Mathematica definitions

Load needed packages for this notebook

Set up defaults

Turn off annoying warning messages

Set default options for specific functions

Visualization functions

Fix time variable for sampled signals

Generate periodic waveform from one period

PeriodicSignal[f, {dmin, dmax}, {t, min, max}] generates a periodic waveform for the interval [min, max]. It is assumed that one period of the function f(t) is defined over the interval [dmin, dmax].

Plot periodic waveforms

PeriodicPlot[f, {dmin, dmax}, {t, min, max}, opts] plots a a periodic waveform for the interval [min, max]. It is assumed that one period of the function f(t) is defined over the interval [dmin, dmax]. The 'opts' argument passed plotting options to the Mathematica function Plot[ ].

Plot discrete-time signal as sequence of amplitude lines

Filtering definitions

FourierRearrange[fft] rearranges the result of an FFT (Mathematica function Fourier[ ]), to a easier to visualize the spectrum represented by 'fft'. The length of the list 'fft' is assumed to be even; if it is not, the last term in 'fft' is dropped.

Filter[n, sampleRate, {lowFreq, highFreq}] generates an ideal discrete filter for an FFT list of length 'n' (sampled at 'sampleRate'), with a bandpass from 'lowFreq' to 'highFreq' (in Hz).

Signal reconstruction