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DSP Filter Range of applications DSP in the digital measurement system has many functions widely used, they can improve the sampling rate is limited due to frequency response, phase response, noise performance, bandwidth expansion and other indicators. Digital measurement system (such as digitizers, digital oscilloscope) of the DSP configuration shown in Figure 1, DSP on the A / D conversion of analog signals after the digital processing of data streams, the most commonly used features a fast Fourier transform (FFT), digital modulation , gain control, encoding / decoding in digital communication known computing, digital measurement systems in the most important function of the digital filter, DSP filter as a software filter can provide more excellent than the hardware filter characteristics. Digital measurement system can be measured using the waveform mathematics Finite Impulse Response (FIR) filters, infinite impulse response can also use (IIR) filter, DSP filters can be regarded as a modified wave shape of the mathematical procedure . As requested, we can design a specific filter, the waveform transform into any shape desired. Because the broad point of view, any system can handle signals as a filter filters, digital oscilloscope, for example, the DC input channel is a low-pass filter, 3dB roll-off point is its frequency bandwidth, in the case of AC input It is the band-pass filter. The main application of DSP filter as follows:
Waveform reconstruction Digital filter shown by A / D converter sampling rate limit, waveform sampling is limited and non-continuous, in order to facilitate observation, must be transformed discrete samples for waveform reconstruction, which is in the samples data points between the Add to digitized waveforms with better visibility and accuracy. In the real-time digital oscilloscope, the measured signal is only a single data collection, using software to reconstruct the waveform is the only option.
Waveform reconstruction is the simplest linear interpolation filter, clearly the two sampling points in a straight line connected to the reconstruction of the waveform not smooth, mutations in the waveform segment visibility even worse. More accurate waveform reconstruction Sinx function using interpolation filters, Sin (x) / X interpolation filter is available to smooth the waveform reconstruction and the absolute value of more accurate and would not introduce confusion frequency. According to sampling theory, the definition of sampling frequency fs = 2fN, fN is the Nyquist frequency, that fN is the highest frequency after the digital needs to use more than brick-type filter can suppress the frequency fN, otherwise it will introduce confusion frequency, resulting in unacceptable measurement error. Such as digital display filter E6000C Mini using 20GS / s sampling rate, fN is equal to 10GHz. In order to ensure maximum bandwidth of 10GHz, 10GHz brick wall type must be the hardware filters. Shown in Figure 2, red line (right) that the fN 10GHz brick wall filters, this theory can not actually filter hardware implementation. Traditionally, analog oscilloscopes with Gaussian roll-off characteristics, with the green line (left) that the-3dB bandwidth of 5GHz, as roll-down section of the curve is very slow, in the-3dB point after that there are more than Nyquist frequency frequency components, as shown in Figure in the slash section. Therefore, the digital oscilloscope is not Gaussian response filter and smooth with the largest response filter, with a basket line (in) that the-3dB bandwidth of 8GHz. The high anti-smooth response filter so that the maximum bandwidth digital oscilloscope close to the Nyquist frequency, the A / D converter sampling rate of 20GS / s, through the Sin (x) / x filter to the waveform reconstruction and DSP After filtering, the-3dB bandwidth of 8GHz available. That is, using Sin (x) / x waveform reconstruction filter can be 0.4 times the sampling frequency fs bandwidth.
Rate smoothing Digital measurement system because the heterogeneity of hardware, leading to the frequency characteristics of lead in the passband not smooth, digital oscilloscope's frequency response curve in the low frequency band with the same magnitude, and then into the high-frequency roll-off section, shown in Figure 2, shown in green line. In fact, the frequency response curve in the band began to deteriorate, in some frequency on the hard experience of peak signal attenuation or building, especially when close to the bandwidth limits the frequency response of the abnormal peak. The frequency bandwidth according to the definition, only refers to-3dB roll-off point, so the circuit design engineers to expand the bandwidth, the construction peak in the high frequency compensation added. Figure 3 is a digital oscilloscope measured frequency response curve, red line (above) show that real-time with 6GHz bandwidth, but also visible in the 3.5GHz and 5.5GHz, respectively, and +2 dB +1 dB response peak construction. As the supplier does not provide the oscilloscope frequency response flatness data not only determine the real-time by-3dB bandwidth, it will surely introduce a serious error rate measurement.
Rate smoothing filters using DSP digital oscilloscope can significantly improve the frequency response amplitude error, blue line (below) is the modified frequency response, amplitude deviation control within 1dB bandwidth remains 6GHz, the original from 3GHz to 5GHz smoothing peak construction. This from the hardware filter frequency response up to peak construction, from software filters to make a smooth frequency response, high sampling rate of the digital oscilloscope, it is very effective hardware / software combination of bandwidth and improve the rate of expansion formation porosity.
Phase correction Digital signal is usually a large number of fundamental and harmonic composition, the digital measuring system will ensure that the measured signal amplitude? Frequency response than, for phase? Frequency response should not introduce phase delay. As the digital oscilloscope's hardware tends to produce high-frequency harmonic phase shift, the result is to increase the signal group delay. In order to eliminate group delay cause signal distortion, only improve the equipment or by the DSP filter bandwidth for phase correction, apparently the latter is the most cost-effective approach. And the rate of formation through the use of the FIR filter of similar design, it is easy to reduce the reconstruction of the waveform of the group delay, so that the measured transient high-speed digital waveform distortion to a minimum within limits.
Noise reduction According to broad-spectrum white noise distribution, the higher the bandwidth of digital measurement system background noise is greater, use many times the average or the DSP filters can significantly reduce background noise, on the real-time digital oscilloscope, only DSP filter is feasible. However, FIR filter to reduce noise, but also lead to real-time bandwidth reduction, the design engineer must make a compromise between noise and bandwidth.
Increase in the bandwidth
As noted above, the wave function reconstruction using Sinx decreased availability of the frequency characteristics of smooth, do not confuse frequency, but the-3dB bandwidth of only a sampling frequency of 1 / 4 (BW = 1/4fs), and in Naikui Sturgeon frequency to sampling frequency fs fN there between the existence of high frequency (Figure 2 slash part). Number
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