Digital Filter Coefficient Generation Program
Window method of FIR filter design The basic idea behind the Window method of filter design is that the ideal frequency response of the filter is equal to 1 for all the pass band frequencies, and equal to 0 for all the stop band frequencies. The filter impulse response is obtained by taking the Discrete Fourier Transform (DFT) of the ideal frequency response.
My question is related to the design of some digital filters. Designing a high-pass digital filter. P.14-5 and a coefficient generation program. DIGITAL FILTERS - COMPUTING THE COEFFICIENTS. On the Digital Filter. Three popular basic approaches for coefficient generation are employed by filter.
Unfortunately, the filter response would be infinitely long since it has to reproduce the infinitely steep discontinuities at the band edges in the ideal frequency response. To create a Finite Impulse Response (FIR) filter, the time domain filter coefficients must be restricted in number by multiplying by a window function of a finite width. The simplest window function is the rectangular window which corresponds to truncating the sequence after a certain number of terms. Rectangular windowing in the time domain will result in a frequency spectrum with the width of the pass band close to the desired value but with side lobes appearing at the band edges (the effects of time domain windowing on the frequency spectrum are discussed in more detail in the page). To suppress the side lobes and make the filter frequency response approximate more closely to the ideal, the width of the window must be increased and the window function tapered down to zero at the ends.
This will increase the width of the transition region between the pass and stop bands but will lower the side lobe levels outside the pass band. Kaiser-Bessel filter generator The Kaiser-Bessel window function is simple to calculate and its parameters can be adjusted to produce the desired maximum side lobe level for a near minimal filter length. To demonstrate the power and simplicity of this technique, a Kaiser-Bessel filter generator is provided below. To use it, set the sample rate and the type of filter desired; low pass, band pass or high pass, then set the frequency of ideal filter edges and the minimum attenuation required in the stop band. Then press the 'CALCULATE FILTER' button.
The filter coefficients are calculated and plotted along with a graph of the frequency response of the filter. The actually algorithm and the JavaScript code to implement it are presented at the bottom of the page.
IIR Filter Design, Software and Examples Iowa Hills Software Digital and Analog Filters IIR Filter Design This IIR filter design program is free. It uses the bilinear transform to synthesize low pass, high pass, band pass, notch, and all pass filters from these polynomials: Butterworth Gauss Bessel The program has two test benches. The first allows you to test the filter with an impulse, square wave, sine wave, or a user defined signal. The program will display both the filtered and unfiltered signal in both the frequency and time domains. It also has an audio test bench that allows you to apply the filter to a wav file which allows you to hear the affects of filtering. The program is available on our If you are more interested in writing your own IIR program, see the. The Code Kit has all the code necessary for generating IIR coefficients from the polynomials listed above.
It also has the code for evaluating the filter's frequency response, as well as the code for implementing the filter. Design Method Using the Bilinear Transform to design an IIR filter is quite simple. The basic procedure is given here, where we substitute the definition for the bilinear transform into H(s). H(z) shows how to calculate the IIR filter coefficients from the analog low pass prototype coefficients A - F and T. T is determined by the desired 3 dB cutoff frequency Omega. The 2nd order analog filter coefficients (e.g. Butterworth coefficients) can be obtained from virtually any filter design book.
More details are given. Filter Stability The stability of an IIR filter is always of some concern. If we start with a stable s plane filter, and we always do, then the bilinear transform is mathematically guaranteed to generate a stable IIR filter.
Instabilities can arise however because of implementation issues (numerical problems). The two most important aspects to consider are the size of the math registers and the type of implementation structure used. This shows the 11 ways the program allows you to test the filter's implementation, in floating point and fixed point.
Zero Input Limit Cycles Zero Input Limit Cycles is the term generally used to describe the effect of the filter's inability to settle at zero after the input goes to zero. By definition an IIR filter has an infinitely long impulse response, but we assume the output will always tend toward zero after the input goes to zero. In some cases however, depending on the type of filter and the number of bits used to implement the filter, the filter's output will approach some small value, and then oscillate indefinitely, or remain at a DC level. This happens because the filter can't clear its registers entirely and the residual re-circulates through the filter indefinitely never allowing the output to settle at zero.
This residual output signal can be large enough to cause problems in some applications. High pass and notch filters are the most susceptible to this phenomenon. Here is an example of limit cycles at the output of a Chebyshev high pass. Avoiding Register Overflow A significant amount of effort went into this program to ensure that the math values generated by these filters are kept to a minimum.
Dfcgen-gtk-0.4.tar.gz
IIR filters differ from FIR filters in obvious ways, but one of the more important, and less obvious differences, is the peak math value generated by the filter. Both FIR and IIR filters generate their peak math value when processing a square wave. With an FIR filter, the peak math value is the same as the amount of overshoot in the filter's step response and is seldom greater than ±1.2 if processing a ±1 square wave. The peak math value generated by an IIR filter however depends on the implementation structure, the polynomial (Butterworth, etc), pass type (low pass, etc.), selectivity (highly selective filters generate larger math values), and the type and frequency of the signal being processed.
The largest math values are generated by square waves of a specific frequency. The worst case frequency is also dependent on all the factors just mentioned. To demonstrate, we list the peak math values generated by these filters in these structures.
All are 8 pole low pass filters with OmegaC = 0.125. The Chebyshev had 0.2 dB Ripple, the Inv Cheby had a 60 dB Stop Band, and the Elliptic had a 0.2 dB Ripple and a 60 dB Stop Band.
Peak Math Values Generated by a ±1 Square Wave Gauss Bessel Butterworth Inv Cheby Chebyshev Elliptic Biquad Form 1 1.4 1.63 3.56 3.9 4.46 4.9 Biquad Form 2 3.4 4.5 25.38 27.0 172.5 86.8 Nth Order Form 1 4.8 8.4 33.82 33.0 78.8 84.2 Nth Order Form 2 88.9 353 91.5E3 71.3E3 3.76E6 11.8E6 10 Pole Inverse Chebyshev Low Pass Filter Example Screen shot of the IIR Filter program (free). Screen shot of the program's test bench. The Pole Zero locations are shown here. Signals may also be plotted in both the time and frequency domains.
Digital Filter Coefficient Calculator
Screen shot of the Audio Test Bench. The Audio Test Bench allows you to filter a wav file, and play the results. This shows the spectrum for a filtered and unfiltered DTMF tone. Copyright 2013 Iowa Hills Software.