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Filter Design Summary
Signaling system in the field, based on spectral analysis of the design and the Fourier transform of the filter are two basic problems. In analog systems, often approaching the desired transfer function of electronic components, in digital systems, the difference equation method is used to approximate the desired transfer function. Implemented in hardware, primarily by a plurality of product gate and the FPGA to complete.
3.FIR filter design
FIR filter is very simple, it is actually an all-zero model (MA moving average model), the filter coefficients comprises only the moving average of B , and autoregressive A =. 1. Filtering process is X and B convolution, and then contact the filter principle, easy to understand, the FIR filter coefficient B is impulse response filter h.
Therefore its design is simple, just set the filter after the frequency response H, impulse response h to obtain ifft performed, directly as the filter coefficients h B filter to the original signal.
As shown above, the frequency response is set to a low-pass filter, attention, digital systems have periodic extension characteristics. It ifft obtained impulse response h (t), attention, t from negative to positive, where it is translated to a positive position, which is caused in response to a zero phase FIR filter of linear phase response becomes reasons. Another point, the original h (t) is not causal, then the translation becomes a cause and effect, so that understanding correct? ?
Further, the longer the resulting h (t) of length, some may be taken, reducing the order.
As shown in FIG seen, longer taken, the resulting frequency response of the frequency response is set closer to the second set point 61 is taken (fftl = 512) frequency response, the frequency response is set almost the same. The first group is taken 21 points frequency response, but also big bad not bad, but the 21-order filter to do, to do with the hardware is quite a waste of resources. See the relative frequency response, as shown below
Let's look at an example, using the above design FIR filter, the filter coefficient h to obtain, directly = filter (h, 1, x ) is filtered with a matlab function y, i.e. h is B , A is a filter, obtained FIG spectrum:
Design of a FIR bandpass, high-pass filter and the like are also very simple, and the above process as follows:
In summary, the FIR filter design and simple, and has a linear phase, the time delay of each frequency component are the same. The drawback is that the required order of more general, to implement a waste of hardware resources.