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DIGITAL FILTERS MADE EASY

Part 2: The Rest of the Story
by Dan Cross-Cole

Start ý All the Pieces ý Using the DSP/FFT System ý Sources and PDF

In Part 1, which is in this monthýs print magazine (Circuit Cellar 122), I consider a Digital Signal Processing (DSP) board for implementing audio band-pass filters. In Part 2, youýll learn how to use a QuickBASIC program to provide a graphical display of the audio filter output. Youýll see how the filter affects the output of your favorite audio device.

For example, the combined system of digital filters and Fast Fourier Transform (FFT) can be used to isolate the bass, midrange, and treble responses of a speaker or audio system. As a ham radio enthusiast, I use the system to isolate Morse code signals to a narrow audio range. I can also use it to display several signals simultaneously and evaluate the audio output from my home-brewed shortwave receivers. I have even used it to compare acoustic guitars by their resonant characteristics.

In Mathematical Methods for Physicists by George Arfken [1], a Fourier series is defined as a representation of a function in a series of sines and cosines such as:

For an ideal representation, m should be without limit. The sines and cosines represent the frequency components of the signal, as well as their relative phases. A limitless m implies high frequencies. For practical calculations, limit m to a reasonable number based on the highest frequency to be measured. Typically, the system will take data at a frequency that is twice the highest frequency of the system. The value of m would then correspond to the highest frequency being measured. (In fact, m = 2pf, in which f equals frequency.)

The QuickBASIC program calculates the constants a_n and b_n using various shortcuts and displays the data on the laptop screen. The FFT routine in the program is taken from Hal Chamberlinýs book, Musical Applications of Microprocessors. [2] If you want to know more, check out this book, it provides detailed explanations. It also has a good coverage of computers and music applications.

To be able to display data in near real time, you must take some samples, perform the calculations, display the results, and then take more samples, repeating the cycle. The key phrase here is "take more samples."

The program takes about 8000 samples per second on a laptop that operates at 40 MHz. The sampling circuit is controlled through a board that plugs into the ISA bus of the laptop docking station. The input to the sampling circuit comes from the output of the DSP board (see Part 1).

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