filters, they have disadvantages such as floating-point precision limitations, numerical instability, quantization noise, and frequency warping.

Types of Filters

Filters alter or remove unwanted frequencies. Depending on the frequency range that they either pass or attenuate, they can be classified into the following types:

  • A lowpass filter passes low frequencies, but rejects (or attenuates) high frequencies. To specify the cut-off frequency, use the Measurement Filter Cutoff Frequency attribute.
  • A highpass filter passes high frequencies, but attenuates low frequencies. To specify the cut-off frequency, use the Measurement Filter Cutoff Frequency attribute.
  • A bandpass filter passes a certain band of frequencies and attenuates others. To specify the bandpass filter, use the Measurement Filter Center Frequency attribute and the Filter Width attribute, where the cut-off frequencies are the center frequency plus or minus one-half width.
  • A bandstop filter attenuates a certain band of frequencies and passes others. To specify the bandstop filter, use the Measurement Filter Center Frequency attribute and the Measurement Filter Width attribute, where the cut-off frequencies are the center frequency plus or minus one-half width.
  • An ideal filter has a gain of one (0 dB) in the passband so that the amplitude of the signal neither increases nor decreases. The stopband (SB) corresponds to that range of frequencies that do not pass through the filter at all and are rejected (attenuated).

Infinite Impulse Response (IIR) Versus Finite Impulse Response (FIR) Filters

Another way to classify filters is by impulse response. An impulse response is the response of a filter to an input that is an impulse (x[0] = 1 and x[i] = 0 for all i ≠ 0). The FFT of the filtered impulse response is known as the frequency response of the filter. The frequency response of a filter tells you what the output of the filter is going to be at different frequencies. In other words, it tells you the gain of the filter at different frequencies. For an ideal filter, the gain should be 1 in the passband and 0 in the stopband. So, all frequencies in the passband are passed as is to the output, but there is no output for frequencies in the stopband.

If the impulse response of the filter falls to zero after a finite amount of time, it is known as a FIR filter. However, if the impulse response exists indefinitely, it is known as an IIR filter. Whether the impulse response is finite (that is, whether the filter is FIR or IIR) depends on how the output is calculated. The basic difference between FIR and IIR filters is that for FIR filters, the output depends only on the current and past input values, whereas for IIR filters, the output depends not only on the current and past input values, but also on the past output values. The advantage of digital IIR filters over FIR filters is that IIR filters usually require fewer coefficients to perform similar filtering operations. Thus, IIR filters execute much faster and do not require extra memory, because they execute in place. The disadvantage of IIR filters is that the phase response is nonlinear. If the application does not require phase information, such as amplitude spectrum analysis, IIR filters may be appropriate. You should use FIR filters for those applications requiring linear phase responses.

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