Principle of FIR Filter
An FIR filter operates through a combination of addition and multiplication functions. When examining the FFT spectrum for a single peak (Fig. 1), it contains all frequency components equally (Fig. 2). For instance, a high-pass filter removes certain low-frequency components, resulting in a frequency spectrum devoid of low-frequency elements (Fig. 4). In an FIR filter, using an appropriately filtered spectrum and converting it back to the time domain, the waveform resembles a small wave (Fig. 3).
This indicates that a high-pass filter can be applied by multiplying the small wave with each data point of the original time-domain data and summing them. This is the basic principle of the FIR filter.
Implementing FIR Filter in LabVIEW
To manually apply an FIR filter, you need to create a set of coefficients to manipulate the original time-domain data points. These coefficients are typically called "taps." In this example, we use 13 taps to perform the FIR filter (Fig. 5). The taps are derived from the small wave obtained in Fig. 3. Applying these taps to a waveform in the time domain produces the same filtering effects as its original frequency-domain spectrum (Fig. 6), since the taps are created by the inverse FFT of the frequency-domain spectrum.
For example, we apply the FIR filter using Filter.vi in LabVIEW or through manual calculation using the taps shown in Fig. 5.
The target data contains three sine waves plus white noise, specifically 10 Hz, 200 Hz, and 450 Hz sine waves (Fig. 7 and 8). Examining the frequency-domain data of the FIR filter (Fig. 6), we observe the absence of the 10 Hz component, a 50% reduction in the 200 Hz component, and no effect on the 450 Hz component. Therefore, this FIR filter effectively removes the 10 Hz component and attenuates the 200 Hz component by 50%. The Filter.vi (blue) and manual FIR filtering (red) are applied as shown below. You can find the Filter.vi in Signal Processing > Waveform Conditioning > Filter.
The results show that the 10 Hz component disappeared, and the 200 Hz component was reduced by 50%. In this VI, the manual method is applied to a data set, but it is crucial that this calculation can be done for each data point individually, allowing real-time monitoring of the results (more detailed explanation and figures will be available in the FPGA section).
Implementing FIR Filter in LabVIEW FPGA for Reconfigurable Scope and FlexRIO
In FPGA, data points can be acquired and manipulated with very low latency. The FIR filter is often used for filtering each data point. In LabVIEW FPGA, the FIR Compiler is very useful for Reconfigurable Scope and FlexRIO. You can find this function in Programming > Xilinx IP > Digital Signal Processing > Filter. The detailed manual is available on the Xilinx page.
The function performs the following calculation for each data point. The basic calculation is the same as the manual method explained in the previous section. Each data point is multiplied by the taps and summed for each time point. This is an example of FIR filtering for the FPGA reading one data point per cycle.
When the FPGA VI reads multiple data points per cycle, the FPGA logic becomes more complex. In an FIR filter, you need to configure it for parallel input by entering the "Input Sampling Frequency" and "Clock Frequency." For example, the NI 5763 reads four data points per cycle at 125 MHz. Thus, the "Clock Frequency" is 125 MHz, and the "Input Sampling Frequency" is 500 MHz. The FIR Compiler automatically calculates the "Number of parallel inputs" as 4. The FPGA size increases with parallel inputs.