There’s a classic technique you need to be aware of when working with the Discrete Fourier Transform, and it’s called Zero-Padding.1 As it turns out, it’s possible to interpolate or “fill-in” the output of the DFT by simply appending zeroes to the end of your input signal. Appending zeroes to the end of your signal doesn’t alter the frequency content of your signal in any undue way, it merely interpolates the output spectrum. You can experiment with zero-padding in Figure 1. Drag the slider at the bottom of the figure to the right to append more zeroes to the end of the input signal.
|Figure 1. Zero Padding the Input Interpolates the Output Spectrum|
You might be surprised to see little mountains and valleys appear in the DFT output as you begin to zero-pad the signal. We’ll devote the entire next section to understanding this phenomenon. For now, let’s move onto a subtle point about zero-padding which can confuse and confound.