DSP Applets: Fourier Series and Digital Filters

For anybody interested, I found these Java applets to be very helpful:

The Fourier Series is the mathematical theory behind the Fourier Transform and the Inverse Fourier Transform. The Fourier Transform allows us to reconstruct any periodic waveform with a number of harmonically related sinusoids. In the applet you can choose the "Playing Frequency", this is the fundamental frequency. It's the lowest in pitch. All other sine waves are multiples of this frequency. This is essentially Additive Synthesis, what Patrick showed us in class with Pure Data. You can recreate common waveforms like triangle, square, and ramp with this by first changing each sinusoid's amplitude and phase in special, mathematically related ways, and then taking the sum. The Inverse Fourier Transform is the opposite process: taking any periodic waveform and observing it's frequency components. This is used in the Digital Filters applet, the "Spectrum" window.

There are also great explanations in the "examples" link for each, and don't forget to turn the sound on!